Statistica - Teste Grila

TESTUL 1 *)

1)

1XFRQVWLWXLHRFRPSRQHQW DDYX LHLQD LRQDOH

a) b) c) d) e) 2)

fondul funciar; mijloacele fixe; 9HQLWXO1D LRQDO3URGXVXO,QWHUQ%UXW 

resursele minerale atrase în circuitul economic; stocurile de materiale.

0XO LPHDYDORULORUFRHILFLHQWXOXLGHFRUHOD LHFDOFXODWvQFD]XOGHSHQGHQ HORUOLQLDUHGLUHFWHHVWH

a) b) c) d) e)

[-1, 1] ; [-1, 0) ; PXO LPHDQXPHUHORUUHDOH

(0, 1] ; [-3, 3] .

3) Într-R SRSXOD LH VWDWLVWLF

 VWUXFWXUDW  SH JUXSH FODVH  UHODWLY RPRJHQH VH FDOFXOHD]  GLVSHUVLD

general ( σ 2 ); media dispersiilor ( σ 2  úL GLVSHUVLD GLQWUH JUXSH  δ 2  (VWH DGHY

UDW  vQ RULFH

VLWXD LHUHOD LD

a) δ 2 > σ 2 ; b) δ 2 ≤ σ 2 ; c) δ 2 = σ 2 + σ 2 ; d) δ 2 < 0 ; e) comparabilitatea dintre δ 2 úL σ 2 nu are sens. 4) În cazul tabelelor Input - Output, ramurile se delimiteaz dup : a) b) c) d) e)

FULWHULXODFWLYLW

LLSUHSRQGHUHQWH

FULWHULXOIXQF LRQDO XQLWDWHDLQVWLWX LRQDO  VHFWRUXOLQVWLWX LRQDO GXS IOX

xurile monetare din economie.

5) 5DWD úRPDMXOXL vQ VHQVXO %LURXOXL ,QWHUQD LRQDO DO 0XQFLL VH FDOFXOHD] 1XP

UXOGHúRPHUL

a) b) c) d) e)

3RSXOD LDFXUHQWDFWLY  3RSXOD LDRFXSDW  5HVXUVHOHGHPXQF  5H]HUYHOHGHPXQF  3RSXOD LDvQYkUVW GHPXQF 

 6XELHFWOD H[DPHQXO GHOLFHQ

*)

1997

 SURFHQWXDO UDSRUWkQG

la:

 )DFXOWDWHD&LEHUQHWLF  6WDWLVWLF  úL,QIRUPDWLF (FRQRPLF VHVLXQHDLXOLH

6) Fenomenele social-HFRQRPLFHGHPDV

VWXGLDWHGHVWDWLVWLF QXVHFDUDFWHUL]HD] 

a) SULQYDULDELOLWDWHvQWLPSúLvQVSD LX b) printr-R OHJH GH DSDUL LH FDUH VH PDQLIHVW  FD WHQGLQ  FH QX SRDWH IL FXQRVFXW  úL YHULILFDW GHFkWODQLYHOXODQVDPEOXOXLúi nu în fiecare caz în parte; c) printr-ROHJHGHDSDUL LHFDUHVHPDQLIHVW FDWHQGLQ FHSRDWHILFXQRVFXW úLYHULILFDW vQ fiecare caz în parte; d) SULQIRUPHLQGLYLGXDOHGHDSDUL LHDVHP Q WRDUH e) SULQ IDSWXO F  HOH VXQW VSHFLILFH OHJLORU VWDWLVWLFH - legi FDUH VH PDQLIHVW  VXE IRUP  GH WHQGLQ  ID  GH FDUH DEDWHULOH vQWkPSO WRDUH vQWU-XQ VHQV VDX DOWXO VH FRPSHQVHD]  reciproc. 7)

5HSUH]HQWDWLYLWDWHDHVWHXUP ULW vQPRGGHRVHELWvQFD]XOFXOHJHULLGDWHORUSULQ

a) b) c) d) e)

UHFHQV PkQW

sondaje statistice; anchete statistice; rapoarte statistice; monografii statistice;

8) Deflatorul Produsului Intern Brut este: a) LQGLFHOHGHSUH XULGHWLS/DVSH\UHV b) indicele volumului fizic de tip Paasche; c) LQGLFHOHGHSUH XULGHWLS)LVKHU d) LQGLFHOHGHSUH XULGHWLS3DDVFKH e) indice al valorii. 9)

([SUHVLDVLQWHWL] ULLYDORULORULQGLYLGXDOHDOHXQHLYDULDELOHVWDWLVWLFHDWRWFHHDFHHHVHQ LDOWLSLF úLRELHFWLYvQWU XQVLQJXUQLYHOUHSUH]HQWDWLYHVWHGDW GH

-

a) medie; b) PHGLDQ  c) YDORDUHPRGDO  d) FRHILFLHQWXOGHFRUHOD LH e) coeficientul de varia LH 10) &DUH LQGLFDWRU VWDWLVWLF QX DUH VHQV V

 VH FDOFXOH]H SHQWUX DQDOL]D VHULLORU GH UHSDUWL LH IRUPDWH

GXS RYDULDELO DOWHUQDWLY "

a) IUHFYHQ HOHUHODWLYH b) media; c) dispersia; d) coeficientul de asimetrie. 11) Într-R SRSXOD LH VWDWLVWLF

 V

-au cules date despre doX

 YDULDELOH QXPHULFH GLVWLQFWH 6HULLOH

IRUPDWHvQXUPDVLVWHPDWL] ULLVXQW

; }. {xi }i =1,7 = {2;2;2;10;18;18;18} {yi }i =1,7 = {9;9;9;10;11;1111 úL

2EVHUYkQGYDULDQWHOHFHORUGRX VHULLVHFRQVWDW F 

a)

VHULDIRUPDW GXS <HVWHPDLRPRJHQ GHFkWFHDIRUPDW GXS ;

b) serLDIRUPDW GXS ;HVWHPDLRPRJHQ GHFkWFHDIRUPDW GXS < c) FHOHGRX VHULLSUH]LQW DFHHDúLRPRJHQLWDWHGHRDUHFHDXDFHHDúLPHGLHúLPHGLDQ HJDOH cu 10; d) QXDUHVHQVFRPSDUDELOLWDWHDRPRJHQLW LLGLQFHOHGRX VHULLGHRDUHFHVXQWIRUPDWHGXS  variabile distincte; e) VHULD IRUPDW  GXS  ; HVWH PDL RPRJHQ  GHRDUHFH DEDWHULOH LQGLYLGXDOH ID  GH YDORDUHD PHGLDQ VXQWPDLPDUL

12) Un circuit economic este considerat circuit închis pentru sectorul A când: a) QXH[LVW LQWU ULvQ$ b) QXH[LVW LHúLULGLQ$ c) QXH[LVW QLFLLQWU ULúLQLFLLHúLULSHQWUXVHFWRUXO$ d) VXPDIOX[XULORUGHLQWUDUHHVWHHJDO FXVXPDIOX[XULORUGHLHúLUH e) fluxurile monetare sunt identice cu fluxurile de bunuri. 13)

ÌQXUPDREVHUY ULLXQHLYDULDELOHQXPHULFH;vQWU RSRSXOD LHVWDWLVWLF V

-

x2, …, xn0HGLDDULWPHWLF

DDFHVWRUD

x HVWHFDOFXODW

-au înregistrat variantele: x1,

vQWU RSULP HWDS GXS UHOD LD

-

1 n ∑ xi (1). În n i =1

SURFHVXOSUHOXFU ULLYDULDQWHOHFXOHVHVXQWJUXSDWHvQ³U´LQWHUYDOHRE LQkQGX

-se o serieGHUHSDUWL LHGH

IUHFYHQ H3HED]DVHULHLIRUPDWHV DUHFDOFXODWQLYHOXOPHGLXXWLOL]kQGUHOD LD

-

r

r

∑ xi ni

∑ ni i =1 i =1

 5H]XOWDWXOXWLOL] ULLFHORUGRX UHOD LLHVWHLGHQWLF

a) b) c) d) e)

1

vQRULFHVLWXD LH QLFLRGDW  DWXQFLFkQGSHQWUXDSOLFDUHDUHOD

iei (2) s-au luat în considerare mijloacele intervalelor;

DWXQFLFkQGLQWHUYDOHOHGHJUXSDUHSUH]LQW IUHFYHQ HHJDOH DWXQFL FkQG IUHFYHQ HOH VXQW QRUPDO UHSDUWL]DWH vQ ILHFDUH LQWHUYDO FkQG IUHFYHQ HOH LQWHUYDOHORU VXQW HJDOH vQWUH HOH úL FkQG vQ UHOD L

a (2) se iau în considerare centrele

intervalelor. 14) 6ROGXOFRQWXOXL³0RGLILFDUHDSDWULPRQLXOXL´UHSUH]LQW



a) economiile nete; b) VROGXOILQDQ ULL c) amortizarea; d) LQYHVWL LLOHEUXWH e) venitul disponibil 15) $PSOLWXGLQHDLQWHUFXDUWLOLF a) b) c) d) e)

vQWU RUHSDUWL LHQRUPDO FRQ LQH

-

GLQQXP UXOREVHUYD LLORU GLQQXP UXOREVHUYD LLORU GLQQXP UXOREVHUYD LLORU WRDWHREVHUYD LLOH QXPDLYDULDQWHOHH[WUHPHDOF URUQXP UHVWHPDLPDUHGHFkWGLQPDVDREVHUYD LLORU

16) În cadrul conturilor macroeconomice, trecereD GH OD FRQFHSWXO ³LQWHUQ´ OD FRQFHSWXO ³QD LRQDO´ se realizeaz în cadrul contului:

a) b) c) d) e)

contul 2 - “Crearea veniturilor”; contul 1 -³3URGXF LH´ contul 3 -³5HSDUWL LDYHQLWXULORU´ contul 4 - “Redistribuirea veniturilor”; vQQLFLXQXOGLQFRQWXULOHPHQ LRQate.

17) Într-R SRSXOD LH VWDWLVWLF

 VH XUP UHVF YDULDELOHOH ; < úL = vQWUH FDUH H[LVW  UHOD LD <

;=

0HGLDDULWPHWLF DYDULDELOHL<HVWHHJDO FXSURGXVXOPHGLLORUYDULDELOHORU;úL=

a) b) c) d) e)

vQRULFHVLWXD LH

forma Z = α + βX ; GHIRUPD X = α + βZ ;

FkQGvQWUH;úL=H[LVW RGHSHQGHQ

OLQLDU GH

FkQGvQWUH;úL=H[LVW RGHSHQGHQ

OLQLDU

FkQGFRYDULDQ DGLQWUH;úL=HVWHQXO  FkQGVHULLOHIRUPDWHGXS ;<=VXQWGLVWULEX LLGHIUHFYHQ HUHODWLYH

18) ,QGLFDWRUXO³3RSXOD LDFXUHQWDFWLY

´QXFXSULQGH

a) VDODULD LLSUH]HQ LODOXFUX b) VDODULD LLDEVHQ LWHPSRUDUGHODOXFUX c) úRPHULL d) patronii; e) HOHYLLúLVWXGHQ LLGHODFXUVXULOHGH]L 19) ÌQ XWLOL]DUHD PHWRGHL UHVWXOXL QHGHVFRPSXV SHQWUX P unui fenomen complex sunt luate în considerare:

VXUDUHD LQIOXHQ HORU L]RODWH DOH IDFWRULORU

a) ponderile perioadei curente ale factorului calitativ; b) SRQGHULOHGLQSHULRDGDGHED] DOHIDFWRUXOXLFDQWLWDWLY c) SRQGHULOHGLQSHULRDGDGHED] DOHIDFWRUXOXLFDOLWDWLY d) SRQGHULOHGLQSHULRDGDFXUHQW DOHIDFWRUului calitativ; e) SRQGHULOH GLQSHULRDGD GHED] LQGLIHUHQW GHQDWXUDFDQWLWDWLY izolat. 20) Într-R

 VDXFDOLWDWLY DIDFWRUXOXL

VHULH GH YDORUL LQGLYLGXDOH DOH XQHL YDULDELOH QXPHULFH REVHUYDW  vQWU R SRSXOD LH

-

VWDWLVWLF YDORDUHDPRGDO HVWH

a) varianta pozLWLY FHDPDLPDUH b) YDULDQWDQHJDWLY GDUPD[LP vQYDORDUHDEVROXW  c) YDULDQWDSR]LWLY VDXQHJDWLY FXFHDPDLPDUHIUHFYHQ d) YDULDQWDFDUHPLQLPL]HD] GLVSHUVLD e) YDULDQWDFDUHvQUHJLVWUHD] FHDPDLPDUHDEDWHUHDEVROXW

GHDSDUL LH

ID

GHPHGLH

21) Se cunosc datele: 3HUED]

INDICATORII - Salariul nominal (mii lei) - Structura cheltuielilor familiilor (%): -P UIXULDOLPHQWDUH -P UIXUL nealimentare - servicii - Modificarea



3HUFXUHQW

600



900

ÌQSHULRDGDFXUHQW ID

GH

SHULRDGD GH ED]  VDODULXO

real: D FUHúWHFX

b) scade cu 18,6 %; 60 25

62 20

15

18

0 0

+25 +40

0

+10

F FUHúWHFX G FUHúWH

de 18,6 ori;

H  FUHúWH FX  PLL

lei.

SUH XULORUvQ 

-P UIXULDOLPHQWDUH -P UIXUL nealimentare - servicii 22) &DUHGLQXUP a) b) c) d) e)

WRDUHOHUHOD LLH[SULP ³)RUPDUHDEUXW DFDSLWDOXOXL´

,QYHVWL LLQHWHGHFDSLWDOIL[SOXVDPRUWL]DUHD ,QYHVWL LLEUXWHGHFDSLWDOIL[SOXVSURILWSOXVPRGLILFDUHDVWRFXULORU )RUPDUHDQHW DFDSLWDOXOX

i fix plus modificarea stocurilor;

)RUPDUHDEUXW DFDSLWDOXOXLIL[SOXVPRGLILFDUHDVWRFXULORU )RUPDUHDEUXW DFDSLWDOXOXLIL[SOXVDPRUWL]DUHDSOXVPRGLILFDUHDVWRFXULORU

23) /D RSW PXQFLWRUL FDUH HIHFWXHD]  DFHOHDúL RSHUD LL vQ FDGUXO XQXL variabilele timp nelucratúLQXP UXOGHRSHUD LL'DWHOHVXQWXUP WRDUHOH Nr. curent Timp nelucrat (u.m.) 1URSHUD LL

1 7 4

2 1 10

3 2 9

4 5 6

5 8 4

6 6 5

7 3 9

VFKLPE V

-au observat

8 4 8

7HQGLQ DOHJ WXULLGLQWUHYDULDELOHHVWHH[SULPDW SULQIXQF LD

a) Yxi = 11,2 − 0,96 xi ; b) Yxi = 11,2 + 0,96 xi ; c) Yxi = −0,96 xi ; d) Yxi = 11,2 + 0,96 xi + 0,04 xi2 ; e) Yxi = 0,96 xi . 24) ÌQ6&1FKHOWXLHOLOHSHQWUXvQO

WXUDUHDGDXQHORUDGXVHPHGLXOXLVXQWFRQVLGHUDWH

a) &RVWGHSURGXF LH b) ,QYHVWL LLQHWH c) ,QYHVWL Li brute; d) Venituri ale consumatorilor; e) Venituri ale statului. 25) 6H FXQRVF GDWHOH FUHúWHUHD SURGXFWLYLW SURGXFWLYLW

LL PHGLL LQGLFHOH SURGXFWLYLW

LL PHGLL SH VHDPD

LLLQGLYLGXDOH,QGLFHOHLQIOXHQ HLVWUXFWXULLDVXSUDSURGXFWLYLW

LLPHGLLHVWH

:

a) b) c) d) e)

100%; 91,7%; 132%; 110%; 85%;

26) ÌQDFWLYLWDWHDGHVWDWLVWLF a) b)

DQDOL]DGLVSHUVLRQDO QXVHXWLOL]HD] SHQWUX

YHULILFDUHDQRUPDOLW

LLUHSDUWL LLORU

HYLGHQ LHUHD P VXULL vQ FDUH XQXO VDX PDL PXO L IDFWRUL VDX R FRPELQD LH D DFHVWRUD  LQIOXHQ HD] vQPRGHVHQ LDOYDULD LDXQHLYDULDELOHUH]XOWDWLYH

c)

DQDOL]DP VXULLvQFDUHYDORULOHUHDOHDOHXQHLFDUDFWHULVWLFLVHDEDWGHODYDORULOHWHRUHWLFH FDOFXODWHGHUHJXO VXEIRUP GHP ULPLPHGLLVDXHFXD LLGHUHJUHVLH

d)

DQDOL]DP VXULLvQFDUHYDULD LLOHXQHL

variabile rezultative sunt sau nu sunt dependente de

factorul de grupare; e)

YHULILFDUHDYDOLGLW

LLPRGHOHORUGHUHJUHVLHVLPSO úLPXOWLSO 

27) 'LVWULEX LDDGHIDPLOLLGXS Nr. copii Nr. familii

0 20

1 65

2 70

QXP UXOGHFRSLLVHSUH]LQW DVWIHOGDWHFRQYHQ LRQDOH 

3 30

4 10

5 5

Total 200

9DORDUHDPHGLDQ vQVHULDSUH]HQWDW HVWH

a) b) c) d) e)

1 copil; 2 copii; 70 familii; 3 copii; 5 copii;

28) 'DF  VWUXFWXUD SH UDPXUL D 3URGXVXOXL ,QWHUQ %UXW VH PRGLILF  vQ IDYRDUHD UDPXULORU FX “necesarul de mijloace fixe pentru RE LQHUHD XQHL XQLW L GH SURGXF LH´ PDL PLF GHFkW QLYHOXO mediu al acestui indicator, atunci, ca urmare a modific ULLIDFWRUXOXLVWUXFWXUDOHILFLHQ DXWLOL] rii PLMORDFHORUIL[HODQLYHOXOHFRQRPLHLQD LRQDOH

a) FUHúWH b) scade; c) U PkQHQHPRGLILFDW  d) nu se SRDWHSUHFL]DVHQVXOPRGLILF e) SRDWHV VFDG  29) 2 VRFLHWDWH FRPHUFLDO

ULL

 D vQUHJLVWUDW OD FLIUD GH DIDFHUL vQ SHULRDGD 6HSW µ 

- Dec. ‘ 96 o -a modificat în de 1,17 ori. În perioada Sept. ‘ 96 - Mai ‘ 97 cifra medie de afaceri a crescut în

FUHúWHUHPHGLHOXQDU FXÌQSHULRDGD'HFµ 0DLµDFHODúLLQGLFDWRUV PHGLH SH OXQ

PHGLHGHODROXQ ODDOWDFX

a) b) c) d) e)

13,5% ; 2,98% ; 3,2% ; 113,4% ; 27%.

30) 7UHL DQJDMD L GH DFHHDúL SURIHVLH úL FDOLILFDUH SHQWUX HIHFWXDUHD XQHL RSHUD LL LGHQWLFH FRQVXP timpiLvQPLQXWH XUP WRUL7LPSXOPHGLXFRQVXPDWHVWH a) 21,7 min./pers. ;



b) c) d) e)

20 min./pers. ; 22,5 min./pers. ; 18,5 min./pers. ; 19 min./pers.

31) &XQRDúWHP GDWHOH 3URGXVXO JOREDO EUXW  XP SRQGHUHD FRQVXPXOXL LQWHUPHGLDU vQ produsul global bruWFRQVXPXOSULYDW FRQVXPXOSXEOLFIRUPDUHDEUXW DFDSLWDOXOXL  ½ consumul privat=10.000 u.m. În aceste condi LL a) Exportul = Importul; b) Exportul > Importul; c) PIB > 100.000 u.m.; d) PIN > 80.000 u.m.; e) Exportul < Importul. 32) În perioada T0 - T1 Produsul Intern Brut a crescut cu 20%, mijloacele fixe cu 30%, iar ponderea

PLMORDFHORU IL[H DFWLYH vQ PLMORDFHOH IL[H VFDGH GH OD  OD  (ILFLHQ D PLMORDFHORU IL[H

active: a) scade cu 105,4% ; b) scade cu 92,3% ; c) FUHúWHFX d) FUHúWHFX e) scade cu 7,7%. 33) Într-RSRSXOD LHVWDWLVWLF

GHXQLW

LFRPHUFLDOHV DXREVHUYDWYDULDELOHOHYDORDUHDDG XJDW 

-

úLYROXPXOPLMORDFHORUIL[HSHQWUXFDUHV DXGHWHUPLQDWGLVSHUVLLOHúLUHVSHFWLY6H

-

FXQRDúWHGHDVHPHQHDF WHQGLQ DOHJ WXULLHVWHH[SULPDWDSULQIXQF LD

Yxi = 119,42 + 0,44 xi .

0 ULPHDFRHILFLHQWXOXLGHFRUHOD LDOLQLDU HVWH

a) b) c) d) e)

0,72 ; -0,75 ; 0,27 ; 0,95 ; 0,44 ;

34) 'HVSUHHYROX LDFLIUHLGHDIDFHULDXQHLVRFLHW ANI PRGLILF ULLUHODWL GH

DIDFHUL

ID



ve a cifrei GH

LFRPHUFLDOHVHFXQRVFGDWHOH

1993 +3

1994 +4

1995 +2

1996 +4

DQXO

precedent ùWLLQG F  FLIUD GH DIDFHUL GLQ  D IRVW GH  POG OHL PRGLILFDUHD PHGLH DQXDO  DEVROXW  vQ

perioada 1992 - 1996 a fost de: a) b) c) d) e)

1,2 mld. lei/an; 1,2 %/an; 2,5 mld. lei/an; 210 %/an; 3 mld. lei/an;

35) 7HQGLQ DOHJ

WXULLGLQWUHGRX YDULDELOHVHH[SULP SULQIXQF LD

OHJ WXULLGLQWUHFHOHGRX YDULDELOHVHFDUDFWHUL]HD] SULQ

a) FRHILFLHQWXOGHFRUHOD LHOLQLDU b) coeficientul lui Spearman;



Yx = a + bx + cx 2 . Intensitatea

c) coeficientul lui Kendall; d) coeficientul lui Bowley; e) UDSRUWXOGHFRUHOD LH 36) 5H]XOWDWHOH H[DPLQ

ULL XQHL VHPLJUXSH OD SUREHOH WHRUHWLFH úL SUDFWLFH DOH XQHL GLVFLSOLQH GH

VSHFLDOLWDWHVXQWXUP WRDUHOH

Studentul TEORIE

A 8 9

35$&7,&

B 3 5

C 9 10

D 2 1

E 7 8

F 10 7

G 4 3

H 6 4

I 1 2

J 5 6

'HSHQGHQ D GLQWUH YDORULOH FHORU GRX  YDULDELOH VH P VRDU  FX DMXWRUXO FRHILFLHQWXOXL GH FRUHOD LHDUDQJXULORUDOOXL6SHDUPDQDF UXLP ULPHHVWH

a) b) c) d) e)

0,855; -0,855; 1,00; -1,00; 0,225;

37) 6HFXQRVFGDWHOH 3URGXVXO1D LRQDO%UXWODSUH XULOHSLH HLXPDORFD LD SHQWUX FRQVXPXO GHFDSLWDOIL[XPúLYHQLWXOQD LRQDOXP0 ULPHD,PSR]LWHORU,QGLUHFWH1HWHHVWH

a) b) c) d) e)

300 u.m.; 400 u.m.; 200 u.m.; 700u.m.; 500 u.m.

38) 3HQWUXRE LQHUHD9HQLWXOXLSHUVRQDODOPHQDMHORUGLQ3URGXVXO1D LRQDO1HWODSUH XULOHSLH HLQX se scad: a) &RQWULEX LLOHOD$VLJXU ULOH6RFLDOH b) Impozitele Indirecte Nete; c) $MXWRDUHOHGHúRPDM d) 3URILWXOQHGLVWULEXLWDOVRFLHW LORU e) ,PSR]LWXOSHYHQLWXOSURILWXO VRFLHW 39) 6HFXQRVFXUP Departamente

A B

LORUILUPHORU 

WRDUHOHGDWH

Procentul programat (al sarcinii de plan) al cifrei de afaceri (%) 105 115

Procentul îndeplinirii programului la cifra de afaceri (%) 110 118

Structura cifrei de afaceri (%) Perioada de Perioada ED]

40 60

FXUHQW

35 65

&DUHLQIRUPD LHVLQWHWLF GLQFHOHSUH]HQWDWHPDLMRVHVWHIDOV "

a) Procentul mediu al îndeplinirii programului la cifra de afaceri a fost de 115,1%; b) Procentul mediu programat (al sarcinii de plan) al cifrei de afaceri a fost de 111%; c) Pe ansamblu cifra de afaceri a crescut în SHULRDGD FXUHQW  ID  GH SHULRDGD GH ED]  FX 27,8%; d) 3H DQVDPEOX FLIUD GH DIDFHUL UHDOL]DW  vQ SHULRDGD FXUHQW  D IRVW PDL PDUH GHFkW FHD SURJUDPDW FX

e)

,QGLFHOHGHGLQDPLF SHDQVDPEOXOGHSDUWDPHQWHORUDIRVWGH

40) /D RVRFLHWDWHFRPHUFLDO

GLQ

vânzarea unui produs s-a realizat în luna mai 1997 o încasare de

 PLOLRDQH OHL &D XUPDUH D PDMRU ULL SUH XOXL ID

 GH PDL  vQFDV ULOH OXQLL PDL  DX

FUHVFXWFXOHL&DUHDUILIRVWvQFDV ULOHOXQLLPDLGDF SUH XOQXV

a) b) c) d) e)

4,5 mil. lei; 3,5 mil. lei; 4 mil. lei; 8 mil. lei; 5 mil. lei.

-ar fi modificat?

TESTUL 2 *)

1) Pe baza unei serii cronologice din perioada 1987- IRUPDW

 GLQ WHUPHQL FRQVHFXWLYL V

-a

DMXQV OD FRQFOX]LD F  WHQGLQ D GH HYROX LH D XQHL YDULDELOH HVWH H[SULPDW  SULQ IXQF LD

Yt = 400 + 60t vQ FRQGL LLOH vQ FDUH ∑ t = 0 ). Valorile estimate ale variabilei analizate pentru

úLvQDFHDVW RUGLQHVXQW

a) b) c) d) e) 2)

1300; 1480; 1600; 1120; 1180; 1240; 340; 280; 220; 460; 520; 580; 760; 820; 880.

3HQWUX GHVFRPSXQHUHD XQXL IHQRPHQ FRPSOH[ SH IDFWRUL GH LQIOXHQ

 FX DMXWRUXO LQGLFLORU VH

SRDWH DSHOD OD PHWRGD VXEVWLWX LHL vQ ODQ  VDX OD PHWRGD UHVWXOXL QHGHVFRPSXV 0HWRGD UHVWXOXL QHGHVFRPSXVVSUHGHRVHELUHGHPHWRGDVXEVWLWX LHLvQODQ 

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a)

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valorilor individuale; b) c) d) e) 4)

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a) b) c) d) e)

700 u.m.; 600 u.m.; 660 u.m.; 960 u.m.; 1340 u.m.

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februarie 1998.

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5)

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d)

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7)



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a)

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b)

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c) d)

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printr-RPHWRG e)

zarea unui interval de eroare, ceea ce face ca RYDORDUHFHUW FLSODVDW vQWU-un interval; i pe baza datelor culese

GHREVHUYDUHWRWDO 

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logice, calculul direct nefiind posibil. 14) 'HVSUH HYROX LD PLMORDFHORU IL[H OD VIkUúLWXO DQXOXL  vQ 5RPkQLD vQ SHULRDGD -1997 se FXQRVFGDWHOHFRQYHQ LRQDOH 

Anii 0RGLILFDUHDID

GHDQXOSUHFHGHQWPOGOHL

1994 194,3

1995 189,8

1996 177,2

ùWLLQGF vQYDORDUHDDEVROXW DXQXLSURFHQWGHFUHúWHUHID

1997 166,9

GHDPLMORDFHORUIL[H

DIRVWGHPOGOHLPRGLILFDUHDPHGLHUHODWLY DQXDO vQSHULRDGD

- 1997 a fost de :

a) b) c) d) e)

114,7 %; 182,05 mld. lei/an; 4,7 %; - 4,7 %; 14,7 %.

15) Ajustarea (determinarea trendului) seriilor cronologice prin metoda mediilor mobile se UHDOL]HD] DWXQFLFkQG

a) IHQRPHQXOSUH]LQW RHYROX LHDSUR[LPDWLYH[SRQHQ LDO  b) LQGLFLLGHGLQDPLF FXED] PRELO SUH]LQW YDORULDSURSLDWHvQWUHHL c) YDULD LDWHUPHQLORUVHULHLSUH]LQW HYLGHQWHUHJXODULW LFLFOLFH d) nu se pot aplica metodele analitice de ajustare; e) YDULD LDWHUPHQLORUVHULHLSUH]LQW RHYLGHQW OLQLDULWDWH 16) ÌQ DQDOL]D GLVSHUVLRQDO  VH XWLOL]HD]  SHQWUX XQ SUDJ GH VHPQLILFD LH  úL QXP UXO JUDGHORU GH libertate (r-1 úLn-r WHVWXO)LVKHU'DF  Fcalculat > Fα , r −1,n − r (din tabel), atunci: a)

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-a efectuat gruparea este într-

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b) se respinge ipoteza cu privire la eJDOLWDWHDPHGLLORUGHJUXS  c) WR L FHLODO L IDFWRUL GH LQIOXHQ  FX H[FHS LD DFHOXLD GH JUXSDUH  GHWHUPLQ

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d) e)

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i variabilei rezultative

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a) a crescut cu 1,2%; b) a crescut cu 23,2%; c) DVF ]XWFX d) DVF ]XWFX e) a crescut cu 1,8%. 18) ,QGLFHOHPHGLXGHGLQDPLF a) b) c)

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aproximativ egale între ele; d) e)

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19) Un circuit economic este considerat circuit închis pentru sectorul A când: a) b)

lori apropiate;

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c) QXH[LVW QLFLLQWU ULúLQLFLLHúLULSHQWUXVHFWRUXO$ d) fluxurile financiare sunt egale cu fluxurile reale; e) VXPDIOX[XULORUGHLQWUDUHHVWHHJDO FXVXPDIOX[XULORUGHLHúLUH 20) Într-R SRSXOD LH VWDWLVWLF

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a) 0,85 x ;

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e)

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a) 56 km/h; b) 53,5 km/h; c) 60 km/h; d) 70 km/h; e) 56,7 km/h.

40 3

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23) ÌQ FD]XO DJUHJ ULL WUDQ]DF LLORU vQ 6&1 WUDQ]DF LLOH HIHFWXDWH vQWUH VXELHFWHOH HFRQRPLFH GLQ sectoare diferite: D VHFRQVROLGHD]  E VHvQVXPHD] 

c) se scad; G XQHOHVHvQVXPHD] LDURDOW FDWHJRUL

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astfel: Candidata Nr. erori Timp dactilo (minute)

A 9 13

B 8 11

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A B

(mil. lei) 18 20

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fizic este:

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b)

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d)

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b)

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completate; c)

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35) 'HQVLWDWHDXQHLUHSDUWL LLVWDWLVWLFHHVWHYL]XDOL]DW

SULQ

a) KLVWRJUDP  b) FXUEDFXPXODWLY GHIUHFYHQ H c) diagrama prin benzi; d) diagrama prin coloane; e) curba de concentrare a lui Lorentz. 36) ÌQ GRX

 SRSXOD LL VWDWLVWLFH $ úL % GH DFHODúL YROXP R YDULDELO  QXPHULF  ; SUH]LQW  DFHOHDúL

YDULDQWH3HQWUXFHOHGRX GLVWULEX LLGHIUHFYHQ HV

-au calculat mediile x A úL x B . Aceste medii

sunt egale deoarece: a) b)

YDORULOHLQGLYLGXDOHGLQ$úL%VXQWLGHQWLFH YDORDUHD ORU GHSLQGH QX QXPDL GH YDORULOH LQGLYLGXDOH FL úL GH IUHFYHQ HOH ORU GLIHULWH GH DSDUL LH

c) d)

VHFDOFXOHD] GXS DFHHDúLPHWRG LDUYROXPXOSRSXOD LLORUVWDWLVWLFHHVWHDFHODúL IUHFYHQ HOHGHDSDUL LHDOHYDORULORULQGLYLGXDOHGLQ$úL%VXQWLGHQWLFHGDUGLIHULWHGHOD RSRSXOD LHODDOWD

e)

vQ$úL%YDORULOHLQGLYLGXDOHVXQWLGHQWLFHúLDXDFHOHDúLIUHFYHQ HGHDSDUL LH

37) ,QGLFHOHSUH urilor consumatorului este calculat ca un indice de tip: a) b) c) d) e)

Paasche; Laspeyres; Fischer; indice al valorii; indice al volumului fizic.

38) 'RL VWDWLVWLFLHQL DX DQDOL]DW DFHOHDúL GDWH UHIHULWRDUH OD ³ vQGHSOLQLULL QRUPHORU´ D  GH PXQFLWRUL GH DFHHDúL SURIHVLH 3HQWUX D FDUDFWHUL]D WHQGLQ D FHQWUDO  D YDULDELOHL XQXO D FDOFXODW PHGLD DULWPHWLF  RE LQkQG  LDU FHO ODOW D FRQVLGHUDW RSRUWXQ  PHGLD S WUDWLF  RE LQkQG

107% (amândoi au efectuat corect calculele). Pentru a caracteriza omogenitatea datelor este QHFHVDU GHWHUPLQDUHDFRHILFLHQWXOXLGHYDULD LH9DORDUHDDFHVWXLDHVWH

a) b) c) d) e)

19,6%; 25%; -75%; SHUVRDQ 

50%.

39) Într-XQ HúDQWLRQ GH  GH DJHQ L HFRQRPLFL V-DX XUP

ULW GRX  YDULDELOH GHSHQGHQWH VWDWLVWLF

SURILWXO QHW PLO OHL  úL QXP UXO PHGLX GH VDODULD L 'HVSUH GLVWULEX LD FRPELQDW  IRUPDW  SH SDWUX LQWHUYDOH HJDOH GXS  SURILW úL SH WUHL LQWHUYDOH GXS  QXP UXO PHGLX GH VDODULD L VH FXQRVF XUP WRDUHOH GDWH SH vQWUHJXO HúDQWLRQ SURILWXO PHGLX D IRVW GH  PLO OHL LDU FRHILFLHQWXO GH YDULD LHDIRVW GH  SURILWXO PHGLXDIRVW GH PLO OHL OD JUXSD DJHQ LORU HFRQRPLFLFX QU PHGLXGHVDODULD LVXESHUVRDQHPLOOHLODJUXSD QUPHGLXGHVDODULD LúLPLOOHL

-

OD JUXSD  úL SHVWH QU PHGLX GH VDODULD L QXP UXO GH DJHQ L HFRQRP

ici pe cele trei grupe sunt

 úL  0 VXUD vQ FDUH PRGLILFDUHD QXP UXOXL PHGLX GH VDODULD L FRQWULEXLH OD YDULDELOLWDWHD SURILWXOXLDJHQ LORUHFRQRPLFLDIRVWGH

a) b) c) d) e)

46,6%; 53,4%; -10%; 110%; 100%.

40) ÌQDQDOL]DVHULLORUGHGDWHVWDWLVWLFHVHXWLOL]HD] QR LXQLOH 1. YDULDELOLWDWHDLQGHSHQGHQ DLQWHUGHSHQGHQ DFRQFHQWUDUHD RPRJHQLWDWHDIRUPDGHUHSDUWL LHSHULRGLFLWDWHD 3URSULHW

a) b) c) d)

LOHSDUWLFXODULW úL úL úL úL

7.

LOH VHULLORUFURQRORJLFHVXQW

TESTUL 3

1)

6H GDX GDWHOH UHIHULWRDUH OD UHSDUWL LD VDODULD LORU XQHL VRFLHW

L FRPHUFLDOH GXS  YHFKLPHD vQ

PXQF 

1UVDODULD L

Grupe (ani)

(0 − 5]

(5 − 10] (10 − 15] (15 − 20] (20 − 25] (25 − 30]

15

peste 30 TOTAL

3 n=49

9HFKLPHDPHGLHDXQXLVDODULDWvQFDGUXOVRFLHW

a) b) c) d) e) 2)

3 5 9 9 5

LLFRPHUFLDOHHVWH

12,5 ani; 21,5 ani; 9,75 ani; 17,5 ani; 24,5 ani.

$JUHJDWHOH PDFURHFRQRPLFH VH GHWHUPLQ  OD SUH XULOH SLH HL VDXOD SUH XULOHIDFWRULORU 7UHFHUHD GHODRFDWHJRULHGHSUH XULODDOWDVHUHDOL]HD] 

a) b) c) d) e)

SUH XOIDFWRULORU

SUH XOSLH HL

SUH XOIDFWRULORU

SUH XOSLH HLLPSR]LWHOHLQGLUHFWH

SUH XOIDFWRULORU

SUH XOSLH HL

SUH XOIDFWRULORU

SUH XOSLH HLVXEYHQ LLOH

SUH XOIDFWRULORU

SUH XOSLH HL VXEYHQ LLOH

- impozitele indirecte; - impozitele indirecte nete; -

3) Indicatorii de rezultate macroeconomice (agregatele macroeconomice) se pot calcula ca LQGLFDWRULGHQDWXU EUXW úLGHQDWXU QHW &DOFXOXOLQGLFDWRULORUvQYDULDQWDQHW VHIDFH

a)

,QGLFDWRULL GH QDWXU  QHW 

 ,QGLFDWRULL GH QDWXU  EUXW   $ORFD LD SHQWUX FRQVXPXO GH

capital fix; b)

,QGLFDWRULL GH QDWXU  QHW  UDSRUWFXVWU LQ WD

c)

 ,QGLFDWRULL GH QDWXU  EUXW   6ROGXO YDORULL DG XJDWH EUXWH vQ

-

tea;

,QGLFDWRULL GH QDWXU  QHW 

 ,QGLFDWRULL GH QDWXU  EUXW   6ROGXO YDORULL DG XJDWH EUXWHvQ

UDSRUWFXVWU LQ WDWHD

d)

,QGLFDWRULL GH QDWXU  QHW 

 ,QGLFDWRULL GH QDWXU  EUXW 

- $ORFD LD SHQWUX FRQVXPXO GH

capital fix; e) 4)

,QGLFDWRULLGHQDWXU QHW 

,QGLFDWRULLGHQDWXU EUXW 

- Exportul net.

9HQLWXO SHUVRQDO GLVSRQLELO 93'  H[SULP  YHQLWXULOH JRVSRG ULLORU PHQDMHORU  FH SRW IL XWLOL]DWHSHQWUXDFRSHULUHDFKHOWXLHOLORUSHUVRQDOHúLSHQWUXHFRQRPLVLUH 9HQLWXO3HUVRQDO'LVSRQLELOVHFDOFXOHD] 

a) VPD = Veniturile personale + Impozitele personale; b) 93' 9HQLWXO1D LRQDO-6ROGXOYDORULLDG XJDWHEUXWHvQUDSRUWFXVWU LQ WDWHD c) VPD = Veniturile personale - Impozitele personale; d) 93' 9HQLWXO1D LRQDO - Impozitele pe veniturile firmelor + Transferurile de la Guvern úLILUPH

e) 5)

93'

9HQLWXO1D LRQDO,PSR]LWHOHSHQWUXDVLJXU ULVRFLDOH'REkQ]LOHSULPLWHGHSRSXOD LH

,QGLFDWRULL PDFURHFRQRPLFL GH UH]XOWDWH DJUHJDWHOH  VH GHWHUPLQ  FD LQGLFDWRUL QRPLQDOL vQ SUH XUL FXUHQWH  úLVDX FD LQGLFDWRUL UHDOL vQ SUH XUL FRPSDUDELOH VDX FRQVWDQWH  &DOFXOXO vQ H[SUHVLHUHDO VHHIHFWXHD] 

a) Agregat real = Agregat nominal -$ORFD LDSHQWUXFRQVXPXOGHFDSLWDOIL[$&&)  b) Agregat real =

$JUHJDW QRPLQDO

Indicele preturilor producatorilor (Laspeyres) $JUHJDW QRPLQDO

c) Agregat real =

Indicele pretului DJUHJDWXOXL (deflatorul PIB) d) $JUHJDWUHDO $JUHJDWQRPLQDO[,QGLFHOHSUH XOui agregatului (deflatorul PIB); e) Agregat real = Agregat nominal x Indicele Paasche.

6)

2VHULHGHWLPSVHUHSUH]LQW JUDILFSULQWU

a) b) c) d) e) 7)

-o:

FRUHORJUDP  GLDJUDP GHVWUXFWXU  FURQRJUDP KLVWRULRJUDP  FDUWRJUDP  FDUWRGLDJUDP 

'DF  VH QRWHD] 

x a - PHGLD DULWPHWLF



x g - PHGLD JHRPHWULF



x h - PHGLD DUPRQLF



xp-

PHGLDS WUDWLF UHOD LDGHRUGLQHGLQWUHPHGLLHVWHXUP WRDUHD

a) x p ≤ x a ≤ x h ≤ x g ; b) x a ≤ x h ≤ x g ≤ x p ; c) x h ≤ x a ≤ x g ≤ x p ; d) x g ≤ x p ≤ x a ≤ x h ; e) x h ≤ x g ≤ x a ≤ x p . 8)

'DF  VH QRWHD] 

x a - PHGLD DULWPHWLF

 [mo

- YDORDUHD PRGDO

VHULHGHUHSDUWL LHFHLWUHLLQGLFDWRULVXQWHJDOL

a) seria este de tip calitativ; b) VHULDHVWHOHSWRFXUWLF  c) VHULDHVWHSODWLFHQWLF  d) VHULDHVWHSHUIHFWVLPHWULF e) seria este de tip normal. 9)

 [me

- YDORDUHD PHGLDQ

 vQWU

-o

x a =xmo = xme) atunci când:



9HULILFDUHD FRQFRUGDQ HL GLQWUH UHSDUWL LD H[SHULPHQWDO  ³HPSLULF ´  RE LQXW  vQWU

-o cercetare

FRQFUHW  úL UHSDUWL LD WHRUHWLF  SUHVXSXV  GH H[HPSOX QRUPDO  VH HIHFWXHD]  FX DMXWRUXO PDL

multor teste.

Expresia: k

(ni − n ⋅ pi )2

i =1

n ⋅ pi

∑

UHSUH]LQW VWDWLVWLFDWHVWXOXL

a) b) c) d) e)

Shapiro - Wilk; Lalliefors; Hi-S WUDWχ2); Kolmogorov-Smirnov; Gnedenko.

10) 3HQWUXDGLPLQXDHURDUHDVLVWHPDWLF

LQWURGXV ODFDOFXOXOGLVSHUVLHLvQWU RVHULHGHUHSDUWL LHSH

-

LQWHUYDOH SULQ IRORVLUHD FHQWUHORU GH LQWHUYDO :)6KHSSDUG D SURSXV R FRUHF LH DVWIHO vQFkW UHOD LDGHFDOFXOHVWH

a) σ ’2 =

∑ xi’ f i ⋅ h 2 − ( x − h ) 2 ; ∑ fi h2 ; 12 p(1 − p) ;

b) σ ’2 = σ 2 − c) σ ’2 =

x i2 fi  ∑ x i fi  ∑ 2  d) σ ’ = −   fi fi ∑  ∑  e) σ ’2 =

∑ (x i − x)

2

100

fi

2

;

.

Unde σ ’2 - YDORDUHD UHFDOFXODW  D GLVSHUVLHL h - P ULPHD LQWHUYDOXOXL GH JUXSDUH xi - valorile caracteristicii; x - media; fi -IUHFYHQ HOHp - media caracteristicii binare. 11) 'HWHUPLQDUHD

YROXPXOXL HúDQWLRQXOXL vQ YDULDQWD ³DOHDWRU VLPSOX UHSHWDW´ VH HIHFWXHD] 

XWLOL]kQGUHOD LD

a) n =

b) n =

zα2 ⋅ σ 2 z 2 ⋅σ 2 ∆2 + α x N 2 n ⋅ N j ⋅ σ 2j k

∑ N j ⋅σ j =1

;

;

2 j 2

 zα + z β   k 2    ; c) n =   z − z  ⋅  1 + 2  p2   p1

1 − p1 1 − p2 d) n = ; p2 1 − p2 lg − lg p1 1 − p1 lg

z2 ⋅σ 2 . e) n = α ∆2

x

12) ,QGLFLL SUH XULORU PHGLL OD SULQFLSDOHOH SURGXVH YkQGXWH SH SLD D varianta: a) b) c) d) e)

U QHDVF  VH GHWHUPLQ  vQ

Laspeyres; Edgeworth; Fischer; Paasche; Marschal.

13) 3H ED]D XQXL VRQGDM Q

 VWXGHQ L HIHFWXDW DOHDWRU vQ FDGUXO IDFXOW

LL V

-au înregistrat diferite -

FDUDFWHULVWLFL 3UHOXFUkQG GDWHOH UHIHULWRDUH OD GRX  GLQWUH DFHVWH FDUDFWHULVWLFL V DX RE LQXW XUP WRDUHOHUH]XOWDWH

Culoarea ochilor GHVFKLV

Culoarea S UXOXL

deschis închis

Total &RHILFLHQWXOGHDVRFLHUHFRQFRUGDQ

a) b) c) d) e)

vQFKLV

6 19 25

23 28 51

vQWUHFHOHGRX FDUDFWHULVWLFLDUHYDORDUHD

0,243; 0,713; 0,980; 0,01; 0,901.

14) 9DORDUHDUDSRUWXOXLGHFRUHOD LHHVWHHJDO a) b) c) d) e)

17 9 26

FXYDORDUHDFRHILFLHQWXOXLGHFRUHOD LHDWXQFLFkQG

UHSDUWL LDHVWHXQLPRGDO  UHSDUWL LDHVWHVLPHWULF  OHJ WXUDGLQWUHYDULDELOHHVWHOLQLDU  OHJ WXUDGLQWUHYDULDELOHHVWHLQYHUV  OHJ WXUDGLQWUHYDULDELOHHVWHGLUHFW 

15) Produsul Intern Brut a fost 109.515 mld. lei în anul 1996, respectiv de 249.750 mld. lei în 1997, VF GHUHD UHFDOFXODW  vQ SUH XUL FRPSDUDELOH  ILLQG  GH - 5DWD LQIOD LHL vQ DQXO  comparativ cu 1996 a fost: a) 244,16%; b) 109,20%;

c) 344,16%; d) 57,20%; e) 144,16%. 16) ,QGLFLLSUH XULORUGHFRQVXPDOSRSXOD LHLvQDQXOID • ODP UIXULDOLPHQWDUe 251,4%; • ODP UIXULQHDOLPHQWDUH • la servicii 276,5%. Ponderile celor trei grupe în totalul cheltuielilor au fost: • P UIXULDOLPHQWDUH • P UIXULQHDOLPHQWDUH • servicii 12%; &XQRVFkQG IDSWXO F  vQ  ID

GHDXIRVW

 GH  FkúWLJXO VDODULDO PHGLX QR

minal net a fost de

GLQDPLFDVDODULLORUUHDOHDIRVWvQHJDO FX

a) b) c) d) e)

77,6%; 112,5%; 177,6%; 100,0%; 47,6%.

17) /DRILUP vQGHFXUVXOXQHLSHULRDGHV-DXvQUHJLVWUDWXUP WRDUHOHGDWH • LQGLFHOHvQ]HVWU ULLWHKQLFHDPXQFLL • modificarea prRFHQWXDO DHILFLHQ HLFDSLWDOXOXLIL[-5%; • LQGLFHOHQXP UXOXLGHVDODULD L 0RGLILFDUHDSURGXF LHLHVWHHJDO FX

a) b) c) d) e)

100%; 0,9576; -7,5%; +12,3%; 112,3%.

18) ,QGLFHOHVLQWHWLFGHJUXS VWDELOLWFDPHGLHDUPRQLF a)

b)

c)

d)

∑ x1 f 1 : ∑ x 0 f 0 ; ∑ f1 ∑ f 0 ∑ x1 ( f 1 + f 0 ) ; ∑ x0 ( f1 + f 0 ) ∑ x 0 f 1 ⋅ ∑ x1 f 1 ∑ x 0 f 0 ∑ x1 f 0

∑ x1 f 1 ∑

1

;

x1 f 1 ix q q q e) n : n −1 = n . q0 q0 q n −1

;

DLQGLFLORULQGLYLGXDOLHVWH

19) Într-RVHULHGHLQGLFLSHQWUXIDFWRUXOFDOLWDWLY[ YDULDQWD³ED] este: a)

b)

c)

d)

e)

PRELO ´úL³SRQGHUHYDULDELO ´

∑ x1 f 0 ; ∑ x2 f 1 ;...; ∑ xi f i −1 ;...; ∑ xn f n−1 ; ∑ x0 f 0 ∑ x1 f 1 ∑ xi −1 f i −1 ∑ xn−1 f n−1 ∑ x1 f 1 ; ∑ x2 f 2 ;...; ∑ xi f 1 ;...; ∑ xn f n ; ∑ x0 f 0 ∑ x1 f 1 ∑ xi −1 f i −1 ∑ xn−1 f n−1 ∑ x0 f 0 ; ∑ x1 f 1 ;...; ∑ xi −1 f i −1 ;...; ∑ xn−1 f n−1 ; ∑ x1 f 1 ∑ x2 f 2 ∑ xi f i ∑ xn f n ∑ x1 f 1 ; ∑ x 2 f 2 ;...; ∑ xi f i ; ...; ∑ x n f n ; ∑ x 0 f 1 ∑ x1 f 2 ∑ xi −1 f i ∑ x n−1 f n ∑ x1 f 1 ; ∑ x1 f 2 ;...; ∑ x1 f i ;...; ∑ x1 f n . ∑ x 1 f 1 ∑ x1 f 2 ∑ x1 f i ∑ x1 f n

20) 5HIHULWRUODDFWLYLWDWHDHFRQRPLF

DXQHLVRFLHW

LFRPHUFLDOHVHFXQRVFXUP WRDUHOHGDWH

9DORDUHDSURGXF LHLPLOOHL

Unitatea

3HUGHED]

3HUFXUHQW

Modificarea valorii pe seama modiILF ULL SUH XULORUPLOOHL

A B

1200 875

1850 1600

0RGLILFDUHD UHODWLY  D YDORULL OD QLYHOXO vQWUHJLL VRFLHW

350 275 L FDX]DW  GH PRGLILFDUHD YROXPXOXL

IL]LFDOSURGXF LHLvQWUHFHOHGRX SHULRDGHDIRVWHJDO FX

a) b) c) d) e) 21) ÌQ

-12,5%; +100,0%; +36,1%; +136,1%; -112,5%.

VWDELOLUHD WUHQGXOXL ³DMXVWDUHD´ VHULHL SHQWUX LGHQWLILFDUHD WHQGLQ HL FHQWUDOH  PHWRGD

PRGLILF ULLPHGLLDEVROXWHVHDSOLF DWXQFL

a) b) c) d) e)

FkQGHYROX LDHVWHH[SRQHQ LDO  FkQGPRGLILF ULOHFXED] PRELO VXQWDSUR[L

mativ egale;

FkQGVHULDHVWHIRUPDW GLQWU XQQXP ULPSDUGHWHUPHQL

-

FkQGVHULDHVWHIRUPDW GLQP ULPLUHODWLYH FkQGVHULDHVWHGHPRPHQWHLQHJDOGLVWDQ DWH

22) 0HWRGDLQIOXHQ HORUL]RODWH³UHVWXOXLQHGHVFRPSXV´ QXVHSRDWHDSOLFDDWXQFLFkQG a) b) c) d) e)

x1 x1 x1 x1 x1

= x0 ; f1 < x0 ; f1 < x0 ; f1 > x0 ; f1 > x0 ; f1

= < > < =

f0; f0; f0; f0; f0.

23) 6HFXQRVFXUP

WRDUHOHGDWH

Ramuri economice

'LQDPLFD9$%ID

Industrie $JULFXOWXU 6LOYLFXOWXU &RQVWUXF LL

Servicii 0RGLILFDUHDSRSXOD LHLRFXSDWHvQID 'LQDPLFDSURGXFWLYLW

GH

(%) 95,0 101,4 78,2 88,8

Structura VAB pe ramuri (%) 36,8 20,8 7,9 34,5

GHDIRVWGH

-2%.

LLVRFLDOHDPXQFLL DIRVWHJDO FX

a) 94,76%; b) 102,51%; c) 104,76%; d) 2,51%; e) 194,76%. 24) Cunoscând valorile observate (Yi úLFHOHDMXVWDWHUHFDOFXODWHSULQWU-un model analitic ( Yi ):

Yi : 98; 109; 121; 145; 152 Yi: 99; 108; 119; 147; 152 &RHILFLHQWXOGHGHWHUPLQD LHDOPRGHOXOXLGHUHJUHVLHSULQFDUHV

a) b) c) d) a)

-a realizat ajustarea este egal cu:

1,215; 0,095; 0,875; 0,962; 0,715.

25) Pentru estimarea fondului de salarizare necesar într-R OXQ  OD R 6& FX  GH DQJDMD L GLQ FDUH  DQJDMD L SHUPDQHQW úL   FRODERUDWRUL V-a organizat un sondaj aleator stratificat SURSRU LRQDOI U UHYHQLUHGHYROXPGLQFROHFWLYLWDWHDJHQHUDO 'LQSUHOXFUDUHDGDWHORUGLQ HúDQWLRQDUH]XOWDWXQVDODULXPHGLXDODQJDMD LORUFXFRQWUDFWGHPXQF GHPLOOHLúLXQVDODULX PHGLXDODQJDMD LORUvQUHJLPGHFRODERUDUHGHPLO

lei, iar dintr-RFHUFHWDUHDQWHULRDU

VHúWLHF 

IDFWRUXO ÄUHJLPXO GH DQJDMDUH´ LQIOXHQ HD]  YDULD LD VDODULXOXL vQ SURSRU LH GH  )RQGXO GH

salarizare estimat pentru întreaga S.C. (pentru o probabilitate de 0,9973, z =3), este:


a) b) c) d) e)

(3,32 mil. lei; 4,28 mil. lei); (2568 mil. lei; 3504 mil. lei); (2656 mil. lei; 3424 mil. lei); (3,21 mil. lei; 4,38 mil. lei); (2800 mil. lei; 3280 mil. lei).

26) 2FUHúWHUHDHILFLHQ HLDFWLYLW LLHFRQRPLFHQXVHUHDOL]HD] GDF  a) LQGLFHOHGHGLQDPLF DHILFLHQ HLIRORVLULL fondurilor fixe este supraunitar; b) GLQDPLFDSURGXF LHLPDUI GHYDQVHD] GLQDPLFDFDSLWDOXOXLIL[ c) LQGLFHOHGHGLQDPLF DQHFHVDUXOXLGHPLMORDFHIL[HHVWHVXSUDXQLWDU d) indicele de dinaPLF DSURGXFWLYLW LLPXQFLLHVWHVXSUDXQLWDU e) GLQDPLFDSURGXF LHLPDUI GHYDQVHD] GLQDPLFDQXP UXOXLGHVDODULD L

27) ÌQOXQDLDQXDULHvQGRX -

ILOLDOHDOHXQHLILUPHV DXvQUHJLVWUDWXUP WRDUHOHGDWH

vQ ILOLDOD $ FHL  DQJDMD L UHSUH]HQWkQG  GLQ WRWDOXO DQJDMD LORU ILUPHL PDX UHDOL]DW R SURGXF LHGHPLOOHL

-

-

;

în filiala B s-a realizat o productivitate medie a muncii de 3,1 mil. lei.

ùWLLQG F  vQ OXQD IHEUXDULH SURGXFWLYLWDWHD PHGLH D PXQFLL SH DQVDPEOX FHORU GRX  ILOLDOH D IRVW GH  PLOLRDQH OHL LDU QXP UXO WRWDO GH DQJDMD L D IRVW GH  PRGLILFDUHD DEVROXW  D SURGXF LHL vQ OXQDIHEUXDULHID

GHLDQXDULHSHDQVDPEOXOILUPHLGDWRUDW PRGLILF ULLQXP UXOXLWRWDOGHDQJDMD L

a fost: a) 178,44 mil. lei; b) 195,96 mil. lei; c) 138 mil. lei; d) 170,4 mil. lei; e) 374,4 mil lei. 28) ÌQDQDOL]DVWDWLVWLF

DVH]RQDOLW

LLXQHL6&5LQGLFLLGHVH]RQDOLWDWHVHGHWHUPLQ DWXQFLFkQG

a)

IHQRPHQXODUHRHYROX LHSHWHUPHQOXQJDVHP Q WRDUHXQHLSURJUHVLLJHRPHWULFH

b)

vQ VHULD FURQRORJLF  VH FRQVWDW  F  PRGLILF ULOH DEVROXWH FX ED]  PRELO  VXQW DSUR[LPDWLY

egale; c) s-a utilizat pentru deteUPLQDUHDWUHQGXOXLRPHWRG d) s-DXWLOL]DWSHQWUXGHWHUPLQDUHDWUHQGXOXLRPHWRG e)

PHFDQLF  DQDOLWLF 

FRPSRQHQWHOHGHWUHQGRVFLODWRULHúLDOHDWRDUHVHFRPSXQGXS XQPRGHOPXOWLSOLFDWLY

29) ,QGLFDWRUXOVWDWLVWLFÄHQHUJLDLQIRUPD LRQDO a)

REOLFLW

b)

WHQGLQ HLFHQWUDOH

c)

YDULD LHL

d)

FRQFHQWU ULLGLYHUVLILF ULL

e)

EROWLULLDSODWL] ULL

2QLFHVFX´HVWHXWLOL]DWvQDQDOL]DVWDWLVWLF D

LL

30) ÌQFRQVWUXF LDFRQWXULORUPDFURHFRQRPLFHGLQFDGUXO6&1QXDUHVROG a)

FRQWXOGHUHSDUWL LHDYHQLWXULORU

b) contul de creare a veniturilor; c)

FRQWXOGHSURGXF LH

d) contul sintetic de bunuri;

e) contul de modificare a patrimoniului. 31) 'DF

GLVWULEX LDXQXLORWGHPLQJLFRQIHF LRQDWHGLQDFHODúLPDWHULDO vQIXQF LHGHGLPHQVLXQH

HVWHQRUPDO úLSHUIHFWVLPHWULF DWXQFLGLVWULEX LDORWXOXLGXS YROXPHVWH

a)

SHUIHFWVLPHWULF 

b)

DVLPHWULF vQFDUHSUHGRPLQ YDORULOHPDUL

c)

DVLPHWULF vQFDUHSUHGRPLQ YDORULOHPLFL

d)

vQIRUP GHÄ8´

e)

QXVHSRDWHSUHFL]DIRUPDGLVWULEX LHL

32) ÌQGHWHUPLQDUHDDJUHJDWHORUPDFURHFRQRPLFHLQGLFDWRULLFDUHH[SULP

S

rodusul domestic iau în

calcul: a)

UH]XOWDWXODFWLYLW

LLSURGXFWLYHDWXWXURUDJHQ LORUGLQLQWHU RUXO

b)

UH]XOWDWXO DFWLYLW

LL SURGXFWLYH D WXWXURU DJHQ LORU QD LRQDOL FDUH úL DX GHVI úXUDW DFWLYLWDWHD

SHWHULWRULXO

c)

d)

e)

-

LL SURGXFWLYH D DJHQ LORU QD LRQDOL FDUH úL DX GHVI úXUDW DFWLYLWDWHD QXPDL

-

ULL

UH]XOWDWXO DFWLYLW WHULWRULXO

ULLQD LRQDOLVDXVWU LQL

ULLVDXvQVWU LQ WDWH

UH]XOWDWXO DFWLYLW SHWHULWRULXO

i

LL SURGXFWLYH D DJHQ LORU QD LRQDOL FDUH úL DX GHVI úXUDW DFWLYLWDWHD SH

ULLFHOSX

-

in 11 luni, în cadrul unui an;

SURGXF LDPHQDMHORUSHQWUXFRQVXPXOSURSULX

TESTUL 4

1)

ÌQ6LVWHPXO&RQWXULORU1D LRQDOHLPSR]LWHOHLQGLUHFWHQHWHIDFRELHFWXO

a) GHELWXOXLFRQWXOXL³3URGXF LH´ b) FUHGLWXOXLFRQWXOXL´3URGXF LH´ c) VROGXOXLFRQWXOXL³3URGXF LH´ d) soldului contului “Venituri”; e) debitului contului de “Modificare a patrimoniului sectorului firme”. 2)

3UHVXSXQHPF VXQWH LLQWHUHVD LvQHIHFWXDUHDWHVWXOXLVWDWLVWLF

H 0 : m = 200 H a : m > 200

úL XWLOL]D L UHJXOD GH GHFL]LH ³6H UHVSLQJH +0 GDF  PHGLD HúDQWLRQXOXL GH  GH XQLW

L HVWH PDL

PDUHGH´'HYLD LDVWDQGDUGvQSRSXOD LHHVWHGH3UREDELOLWDWHDFRPLWHULLXQHLHURULGHJHQXO

întâi este: a) b) c) d) e) 3)

13,36%; 6,68%; 43,32%; 0,4332; 3,34%.

6DODULD LL XQHL VRFLHW

L FRPHUFLDOH DX XQ VDODULX PHGLX GH  PLL OHL 3DWURQXO KRW U úWH V 

P UHDVF VDODULXOILHF UXLDQJDMDWGHRUL1RXOVDODULXPHGLXYDIL

a) b) c) d) e) 4)

750 mii lei; 780 mii lei; 975 mii lei; 576,9 mii lei; 880 mii lei.

,QFOXGHUHD UHVXUVHORU PLQHUDOH vQ DYX LD QD LRQDO  VH UHDOL]HD]  SULQ FRQVWLWXLUHD XQRU

trepte de

DWUDJHUHvQFLUFXLWXOHFRQRPLFDODFHVWRUUHVXUVHGLQSXQFWGHYHGHUHDOJUDGXOXLGHFXQRDúWHUHD DFHVWRUD úL DO SRVLELOLW

LORU GH H[SORDWDUH 1XP UXO GH WUHSWH vQ FDUH VH FXSULQG DFHVWH UHVXUVH

minerale sunt: a) b) c) d) e) 5)

2; 4; 3; 5; 8.

1XP UXO DQJDMD LORU XQHL FRPSDQLL FDUH DEVHQWHD]  OXQHD DUH DSUR[LPDWLY R GLVWULEX LH 3RLVVRQ LDUQXP UXOPHGLXGHDEVHQ LGLQDFHDVW ]LDV SW PkQLLHVWH3UREDELOLWDWHDFDPDLSX LQGH DQJDMD LV DEVHQWH]HvQWU R]LGHOXQLDV SW PkQLLHVWH

-

a) 25,10%; b) 19,31%; c) 2,6%;

d) 51,84; e) 26,74%. 6)

)LH R FROHFWLYLWDWH VWDWLVWLF  VLVWHPDWL]DW  vQ  JUXSH GXS  YDORULOH FDUDFWHULVWLFLL GH JUXSDUH ; úL

r

în mJUXSHGXS

YDORULOHYDULDELOHLDQDOL]DWH<úLSHQWUXFDUHV

σ i2

GLVSHUVLD WRWDO 

 GLVSHUVLLOH GH JUXS  

i = 1, r ), σ

2

-au calculat dispersiile: σ 2 =

 PHGLD GLVSHUVLLORU GH JUXS 

δ 2=

dispersia dintre grupe. &RQWULEX LDIDFWRUXOXLGHJUXSDUH;ODYDULD LDJHQHUDO DYDULDELOHL<VHP VRDU FXLQGLFDWRUXO

a) R = 2

2

σ

;

σ2 δ2 ; b) R 2 = σ2 δ2 c) R 2 = 1 − ; σ2 r

∑

d) R 2 = i =1

∑ (y j − y ) m

σ i2 ni . :

r

j =1

∑ ni .

e) R =

j =1 2

m

i =1 j =1

r

;

m

∑ ∑ (y j − y i ) 2

n. j

∑ n. j

i =1

r

2

∑ (y j − y ) m

nij :

m

j =1

2

n. j .

m

∑ ∑ nij

∑ n. j

i =1 j =1

j =1

 /HJ WXULOHGLQWUHIHQRPHQHOHHFRQRPLFR VRFLDOHGHPDV VXQW

-

a) b) c) d) e)

OHJ WXULIXQF LRQDOH OHJ WXULFDUHVHVXSXQDF LXQLLOHJLORUVWRFKDVWLFH OHJ WXULFHSRWILSXVHvQHYLGHQ

ODQLYHOXOILHF UHLXQLW

LvQSDUWH

OHJ WXULFDUHVHVXSXQDF LXQLLOHJLORUGLQDPLFH OHJ WXULXQLYRFGHWHUPLQDWH

 6HFRQVLGHU XQWDEHOGHFRQWLQJHQ

{[(x , y )n ]; j ∈ J , k ∈ K} j

k

FRUHOD LH vQIRUPDVDJHQHUDO

:

jk

&RYDULDQ DGLQWUHYDULDELOHOH;úL<&RY;< FDOFXODW SHED]DWDEHOXOXLHVWH

(

)(

)

a) Cov( X , Y ) =

1 ∑ ∑ x j − x y k − y n. j ; n j k

b) Cov ( X , Y ) =

1 ∑ ∑ x j yk n jk − xy ; n j k

c) Cov( X , Y ) = d) Cov ( X , Y ) =

(

)(

)

1 ∑ ∑ x j − x yk − y ; n j k

xj − x 1 nij ; ∑∑ n j k yk − y

∑ ∑ (x j − x)(y j − y)nij j

e) Cov ( X , Y ) =

9) 'DF

k

.

nσ x σ y

 vQ WDEHOXO GH FRQWLQJHQ

 GHILQLW OD SUREOHPD   QRW P

Uj =

xj − x

σx

 úL

Vk =

yk − y , σy

atunci: a) Cov ( X , Y ) = σ x σ y Cov (U ,V ) ; b) Cov ( X , Y ) ≠ σ x σ y Cov (U ,V ) ; c) Cov ( X , Y ) =

Cov (U ,V ) ; σ xσ y

d) Cov ( X , Y ) − Cov (U ,V ) = σ xσ y ; e) Cov ( X , Y ) = σ U σ V Cov (U ,V ) .

10) 3UHFL]LDHVWLP

ULLSDUDPHWULORU SRSXOD LHLJHQHUDOH SHED]DGDWHORUGH VRQGDMGHSLQGHGHHURULOH

GHvQUHJLVWUDUHúLGHHURULOHGHUHSUH]HQWDWLYLWDWH3HQWUXDPD[LPL]DSUHFL]LDHVWLP ULORU

a)

HVWH VXILFLHQW V  VH HOLPLQH VXUVHOH HURULORU GH vQUHJLVWUDUH SULQ GLIHULWH PRGDOLW

verifLFDUHDYHULGLFLW b) c)

L GH

LLGDWHORUFXOHVH

HVWHVXILFLHQWV DFRUG PXQLW

LORUSRSXOD LHLVWDWLVWLFHúDQVHHJDOHGHDILLQFOXVHvQHúDQWLRQ

HVWH QHFHVDU V  HOLPLQ P HURULOH GH UHSUH]HQWDWLYLWDWH SULQ UHVSHFWDUHD SULQFLSLLORU VHOHF LHLDOHDWRDUH

d) este necesar

V  HOLPLQ P HURULOH GH vQUHJLVWUDUH VXUVHOH HURULORU VLVWHPDWLFH GH

UHSUH]HQWDWLYLWDWHúLV PLQLPL] PHURULOHDOHDWRDUHGHUHSUH]HQWDWLYLWDWH

e)

HVWH QHFHVDU V  HOLPLQ P HURULOH GH vQUHJLVWUDUH úL QRQU VSXQVXULOH OD vQWUHE ULOH GLQ

chestionare.

11) ClasifiFDUHD DFWLYLW

LORU HFRQRPLFR VRFLDOH GLQ HFRQRPLD QD LRQDO  VH UHDOL]HD]  SH FDWHJRULL

-

GLYL]LXQLJUXSHúLVDXFODVH

a) b) c) d) e)

2FDWHJRULHHVWHPDLRPRJHQ GHFkWRGLYL]LXQHJUXS VDXFODV  *UXSDGHDFWLYLW

LSUH]LQW FHDPDLPDUHRPRJHQLWDWHvQUDSRUWFXFHO

elalte;

2JUXS HVWHPDLRPRJHQ GHFkWRFDWHJRULHVDXGLYL]LXQHGDUPDLHWHURJHQ GHFkWRFODV  &ODVDGHDFWLYLW

LHVWHPDLHWHURJHQ GHFkWRFDWHJRULHGLYL]LXQHVDXJUXS 

'LYL]LXQHD HVWH PDL RPRJHQ  GHFkW R JUXS  VDX FODV  GDU PDL HWHURJHQ  GHFkW R FDWHJRULHGHDFWLYLW

L

&RQGL LD QHFHVDU  FD H[SUHVLD

F (β 0 , β 1 ) = ∑ (yi − β 0 − β 1xi ) β0úLβ1V

GHULYDWHOHVDOHSDU LDOHvQIXQF LHGH

i

ILHHJDOHFX]HUR

2

V  ILH PLQLP  HVWH DFHHD FD

dF =0 dβ 0 dF =0 dβ 1 12) 6ROX LDDFHVWXLVLVWHPGHHFXD LLHVWHFXSOXOGHYDORri (b0, b1)FRUHVSXQ]

WRUSDUDPHWULORU

β0, β1)

definit prin:

a) b1 = b) b1 =

Cov(x , y)

σ 2x Cov(x , y ) nσ x σ y

úL

b0 = y − b1 x ;

úL

b0 = y − b1 x ;

c) b1 = y − b0 x úL b0 =

Cov(x , y )

σ 2x

;

d) b1 = b0 = y ; Cov(x , y ) e) b1 = b0 = . σ 2x 13) 6H

úWLH

F 

σ 2y =

Yi = b0 + b1 xi 'DF

(

)

( ) (1 − r ) (1 − r ) (1 − r ) (1 − r )

úL

b) σ 2y.x > σ 2y

2

úL

σ 2y = σ 2y .x + σ Y2 ;

2

úL

σ 2y = σ 2y .x + σ Y2 ;

2

úL

σ 2y < σ 2y .x + σ Y2 ;

2

úL

σ 2y > σ 2y .x + σ Y2 .

d) σ 2y.x > σ 2y e) σ 2y.x < σ 2y 14) 2 YDULDELO

)

úL

σ Y2 =

(

)

2 1 Yi − y ∑ n i

unde

UHVWHFRHILFLHQWXOGHFRUHOD LHGLQWUHYDULDELOHOH<úL;DWXQFL

a) σ 2y .x = σ 2y 1 − r 2

c) σ 2y.x = σ 2y

(

2 2 1 1 yi − y ;σ 2y.x = ∑ yi − Yi ∑ r i n i

σ 2y < σ 2y .x + σ Y2 ;

 FRPSOH[  < HVWH H[SULPDW  vQ IXQF LH GH IDFWRULL DEFGHIJK D F URU LQIOXHQ



WUHEXLH L]RODW  5HOD LD GLQWUH < úL IDFWRULL V L ILLQG PXOWLSOLFDWLY  SHUPLWH R GHVFRPSXQHUH vQ

trepte de forma:

P este par

Calcularea unei a doua sume mobile (de ordinul 2)

Divizarea prin 2 P

$IODUHDQXP UXOXLGH

termeni din care se FDOFXOHD] PHGLLOH

mobile (ordinul de filtraj = p∈ N)

Calculul sumelor mobile

P este impar

b)

Aflarea valorilor DMXVWDWHúLWUDVDUHD

trendului pe grafic

Divizarea prin 2 P

'DF  S HVWH SDU HVWH QHFHVDU V  FDOFXO P PHGLL PRELOH SDU LDOH GH RUGLQXO  DSRL SH ED]D DFHVWRUD PHGLL PRELOH SDU LDOH GH RUGLQXO  úDPG SkQ  DMXQJHP OD PHGLLOH

finale (valorile ajustate) plasate în dreptul termenilor reali;

 p + 1  2  termeni reali;

c)

'DF SHVWHLPSDUVHSLHUGSULQDMXVWDUHXQQXP UGH

d) e)

'DF SHVWHSDUVHSLHUGSULQDMXVWDUHXQQXP UGHSWHUPHQLUHDOL 1XP UXOYDORULORUDMXVWDWHHVWHDFHODúLLQGLIHUHQWGHQDWXUDOXL

17) ,QGLFHOHPHGLXGHGLQDPLF

SHQWUXXQRUL]RQW

p ∈N .

de timp 1, T VHFDOFXOHD]

LQGLFLORUGHGLQDPLF FXED] PRELO GLQRUL]RQWXO

FDPHGLHJHRPHWULF D

1, T FXFRQGL LDFDDFHúWLDV

SUH]LQWHYDORUL

DSURSLDWHV ILHRPRJHQL $FHDVW FRQGL LH

a) HVWHIDFXOWDWLY  b) este LPSRUWDQW úLWUHEXLHUHVSHFWDW GHRDUHFHLQGLFHOHPHGLXVHSRDWHFDOFXODúLvQIXQF LH doar de termenii extremi (y1 úL \T  I U  V  VH LQ  VHDPD GH HYROX LD IHQRPHQXOXL vQ interiorul orizontului de timp; c) QXHVWHQHFHVDU GHRDUHFHHDH[FOXGHQHFHVLWDWHDUHSUH]HQWDWLYLW LLPHGLHLFDOFXODWHvQWU-o serie de date statistice; d) QX HVWH QHFHVDU  GHRDUHFH vQ RULFH VHULH FURQRORJLF   PHGLD JHRPHWULF  VW  OD ED]D GHWHUPLQ ULLLQGLFHOXLPHGLXGHGLQDPLF 

e)

WUHEXLH UHVSHFWDW  QXPDLDWXQFLFkQG RUL]RQWXO GHWLPS

1, T al seriei cronologice nu este

mai mic de 5 ani. 18) 3HQWUX GHWHUPLQDUHD DJUHJDWHORU PDFURHFRQRPLFH VH XWLOL]HD]

 GDWH GLQ XUP WRDUHOH FRQWXUL

QD LRQDOH   FRQWXO VLQWHWLF GH EXQXUL   FRQWXOPRGLILF ULL SDWULPRQLXOXL   FRQWXO GH FUHDUH D

vHQLWXULORU   FRQWXO SURGXF LH   FRQWXO GH UHSDUWL LH D YHQLWXULORU   FRQWXO GH UHGLVWULEXLUH D YHQLWXULORU FRQWXOGHILQDQ DUHDPRGLILF ULLSDWULPRQLXOXL FRQWXOXWLOL] ULLYHQLWXULORU &DUHGLQWUHYDULDQWHOHGHPDLMRVHVWHIDOV 

a) Soldul contului 4) este produsul intern brut; b) 3URGXVXOLQWHUQEUXWODSUH XOIDFWRULORUHVWHVROGXOFRQWXOXL  c) 9HQLWXOQD LRQDOHVWHVROGXOFRQWXOXL 

d) 9HQLWXOQD LRQDOGLVSRQLELOHVWHVROGXOFRQWXOXL  e) 9HQLWXOQD LRQDOGLVSRQLELOHVWHUHVXUV SHQWUXFRQWXO . 19) Pe baza tabelului de date punctuale prezentat mai jos: i xi

1 1

2 2

3 1

4 3

5 2

6 1

7 1

8 2

FDOFXOD LFXDUWLOHOH

Q1, Q2úLQ3. Valorile acestora sunt:

a) b) c) d) e)

Q1=1; Q2=2; Q3=3; Q1=1; Q2=(1,2); Q3=2; Q1=3; Q2=(1,2); Q3=2; Q1=1; Q2=3; Q3=2; altele decât cele prezentate în variantele anterioare;

20) Într-o colectivitate s-DXFXOHVGDWHOHSHQWUXGRX {xi }i =1,8 = {4;1;1;5;6;3;2;1}

YDULDELOHVWDWLVWLFHRE LQkQGX

-se:

{yi }i =1,8 = {100;90;40;80;70;50;100;70}

ÌQSULYLQ DRPRJHQLW

a) b) c) d) e)

LLFHORUGRX VHULLVHSRDWHDILUPD

VHULDDOF WXLW GXS YDULDELOD;HVWHPDLRPRJHQ GHFkWFHDGXS < VHULDIRUPDW GXS <HVWHPDLRPRJHQ GHFkWFHDGXS ; VHULDDOF WXLW GXS YDULDELOD;HVWHPDLRPRJHQ GHRDUHFHYDORULOHVXQWPDLPLFL QXVHSRDWHFRPSDUDRPRJHQLWDWHDFHORUGRX VHULLILLQGYRUEDGHYD

riabile diferite;

ILLQGYRUEDGHDFHHDúLFROHFWLYLWDWHRPRJHQLWDWHDFHORUGRX VHULLHVWHDFHHDúL

21) $QDOL]D LXUP

WRDUHOHFDWHJRULLGHSHUVRDQHGHDQLúLSHVWHGLQWU RSHULRDG GHUHIHULQ

-



  SHUVRDQH FDUH QX OXFUHD]  QHDYkQG XQ ORF GH PXQF    SHUVRDQH FDUH VXQW vQ F XWDUHD XQXL ORF GH PXQF    SHUVRDQH FRQFHGLDWH   SHUVRDQH FDUH VXQW GLVSRQLELOH V  vQFHDS  LPHGLDW F XWDUHDXQXLORFGHPXQF  SHUVRDQHvQF XWDUHDSULPXOXLORFGHPXQF  SHUVRDQHFDUHGXS  RvQWUHUXSHUHYROXQWDU DDFWLYLW

LLVROLFLW UHOXDUHDDFHVWHLD SHUVRDQHVH]RQLHURFXSDWHDIODWHvQ

RFXSDUHDXQXLSHUPDQHQWORFGHPXQF  ÌQ GHWHUPLQDUHD QXP UXOXL GH úRPHUL vQ VHQVXO GHILQL LHL GDWH GH %LURXO ,QWHUQD LRQDO DO 0XQFLLGHILQL LDVWDQGDUG VHFXSULQGH

a) úL b) 1,úL c) úL d) úL e) úL   /X P vQ FRQVLGHUDUH WDEHOXO GH FRQWLQJHQ

GLVWULEX LLOH FRQGL LRQDWH DOH OXL < GH ; FXQRVFPHGLLOHúLGLVSHUVLLOH

y (x j ) =

1 ∑ n jk yk n j. k

úL

σ 2y (x j ) =

{(y

k

 FRUHOD LH 

{[(x , y )n ]; j ∈ J , k ∈ K} j

}

)

, n jk , j fixat , k ∈ K

[

jk

úL

 3HQWUX DFHVWHD GLQ XUP  VH

]

2 1 y k − y ( x j ) n jk , ∑ n j. k

IUHFYHQ D PDUJLQDO DVRFLDW YDULDQWHL

k

cu

n j . = ∑ n jk efectivul k

xj.

Dispersia variabilei Y ( σ 2y vQIXQF LHGHHOHPHQWHSUH]HQWDWHvQLSRWH]

VHSUH]LQW DVWIHO

[

]

a) σ 2y =

2 1 1 n j .σ 2y (x j ) + ∑ n j . y ( x j ) − y ; ∑ n j n j

b) σ 2y <

2 1 n j. y( x j ) − y ; ∑ n j

c) σ 2y <

1 ∑ n j.σ 2y ( x j ) ; n j

d) σ 2y =

2 1 1 n j.σ 2y ( x j ) − ∑ n j. y ( x j ) − y ; ∑ n j n j

e) σ 2y >

1 1 n j .σ 2y ( x j ) + ∑ n j . y ( x j ) − y ∑ n j n j

[

]

[

GHLQIOXHQ

]

[

]

2

 FX FRYDULDQ D GLQWUH < úL FHLODO L IDFWRUL

FXH[FHS LDIDFWRUXOXL;

23) Luându-se în considerare elementele prezentate în ipoteza pUREOHPHL   SURSRU LD YDULD LHL PHGLLORUFRQGL LRQDWHvQGLVSHUVLDJHQHUDO DYDULDELOHL<HVWHQXPLW JUDGGHGHWHUPLQD LHúLHVWH QRWDW FX

R y2.x &DUHGLQXUP

WRDUHOHDILUPD LLQXHVWHDGHY UDW 

a) 0 ≤ R y2.x ≤ 1 ; b) R y2.x = 0 GDF c) R y2.x = 1 GDF

WRDWHPHGLLOHFRQGL LRQDWHDOHOXL\vQIXQF LHGH[VXQWHJDOHvQWUHHOH ILHF UHLYDORUL[jvLFRUHVSXQGHRXQLF YDORDUHDYDUDELOHL\

d) R y2.x = 0  GDF

 PHGLLOH FRQGL LRQDWH DOH OXL \ vQ IXQF LH GH [ VXQW GLVWLQFWH GRX  FkWH

GRX 

e) R y2.x H[SULP

P VXUDvQFDUHIDFWRUXOGHLQIOXHQ

H[SOLF YDULD LDYDULDELOHL\

24) (URULOHDOHDWRDUHGHUHSUH]HQWDWLYLWDWHvQWkOQLWHvQFD]XORUJDQL] fi evitate ci diminuate: a)

GHRDUHFH XQLW

ULLRULF UXLWLSGHVRQGDMQX

pot

LORU GLQ SRSXOD LLOH VWDWLVWLFH OL VH DFRUG  DFHHDúL úDQV  GH DSDUL LH vQ

HúDQWLRDQH

b)

GHRDUHFH vQ HúDQWLRDQH VH FXSULQG QXPDL S U L GLQ SRSXOD LL VWDWLVWLFH úL SULQ XUPDUH QX

pot reproduce identic, decât întâmpO extrase; c) d) e)

WRU VWUXFWXULOH SRSXOD LLORU GLQ FDUH DFHVWHD DX IRVW

DWXQFLFkQGFRQWUROXOGDWHORUFXOHVHVHUHDOL]HD] SULQFHOHPDLDGHFYDWHPHWRGH DWXQFLFkQGVHXWLOL]HD] ED]HGHVRQGDMDFWXDOL]DWHFRUHVSXQ] WRU DWXQFL FkQG VH IRUPHD]  GLQ DFHHDúL SRSXOD LH WRDWH HúDQWLRDQHOH SRVLELOH FKLDU GDF  HOH DXDFHODúLYROXP

25) 3HQWUX FRPSDUDUHD SUH XULORU SURGXVHORU GLQWU-R LQGLFHGHJUXSGHSUH 

DU  FX FHOH GLQWU R DOW  DU  VH XWLOL]HD]  XQ

-

a) de tip Laspeyres; b) de tip Paasche; c) de tip Fischer; d) IRUPDWGXS PHWRGDVXEVWLWXLULLvQO Q XLWH e) IRUPDWGXS PHWRGDUHVWXOXLQHGHVFRPSXV 26) Estimatorul unui parametru θVHQRWHD]  θ $FHVWHVWLPDWRUHVWHQHGHSODVDWGDF a)

GLIHUHQ DGLQWUHPHGLDVDúLYDORDUHDSDUDPHWUXOXLHVWHGLIHULW GH]HUR

b)

GDF PHGLDVDHVWHHJDO FXYDORDUHDSDUDPHWUXOXL

( M (θ ) = θ );

D(θ ) → 0 FkQG YROXPXO HúDQWLRQXOXL SRSXOD LHLJHQHUDOH n → N ); d) dispersia sa este miniP SHQWUXXQYROXPIL[DWDOHúDQWLRQXOXL e) GLVSHUVLDHVWLPDWRUXOXLHVWHPD[LPDO  c)

GLVSHUVLD VD HVWH PLQLP  

27) ÌQFDOFXOXOSURGXFWLYLW



( M (θ − θ ≠ 0) ;

WLQGH F WUH YROXPXO

LLVRFLDOHDPXQFLLVHLDvQFRQVLGHUDUH

a) b) c) d)

SRSXOD LDRFXSDW WRWDO 

e)

SRSXOD LDRFXSDW WRWDO GLPLQXDW FXVDODULD LLRUJDQL]D LLORUSROLWLFHúLREúWHúWL

SRSXOD LDDFWLY  SRSXOD LDRFXSDW WRWDO GLQFDUHVHVFDGHSRSXOD LDGLQDUPDW  SRSXOD LD RFXSDW  WRWDO  GLPLQXDW  FX SRSXOD LD RFXSDW  vQ DUPDW  úL FX VDODULD LL RUJDQL]D LLORUSROLWLFHúLREúWHúWL

28) 3HQWUX D VWXGLD HYHQWXDOD LQIOXHQ

a culorii

DPEDODMXOXL DVXSUD XQXL QRX WLS GH V SXQ VH

VWXGLD]  XQ HúDQWLRQ GH PHQDMH 6H WULPLW ILHF UXL PHQDM GLQHúDQWLRQ SDWUX EXF

L GH V SXQ

GHDFHHDúLFRPSR]L LHGLQWLSXODQDOL]DWGDUDPEDODWHvQFXORULGLIHULWHURúXDOEEOHXúLYHUGH 

Pentru a testDSUHIHULQ DPHQDMHORUROXQ

PDLWkU]LXILUPDSURGXF WRDUHRIHU JUDWXLWEXF

LFX

FXORDUHD GRULW  D DPEDODMXOXL ÌQ XUPD VLVWHPDWL] ULL GDWHORU REVHUYDWH V D RE LQXW XUP WRDUHD

-

serie: Culoarea Nr. menaje

5RúX

Alb 74

51

Bleu 30

Verde 45

TOTAL 200

Pentru o probabilitate 0,1%: a)

VH UHVSLQJH LSRWH]D SRWULYLW F UHLD FXORDUHD DPEDODMXOXL QX DU LQIOXHQ D YROXPXO YkQ] ULORUGHRDUHFH

b)

χ 2calc. = 20,04 > χ 20,1%;3 = 16,3 ;

VHDFFHSW LSRWH]DSRWULYLWF UHLDFXORDUHDDPEDODMXOXLQXDULQIOXHQ DYROXPXOYkQ] ULORU

2 2 deoarece χ calc . = 20,04 > χ 0,1%; 3 = 16,3 ; 2 2 c) nu se poate lua nici o decizie deoarece χ calc . = χ 0,1%;3 = 16,3 ; d) VH UHVSLQJH LSRWH]D DEVHQ HL LQIOXHQ HL FXORULL DPEDODMXOXL DVXSUD YROXPXOXL YkQ] 2 2 GLQWLSXOGHV SXQDQDOL]DWGHRDUHFH χ calc. = 10 < χ 0,1%;3 = 16,3 ; e) nu se poate lua o decizie deoarece testul χ2 nu poate fi utilizat.

29) 1XP

ULORU

UXO PD[LP GH HúDQWLRDQH GH DFHODúL YROXP Q FDUH SRW IL IRUPDWH SULQ DFHODúL SURFHGHX

DOHDWRUvQYDULDQW QHUHSHWDW I U UHYHQLUH GLQWU RSRSXOD LHVWDWLVWLF GHYROXP1HVWH

-

a) nN; b) Nn;

c) ANn ; n d) C N ; e) n!.

30) 6H QRWHD]

 HVWLPDWRUXO SDUDPHWUXOXL

[]

[]

θ cu θ  LDU PHGLD úL GLVSHUVLD HVWLPDWRUXOXL FX M θ

respectiv cu D θ . Estimatorul θ este abVROXWFRUHFWGDF

(

a) este nedeplasat M (θ ) = θ

)

úLFRQYHUJHQW

 úL



D(θ ) → 0 GDF  n → N );

b) M (θ ) → θ úL D(θ ) → 0 când n → N ; c) D θ este minim , dar nenul SHQWUXXQYROXPIL[DWDOHúDQWLRQXOXL

[]

n→ N; ( ) D(θ ) → 0 e) ( M (θ ) = θ ) , indiferent de valoarea dispersiei estimatorului (pentru orice D[θ ] ). d) M (θ ) − θ ≠ 0

úL

GDF 

31) Statisticianul enJOH] <XOH   SUHFL]HD]

 FRQGL LLOH SH FDUH WUHEXLH V  OH vQGHSOLQHDVF 

LQGLFDWRULLVLQWHWLFLDLUHSDUWL LLORUVWDWLVWLFHúLDQXPH

1) 2) 3) 4) 5) 6)

V ILHGHILQLWvQPRGRELHFWLY V GHSLQG GHWRDWHREVHUYD LLOHGLQVHULH V DLE RVHPQLILFD LHFRQFUHW  V ILHVLPS

lu de calculat;

V ILHSX LQVHQVLELOODIOXFWXD LLOHGHVHOHF LH V VHSUHWH]HXúRUODFDOFXOHDOJHEULFH

$FHVWHFRQGL LLvQWRWDOLWDWH

a) sunt respectate de medie; b) sunt respectate de dispersie; c) VXQWUHVSHFWDWHGHFRYDULDQ  d) sunt respectate de valoarea PRGDO  e) QXVXQWUHVSHFWDWHGHQLFLXQLQGLFDWRUDOWHQGLQ HLFHQWUDOHVDXDOYDULD LHL 32) Media ( x  D XQXL HúDQWLRQ GH PDUH YROXP  n  SRDWH IL FRQVLGHUDW QRUPDO GHPHGLH

x 0 úLDEDWHUHPHGLHS

WUDWLF HURDUHPHGLH 

 F  XUPHD]  R GLVWULEX LH

σ , în cazul unui sondaj simplu n

cu revenire. Pentru o probabilitate 1-α intervalul de estimare (sau de încredere) a parametrului x 0 este:

x − x 0 ≤ zα

UHODWLY

σ n

Pentru ca preciziD HVWLPD LHL V  ILH PDL PLF GLQ x 0 YROXPXOHúDQWLRQXOXLHVWH

z σ a) n ≤ α ⋅ 2

2

k 2 x 20

;

 VDX HJDO  FX N SUHFL]LH IL[DW  vQ YDORDUH

b) n ≥ c) n =

zα2 2

⋅ (CV )

2

XQGH&9

FRHILFLHQWXOGHYDULD LH

k σ2

;

k 2 x0

d) n =

zα2 k 2 σ 2

;

x0 e)

PDLPDUHGHGHXQLW

L

33) 8Q FRQWURORU GH FDOLWDWH úWLH F YL]LELOHGHVXSUDID V J VHDVF H[DFW

a) b) c) d) e)

 SUREDELOLWDWHD FD SH XQ QRX DXWRPRELO V  J VHDVF  GHIHFWH

]JkULHWXUL HVWHGH

‰. Probabilitatea ca dintr-un lot de 2500 de automobile 2 automobile cu defecte vizibile este:

7,5%; 3,66%; 92,5%; 7,32%; 15%.

34) Într-un proces de verificare a ipotezelor statistice nivelul de încredere reprezint probabilitatea: a) b) c) d) e)

α; 1-α; β; 1-β; α+β.

35) &RQWXO³3URGXF LH´DOVHFWRUXOXLILUPHVHSUH]LQW 1.

Cheltuieli

pentru

produse

LQWHUPHGLDUHúLGHLQYHVWL LLGLQLPSRUW

2. Amortizarea capitalului fix 3. Impozite indirecte brute 6XEYHQ LLGHH[SORDWDUH

5. Salarii 'REkQ]LúLUHQWH

VLQWHWL

c astfel:

ÌQFDV ULGLQYkQ]DUHDGHEXQXULF WUHDOWHVHFWRDUH

-YkQ] -YkQ] -YkQ]

ULGHEXQXULGHFRQVXPF WUHPHQDMH ULGHSURGXF LHLQWHUPHGLDU F WUHVHFWRUXOSXEOLF ULSULQH[SR

rt

,QYHVWL LLEUXWHLQFOXVLYLPSRUWXULOH

-LQYHVWL LLEUXWHvQEXQXULGHFDSLWDO -LQYHVWL LLEUXWHvQVWRFXUL

7. Profitul din DFWLYLWDWHDGHSURGXF LH 3HED]DHOHPHQWHORUDFHVWXLFRQWVHSRWFDOFXODPDLPXO LLQGLFDWRUL&DUHUHOD LHGLQFHOHSUH]HQWDWH PDLMRVHVWHIDOV 

a)

9DORDUHDDG XJDW ODSUH XOSLH HL

9DORDUHDDG XJDW QHW ODSUH XOIDFWRULORU 

impozitele indirecte nete (3-4) + amortizarea capitalului fix (2); b)

9DORDUHD DG XJDW  EUXW  OD SUH XO IDFWRULORU

 YDORDUHD DG XJDW  OD SUH XO IDFWRULORU

(5+6+7) + amortizarea (2); c) 9DORDUHDDG XJDW QHW ODSUH XOSLH HL 9DORDUHDDG d) Soldul contului: (1+2+3+4+5+6+7)-(8+9)=0; e) Soldul contului: (1+2+3+4+5+6+7)-(8+9)≠ 0.

XJDW EUXW ODSUH XOSLH HL

- amortizarea;

36) 6

 VH SUHFL]H]H FDUH GLQ VHULLOH GH UHSDUWL LH FDUDFWHUL]DWH SULQ XUP WRDUHOH VHWXUL GH YDORUL

SUH]LQW RDVLPHWULHSR]LWLY 

a) b) c) d) e)

x = 31,2 ; Me=31,2; Mo=31,2; x = 2850 ; Me=3150; Mo=3300; x = 151,25 ; Me=138,75; Mo=112,58; x = 180 0H 0R úL x = 0 ; Me=0; Mo=0.

 ,QGLFLLDQXDOLDLSUH XULORUGHFRQVXPODP UIX

Anul Indice (an precedent = 100)

1991 286,2

rile alimentare în perioada 1991-1994 au fost: 1992 336,6

1993 348,9

1994 236,2

Sursa: Anuarul Statistic al României, 1995, pag. 411 ,QGLFHOHPHGLXDOSUH XULORUGHFRQVXPODP UIXULOHDOLPHQWDUHvQDFHDVW SHULRDG DIRVW

a) 1,985; b) 298,50%; c) 301,975; d) 261,2%; e) 2,612.   'DF  vQWU R VHULH GH UHSDUWL LH UHOD LD RELHFWLY  GLQWUH GDWH [i  FRQGXFH OD GHFL]LD FD WHQGLQ D

-

FHQWUDO V RFDUDFWHUL] PFXPHGLDJHRPHWULF 

-

FHQWUDO HVWHDFHDYDORDUH

x g ) atXQFLDEDWHUHDPHGLHS

WUDWLF ID

GHWHQGLQ D

σ x pentru care avem: g

2

a) log σ x = g

x  1   log i  ; ∑ n i  xg 

(

)

b) σ x = g

2 1 xi − x g ; ∑ n i

c) σ x = g

1  1 1  −  ∑ n i  xi x g 

d) σ x = g

1 ∑ xi − x g ; n i

e) σ x = g

1  xi  ∑  . n i  x g 

(

2

;

)

 &LUFXLWXOHFRQRPLFUHIOHFW vQHVHQ

WUDQ]DF LLOHGLQWUHVXELHFWHOHHFRQRPLFHÌQFDGUXODFHVWRUD

XQORFLPSRUWDQWvORFXS WUDQ]DF LLOHGHSLD

$FHVWHDVXQW

a) transferuri curente (impozite, pensii, ajutoare sociale, etc.); E VXEYHQ LL

c) transferuri de patrimoniu; d) transferuri unilaterale; e) transferuri bilaterale.

 *UDILFHOHVWDWLVWLFHvQFRRUGRQDWHSRODUHVHXWLOL]HD] vQPRGFXUHQWSHQWUXYL]XDOL]DUHD D RULF UHLVHULLGHGDWHVWDWLVWLFH E VHULLORUGHUHSDUWL LH

c) eYROX LHLWUHQGXOXLGLQHYROX LDXQXLIHQRPHQ G HYROX LHLXQXLIHQRPHQDIHFWDWGHRVFLOD LLVH]RQLHUH H WHQGLQ HLOHJ WXULLGLQWUHYDULDELOHúLDOHJHUHDPRGHOXOXLGHUHJUHVLH

TESTUL 5  5DWDúRPDMXOXLVHFDOFXOHD] FXUHOD LD

ocupati ; ocupati + neocupati neocupati b) ; forta de munca neocupati c) ; ocupati neocupati d) ; populatia in varsta mai mare de 15 ani

a)

H QLFLXQDGLQWUHUHOD LLOHSUHFHGHQWH  6H FXQRVFXUP WRDUHOH GDWHSULYLQGQXP UXOGHIDFWXULvQWRFPLWHGH6&$QRQLPXV 65/vQ

luna noiembrie 1997: Data Nr. facturi 1 6 2 10 3 12 4 10 5 8 6 9 7 10 8 11 9 12 10 9

Data 11 12 13 14 15 16 17 18 19 20

Nr. facturi 10 14 6 18 13 9 14 12 17 12

I Grupe de zileGXS  nr. de facturi 0-5 6 - 11 11 - 15 15 - 20

Data 21 22 23 24 25 26 27 28 29 30

II Nr. zile

Grupe de ]LOHGXS

nr. de facturi 0 -5 6 - 10 11 - 15 16 - 20

1 13 13 3

A. QXP

III Nr. zile

Intervale de timp

Nr. facturi

1 16 10 3

0-6 7 - 14 15 - 22 23 - 30

55 90 103 82



IV

Intervale ale UXOXL

zilnic de facturi (0-5] ( 5 - 10 ] (10 - 15 ] (15 – 20]

B. Nr. de zile 1 13 13 3

Nr. facturi 14 12 11 10 8 4 12 9 12 16

V

Intervale ale QXP

UXOXL

de facturi [0-5) [ 5 - 10 ) [10 - 15 ) [15 – 20)

3RSXOD LDVWDWLVWLF VWXGLDW HVWHVWUXFWXUDW úLSUH]HQWDW vQ

Nr. de zile 1 9 17 3

a) Tabelul I; b) Tabelul II; c) Tabelul III; d) Tabelul IV; e) Tabelul V. 3) Cadranul II al Tabelului Input- Output cuprinde: D YDORDUHDDG XJDW EUXW  E SURGXF LDILQDO  F SURGXF LDLQWHUPHGLDU  G FRHILFLHQ LLF

heltuielilor totale;

H FRHILFLHQ LLFKHOWXLHOLORUGLUHFWH

4) 3HQWUXGHVDODULD LDLXQHLVRFLHW

LFRPHUFLDOHIRQGXOGHVDODUL]DUHDIRVWvQWU ROXQ GH

-

PLOLRDQH OHL ùWLLQG F  FHL PDL PXO L GLQWUH VDODULD L DX DYXW XQ VDODULX GH  PLL OHL L

ar

FRHILFLHQWXOGHDVLPHWULHDOUHSDUWL LHLGXS VDODULXDIRVWGH FRHILFLHQWXOGHYDULD LHDIRVW

-

a) 24,5%; b) 200%; c) -25,52%; d) 37,5%; e) 26,67%.

5) 'LVWULEX LDXQXLORWGHDXWRPRELOHGXS

FRQVXPXOGHFDUEXUDQWODNPSDUFXUúLHVWH

IQWHUYDOHGHYDULD LHDFRQVXPXOXLO 6,2 - 6,6 6,6 - 7,0 7,0 - 7,4 7,4 - 7,8 7,8 - 8,2 8,2 - 8,6 8,6 - 9,0 9,0 - 9,4 9,4 - 9,8 Total Utilizând

testul

χ2

SHQWUX

YHULILFDUHD

Nr. automobile 4 12 44 90 107 86 36 15 6 400 FDUDFWHUXOXL

UHSDUWL LHL

H

mpirice,

pentru

χ α2 = 0,05;l = 6 = 12 ,5916 se poate afirma: 2 a) χ 2calc > χ tab ;

b) QX VH DFFHSW FRQFRUGDQ

 LSRWH]D FRQIRUP F UHLD vQWUH GLVWULEX LD HPSLULF  úL FHD WHRUHWLF  H[LVW 



c) χ 2calc = 3,44 ; d) χ 2calc = 8,12 ; e) χ 2calc = 12 ,5916.

6) 2 FRPSDQLH FDUH SURGXFH XQ QRX WLS GH vQJU

ú PkQW DJULFRO HVWH LQWHUHVDW  vQ VWXGLHUHD UHOD LHL

GLQWUHSURGXF LDGHURúLL< úLFDQWLWDWHDGHvQJU ú PkQWDSOLFDW; 2VXSUDID RSWSDUFHOHGHP ULPLHJDOHSHFDUHVXQWDSOLFDWHFDQWLW URúLLNJ úLFDQWLW

HVWHGLYL]DW vQ

LGLIHULWHGHvQJU ú PkQW3URGXF LLOHGH

LOHGHvQJU ú PkQWDSOLFDWNJ vQUHJLVWUDWHSHQWUXILHFDUHSDUFHO VXQW

xi yi

1 25

1,5 31

2 27

2,5 28

3 36

3,5 35

4 32

4,5 34

(FXD LDGHUHJUHVLHSHWQUXGHVFULHUHDGHSHQGHQ HLGLQWUHFHOHGRX YDULDELOHHVWH

a) b) c) d) e)

y = 24,45 − 2,38 x ; y = 2,38 + 24,45x ; y = 24,45 + 2,38 x ; y = 32 + 2,01x ; y = 32 − 2,01x ;

 'LPLQXHD] DYX LDQD LRQDO 

a) rezervele de devize; b) rezervele de aur; F UH]HUYHOHGHPRQHG QD LRQDO GH LQXWHGHDOWH G EXQXULOHQD LRQDOHDIODWHSHWHULWRULXODOWRU H FUHDQ HOHDVXSUDDOWRU

UL

8) Într-RUHSDUWL LHGHIUHFYHQ HIUHFYHQ DUHODWLY

a)

QXP UXOXQLW

E SRQGHUHDXQLW

UL

UL

FXPXODW FUHVF WRUDJUXSHL

iDUDW



LORUVWDWLVWLFHFDUHDXYDORULOHFDUDFWHULVWLFLLPDLPLFLVDXHJDOHFX LORUVWDWLVWLFHGLQJUXSD vQWRWDOXOFROHFWLYLW

i

LLVWXGLDWH

xi;

c) QXP UXOXQLW LORUVWDWLVWLFHFDUHDXYDORULOHFDUDFWHULVWLFLLPDLPDULVDXFHOSX LQHJDle cu xi; d) ponderea unit LORU VWDWLVWLFH FDUH DX QLYHOXO FDUDFWHULVWLFLL PDL PLF VDX HJDO FX xi, în WRWDOXOFROHFWLYLW

e)

SRQGHUHD XQLW

LLVWXGLDWH

LORU VWDWLVWLFH FDUH DX QLYHOXO FDUDFWHULVWLFLL PDL PDUH VDX HJDO FX

WRWDOXOFROHFWLYLW

LLVWXGLDWH

xi, în

.

9) 8Q DQDOLVW ILQDQFLDU HVWH LQWHUHVDW vQ D GHWHUPLQD VDODULXO PHGLX DFRUGDW DQJDMD LORU ILUPHL (O FXOHJH GDWH SULYLQG VDODULXO PHGLX SH ILHFDUH GLQ FHOH SDWUX ILOLDOH DOH ILUPHL úL IRQGXO GH

salarizare: Filiala 1 2 3 4

Salariul mediu (mii lei) 540 620 480 700

6DODULXOPHGLXSHvQWUHDJDILUP HVWH

a) 573,168 mii lei; b) 585,5 mii lei; c) 825,325 mii lei; d) 460,5 mii lei; e) 632,375 mii lei.

Fondul de salarizare (mil. lei) 45,90 33,48 16,80 19,60

 5HSDUWL LDYHQLWXULORUHVWHHYLGHQ LDW vQFRQWXO

D SURGXF LH E ILQDQ DUH

c) modificarea patrimoniului; d) redistribuirea venitului; e) contul sintetic de bunuri.

11) 8QIDEULFDQWGHDXWRPRELOHGHWHUPLQ

F GLQUH]HUYRDUHOHGHEHQ]LQ PRQWDWHSHPRGHOXO

 VXQW GHIHFWH 'DF   PDúLQL VRVHVF SHQWUX UHYL]LH SUREDELOLWDWHD FD  GLQ  PDúLQL V 

necesite înlocuirea rezervorului este: a) 22,69%; b) 9,72%; c) 12%; d) 30%; e) 70%.  $QDOL]D LXUP WRDUHOHPRGDOLW

LGHFRQWURO

1) controlul de volum; 2) controlul cantitativ-numeric; 3) controlul financiar-contabil; 4) FRQWUROXO ORJLF   FRQWUROXO &XU LL GH FRQWXUL   WHVWH GH YHULILFDUH D VHPQLILFD LHL LQGLFDWRULORU FDOFXOD L ÌQ WRDWH HWDSHOH FHUFHW ULL VWDWLVWLFH HVWH QHFHVDU  YHULILFDUHD DXWHQWLFLW

LL GDWHORU úL

eliminareaHURULORUGHREVHUYDUHFDOFXOúLHVWLPDUHÌQDFHVWVHQVHVWHQHFHVDU D úL E úL F úL G úL H úL

 )DFSDUWHGLQIRU DGHPXQF 

a) persoanele casnice; b) pensionarii; F úRPHULL G SHUVRDQHOHI U XQORFGHPXQF FHUHQXQ

V PDLFDXWHORFGHPXQF 

H QLFLXQDGLQFDWHJRULLOHPHQ LRQDWH

14) 3HQWUX GLVWULEX LD XQHL YDULDELOH DOHDWRDUH ; VH FXQRDúWH F



P(x i ≤ 151,33) = 0,5 , valoarea

quartilei întâi este 105,86 iarYDORDUHDTXDUWLOHLWUHLHVWH6HULDGHGLVWULEX LH D HVWHSURIXQGDVLPHWULF VSUHYDORULOHPLFLDOHYDULDELOHL E DUHRDVLPHWULHPRGHUDW SR]LWLY  F DUHRDVLPHWULHPRGHUDW QHJDWLY 

d) nu se poate preciza felul asimetriei; e) este profXQGDVLPHWULF VSUHYDORULOHPDULDOHYDULDELOHL

15) 8QDQDOLVWGHPDUNHWLQJXUP

UHúWHvQOXQLHIHFWXOUHFODPHORUDVXSUDYHQLWXULORUGLQYkQ] UL(O

vQUHJLVWUHD]  FKHOWXLHOLOH FX UHFODPD ;  PLOLRDQH OHL  úL YHQLWXULOH GLQ YkQ] UL <  VXWH

milioane lei)ÌQXUPDSUHOXFU

∑ xi = 15;∑ yi = 10;∑ i

i

ULLGDWHORURE LQH

∑ xi yi = 37; (i = 1,5)

x i2 = 55;

i

 ÌQ LSRWH]D XQHL GHSHQGHQ H  OLQLDUH

i

HFXD LDGUHSWHLGHUHJUHVLHHVWH

a) b) c) d) e)

y = 0,7 − 0,1x ; y = −0,1 + 0,7 x ; y = 2 − 0,7 x ; y = 3,7 + 5,5x ; y = 0,7 x .

 $QDOL]D LXUP WRDUHOHQR LXQL   DXWRQRPLH   FRQILGHQ LDOLWDWH   WUDQVSDUHQ GHRQWRORJLH SURIHVLRQDO    LQGHSHQGHQ

   VSHFLDOL]DUH   SURSRU LRQDOLWDWH  

 SROLWLF    HODERUDUHD GHFL]LL

lor; 9) argumentarea

DF LXQLORUGXS GHFODQúDUHDORU SUHOXFUDUHDGDWHORU REVHUYDUH $FWLYLWDWHDVWDWLVWLFLLSXEOLFHWUHEXLHV VHGHVI úRDUHUHVSHFWkQGXUP WRDUHOHSULQFLSLL D úL E úL

c) 3, 4, 5, 6,úL G úL H úL  5HFHQV PkQWXOFDPHWRG GHREVHUYDUHVWDWLVWLF 

a)

QXSUHVXSXQHFXOHJHUHDGDWHORUGHODWRDWHXQLW

LOHSRSXOD LHLVWDWLVWLFHELQHGHOLPLWDW 

b) are exclusiv un caracter demografic; F VHvQFDGUHD] vQVIHUDREVHUY ULORUFXFDUDFWHUSHUPDQHQW G VHRUJDQL]HD] FXRDQXPLW SHULRGLFLWDWH

e)

VHRUJDQL]HD] RULGHFkWHRUL6WDWLVWLFD218GHFODQúHD] UHFHQV PLQWHvQ

18) ÌQPRGVLQWHWLFRIHUWDQD LRQDO

ULOHPHPEUH

GHEXQXULúLVHUYLFLLHVWHH[SULPDW GH

a) VN; b) PNNpp; c) PNBpp; d) PNBpf; e) PIBpf.  )LH;úL<GRLYHFWRULFXQFRPSRQHQWH

X = (x i ) úL Y = (yi ) cu i = 1, n . ’

’

'LVWDQ DOXL0LQNRYVNLHVWHGDW GHUHOD LD

1

'DF S

n p p d ( X , Y ) = ∑ xi − y i  cu p ∈ N * . i =1 

VHRE LQHGLVWDQ DDEVROXW LDUGDF S

VHRE LQHGLVWDQ DHXFOLGLDQ 

3ULQ H[WHQVLH V  FRQVLGHU P R SRSXOD LH VWDWLVWLF  FX Q XQLW

x1, x2, ... , xr0DWULFHDGLVWDQ HORUGLQWUHXQLW

(

)

L OD FDUH VH REVHUY  YDULDELOHOH

LFDOFXODWHSHQWUXILHFDUHSHUHFKH

de forma d ij = d x i , x j : D QXSUH]LQW LQWHUHVSHQWUXDQDOL]DVWDWLVWLF 

xi, yi), cu elemente

b) SUH]LQW

LQWHUHVSHQWUXDQDOL]DYDULD LHLúLDGHRVHELULORUGLVLPLODULW

LORU GLQWUHXQLW

L

c QXSUH]LQW LQWHUHVSHQWUXVWUXFWXUDGDWHORUFXOHVH d) are toate elementele nenule;

e)

DUHFRPSRQHQWHQXOHSHDPEHOHGLDJRQDOHúLHOHPHQWHOHVLPHWULFHID

20) 2YDULDELO

DOHDWRDUH;XUPHD] RUHSDUWL LHQRUPDO GHSDUDPHWULL

GHGLDJRQDOH

x úL σ 2 GDF

DUHGHQVLWDWHD

GHUHSDUWL LH

1

a)

σ

2

2  1 exp − x− x ; 2 2π  2σ 

(

)

b)

2  1 1 exp − x− x ; σ  2σ 2 

c)

2  1 exp − x− x ; σ 2π  2σ 2 

d)

2  1 exp − x+ x ; 2 σ 2π  2σ 

e)

2  1 exp  2 x − x  . σ 2π  2σ 

(

)

(

1

(

1

(

1

21) 6H FXQRDúWH IDSWXO F LQGLYLGXDOH ID

∑ (xi − x) = 0 ;

i =1

n  1

∑  x

i =1

i

n

c)

−

1  = 0; xh 

∑  xi2 − x p  = 0 ; 2

i =1 n

d)

x

∏ x gi

= 1;

i =1

e) x = x h = x p = x g . unde: x

)

 PHGLD H[SULP  WHQGLQ D FHQWUDO  LDU SH DQVDPEOX DEDWHULOH YDORULORU

n

b)

)

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DILUPD LDHIHFWXDW 

a)

)

PHGLDDULWPHWLF

xh

PHGLDDUPRQLF

xp

PHGLDS WUDWLF

xg

PHGLDJHRPHWULF 

22) Trecerea de la venituOQD LRQDOODYHQLWXOGLVSRQLELOVHUHDOL]HD]

vQFDGUXOFRQWXOXL

a) repartizarea veniturilor; b) modificarea patrimoniului; F ILQDQ DUH

d) redistribuirea veniturilor; H QXVHUHDOL]HD] vQFDGUXOXQXLDQXPLWFRQWPDFURHFRQRPLF

23) Cifra de afaceriD XQHL VRFLHW

LFRPHUFLDOH DFUHVFXWvQSHULRDGDLDQ

GH OD R OXQ  OD DOWD ÌQ SURJUDPXO VRFLHW

- dec. 1996 cu 10%

LL FRPHUFLDOH HVWH SUHY ]XW FD FLIUD GH DIDFHUL vQ

perioada ian. 1990 - GHF  V  vQUHJLVWUH]H XQ LQGLFH PHGLX DQXDO GH  3HQWru perioada ian. 1996 - dec. 1998 indicele mediu anual care trebuie realizat este: ,  79 log 1,3 − 45 log 11 a) anti log ;   24 ,   log 1,3 − log 11 b) anti log ;   2 c) 120%; d) 95%; e) 118,1%.

24) 3HQWUX DSUHFLHUHD P

VXULL vQ FDUH XQ IDFWRU VHPQLILFDWLY GH LQIOXHQ

 GHWHUPLQ  R YDULDELO 

GHSHQGHQW VHFDOFXOHD] DWkWFRHILFLHQWXOGHFRUHOD LHFkWúLUDSRUWXOGHFRUHOD LH9DORULOHFHORU GRLLQGLFDWRULILLQGLGHQWLFHDWXQFLOHJ WXUDVWDWLVWLF GLQWUHFHOHGRX YDULDELOHHVWH D OLQLDU  E KLSHUEROLF  F SDUDEROLF 

d) logiVWLF



H H[SRQHQ LDO 

25) 8QúRPHUFDUHFDXW

XQORFGHPXQF vQWU RDQXPLW LQGXVWULHFXOHJHLQIRUPD LLGHVSUHVDODULXO

-

RIHULW GH ILUPHOH GLQ DFHDVW  LQGXVWULH 3UHVXSXQHP F  GLVWULEX LD VDODULXOXL RIHULW DQJDMD LORU GH FDOLILFDUH VLPLODU  SRDWH IL DSUR[LPDW  FX R GLVWULEX LH QRUPDO  GH PHGLH  PLL OHL úL DEDWHUH PHGLH S WUDWLF  GH  PLL OHL ÌQ SOXV SUHVXSXQHP F  PXQFLWRUXOXL L VH RIHU   PLL OHL GH F WUH SULPD ILUP  FRQWDFWDW  3URSRU LD RIHUWHORU VDODULDOH FDUH DU SXWHD V  VH VLWXH]H SHVWH DFHVW

nivel este: a) 4,01%; b) 8,02%; c) 54,01%; d) 91,98%; e) 45,99%.

26) 6H FXQRDúWH IDSWXO F

 vQWU R UDPXU  GH DFWLYLWDWH YDULDELOD VDODULXO PHGLX EUXW <  HVWH

-

GHSHQGHQW  SULQWUHDOWHOH GHJUDGXO PHGLX GH vQGHSOLQLUH DO QRUPHORU ;1  úLJUDGXO PHGLX vQ]HVWUDUH WHKQLF  D PXQFLL ;2  &RQWULEX LD FHORU GRL IDFWRUL ;1

PHGLXEUXW< HVWHHYDOXDW SULQ

a) R y2/ x ,x = ry2/ x + ry2/ x ; 1 2 1 2 b) R y / x1,x2 =

ry2/ x + ry2/ x − 2 ry / x ry / x 2 rx1x2 1 2 1 1 − rx2 x

1 2

;

de

úL ;2 OD YDULD LD VDODULXOXL

c) R y / x1,x2 = ry2/ x + ry2/ x − 2ry / x ry / x 2 rx1x2 ; 1 2 1 d) rx1x2 = 0 ; ry2/ x + ry2/ x 1 2

e) R y / x1,x2 =

1 − rx2 x

.

1 2

 &RQVLGHU PGDWHOH 9DORDUHDDG

Ramura 1 2

XJDW

EUXW

POGOHL

(ILFLHQ DPLMORDFHORUIL[H

3000 1000

0,5 0,8

(ILFLHQ DPLMORDFHORUIL[HSHWRWDODIRVW

a) 0,5751; b) 0,6500; c) 0,5517; G QXSRDWHILFDOFXODW 

e) 1,3.

28) ÌQ HYROX LD VD vQGHOXQJDW

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-a dezvoltat continuu atât sub aspectul obiectului de

VWXGLX GDU PDL DOHV DO SHUIHF LRQ ULL úL GLYHUVLILF ULL PHWRGHORU GH DERUGDUH DOH RELHFWXOXL ÌQ WRDWHPRPHQWHOHGH]YROW ULLVWDWLVWLFDVHRFXS GHDFHO

e fenomene:

D FDUHVHSURGXFODRDQXPLW XQLWDWHGHREVHUYDUH

b) care se produc în mod identic; c) exclusiv tehnice; d) care se produc într-XQ QXP UHJXODULW

U PDUH GH FD]XUL SUH]LQW  vQ SURGXFHUHD ORU DQXPLWH

LúLFDUHSRWILGHQXPLWHIHQRPHQHGHPDV

H FDUHDXODRULJLQHXQVLQJXUIDFWRUGHLQIOXHQ

;



29) 8QHOHPHQWLPSRUWDQWDOXQXLSURJUDPGHREVHUYDUHHVWHWLPSXOREVHUY

ULL$FHVWD

D HVWHWLPSXOODFDUHVHUHIHU GDWHOHVDXWLPSXOvQUHJLVWU ULLGDWHORU

b) nu este altceva decât timpul la care se reIHU

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PRPHQWSHQWUXvQUHJLVWU ULOHVWDWLFH VDXRSHULRDG SHQWUXvQUHJLVWU ULOHGLQDPLFH  F QXHVWHDOWFHYDGHFkWSHULRDGDvQFDUHVHvQUHJLVWUHD] GDWHOHVWDWLVWLFH

d) HVWH SULYLW úL SULQ XUPDUH SUHFL]DW FD WLPS ODFDUH VH UHIHU

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WLPSvQFDUHVHUHDOL]HD] vQUHJLVWUDUHDGDWHORU

e) nu este altceva decât data la care operatorii statistici trebuie s prezinte datele culese.  'LVSHUVLDFDOFXODW SULPPHWRGDPRPHQWHORUHVWH

a) momeQWXOLQL LDOGHRUGLQXOGRL

b) PRPHQWXOLQL LDOGHRUGLQXOSDWUXvPS

U LWODPRPHQWXOLQL LDOGHRUGLQXOGRLODS WUDW

F PRPHQWXOFHQWUDWGHRUGLQXOGRLODS WUDW

d) PRPHQWXOLQL LDOGHRUGLQXOGRLPLQXVPRPHQWXOLQL LDOGHRUGLQXOvQWkLODS WUDW e) momentulFHQWUDWGHRUGLQXOGRLPLQXVPRPHQWXOLQL LDOGHRUGLQXOXQXODS WUDW 31) Scala de interval: D DUHWRDWHFDUDFWHULVWLFLOHVFDOHORURUGLQDOHúLGHUDSRUW

b) DUH WRDWH FDUDFWHULVWLFLOH VFDOHL RUGLQDOH úL vQ SOXV GLVWDQ D VDX GLIHUHQ D GLQWUH GRX numereDOHVFDOHLDUHVHPQLILFD LHFRQFUHW





c)

HVWH R VFDO  QXPHULF  úL vQ SOXV UDSRUWXO GLQWUH GRX  SXQFWH DOH VFDOHL HVWH LQGHSHQGHQW GHXQLWDWHDGHP VXU 

G SUH]LQW PXOWHGLQFDUDFWHULVWLFLOHVFDOHLRUGLQDOH H PDLHVWHQXPLW úLVFDO GHUDSRUWVDXVFDO GLVFUHW 

32) Într-R UHSDUWL LH QRUPDO

 YDORDUHD ID

 GH FDUH  GLQ YDORULOH LQGLYLGXDOH VXQW PDL PLFL LDU

75% din valorile individuale sunt mai mari este: a) cuartila a doua; b) cuartila a treia; c) cuartila întâi; G YDORDUHDPRGDO 

e) valoareaPHGLDQ



33) 2 DJHQ LH GH vQFKLULDW DXWRPRELOH KRW

U úWH V

timp de un an. Managerul firmei presupune c

-VL YkQG

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GLVWDQ DSDUFXUV GHPDúLQLLQIOXHQ HD] FRVWXOGH

vQWUH LQHUHDODXWRYHKLFXOHORUúLGHFLSUH XOGHYkQ]DU

e al acestora. Pentru a verifica presupunerea

VD VH vQUHJLVWUHD]  SHQWUX  GH PDúLQL GLVWDQ D SDUFXUV  vQ XOWLPXO DQ PLL NP  úL FRVWXO GH vQWUH LQHUHVXWHPLLOHL 6HDOF WXLHVFDVWIHOJUXSHGXS GLVWDQ DSDUFXUV VXEPLLNP

60 mii km, 60 -  PLL NP úL  VDX SHVWH  PLL NP ÌQ XUPD VLVWHPDWL]

-

ULL GDWHORU VH RE LQ

XUP WRDUHOHLQIRUPD LL *UXSHGXS SDUFXUV

GLVWDQ D

&RVWXOvQWUH LQHULLVXWHPLLOHL

Total

PLLNP

5-7 16 10%

sub 40 40 - 60

7-9 32 25%

ÌQ JUXSD D WUHLD GXS  GLVWDQ D SDUFXUV  

9 - 11 12 35%

11 - 13 30%

60 100%

-80 mii km) s-au înregistrat date pentru 40 de

PDúLQLFRVWXOPHGLXGHvQWUH LQHUHILLQGOHLFXXQ FRHILFLHQWGH YDULD LHGHLDU vQ JUXSD D SDWUD  úL SHVWH  PLL NP  V

-au îQFDGUDW  GLQ PDúLQL FKHOWXLHOLOH WRWDOH DX IRVW

OHLLDUDEDWHUHDPHGLHS WUDWLF PLLOHL 'LVWDQ DSDUFXUV LQIOXHQ HD] YDULD LDFKHOWXLHOLORUGHvQWUH LQHUHvQSURSRU LHGH

a) 51,04%; b) 71,44%; c) 48,96%; d) 69,97%; e) 28,56%.

34) ÌQ XWLOL]DUHD PHWRGHL WDEHOXOXL GH FRUHOD LH SHQWUX DQDOL]D OHJ

WXULORU GLQWUH IHQRPHQH GDF 

IUHFYHQ HOHVXQWDSUR[LPDWLYHJDOUHSDUWL]DWHvQLQWHULRUXOWDEHOXOXLDWXQFL D OHJ WXUDHVWHQHOLQLDU  E OHJ WXUDHVWHOLQLDU GLUHFW  F OHJ WXUDHVWHLQYHUV  G OHJ WXUDHVWHGLUHFW  H OHJ WXUDHVWHVODE VDXQXH[LVW OHJ WXU

35) Într-R VHULH VWDWLVWLF

între variabile.

 vQWUH SULQFLSDOHOH WLSXUL GH PHGLL PHGLD DULWPHWLF  PHGLD DUPRQLF 

PHGLDS WUDWLF PHGLDJHRPHWULF H[LVW XUP WRDUHDUHOD

a) x h ≤ x g ≤ x ≤ x p ; b) x g ≤ x h ≤ x ≤ x p ;

ie:

c) x h ≤ x ≤ x p ≤ x g ; d) x ≤ x h ≤ x g ≤ x p ; e) x = x h = x g = x p GDF

VHULDHVWHSHUIHFWVLPHWULF 

36) 3HQWUX R VHULH GH GLVWULEX LH GH IUHFYHQ H FX WHQGLQ ( d x ID GHDEDWHUHDWLS σ x ) este:

 GH QRUPDOLWDWH DEDWHUHD PHGLH OLQLDU 

a) d x > σ x ; b) d x = σ x ; 4 c) d x ≈ σ x ; 5 2 d) d x ≈ σ x ; 3 e) d x ≈ σ 2x . 37) VHQLWXOEUXWGLVSRQLELOODQLYHOXOHFRQRPLHLQD LRQDOHVHFDOFXOHD]



a) VN+Amortizarea; E 916ROGXOYHQLWXULORUGLQWUDQVIHUXULvQUDSRUWFXVWU LQ WDWHD

c) b) + Amortizarea; d) a) -6ROGXOYHQLWXULORUGLQWUDQVIHUXULvQUDSRUWFXVWU e) PIB - b).

38) 8QGLVWULEXLWRUGHVXFXULOLYUHD]

LQ WDWHD

FDUWRDQHGHFkWHVWLFOHúLFXQRDúWHSUREDELOLWDWHDS

 FD

R VWLFO  V  VH VSDUJ  SH GXUDWD WUDQVSRUWXOXL 'DF  VH WUDQVSRUW   GH FDUWRDQH QXP UXO FDUWRDQHORUvQFDUHVHYRUJ VLGRX

sau mai multe sticle sparte este de aproximativ:

a) 85; b) 14; c) 3960; d) 41; e) 40.  &DUHGLQREVHUY ULOHVWDWLVWLFHSUHFL]DWHPDLMRVQXDXXQFDUDFWHUSHUPDQHQW D EXJHWHOHGHIDPLOLHVDXDQFKHWHOHLQWHJUDWHvQJRVSRG ULL 

b) rapoartele statistice; c) statisticile fiscale; G vQUHJLVWU ULOHF V WRULLORUQDWDOLW H UHFHQV PLQWHOHVWDWLVWLFH

LLPRUWDOLW

LLHWF

TESTUL 6

1)

ÌQWUH3,%úL31%H[LVW QXPDLUHOD LD

a) b) c) d) e)

>; <; =;

≥; ≤ ≥.

2) Într-o serie de reparWL LH SH LQWHUYDOH IRUPDW

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LQIOXHQ DW GH

a)

OLPLWHOHLQIHULRDUHúLVXSHULRDUHDOHLQWHUYDOHORUH[WUHPH

b)

GHIUHFYHQ HOHGHDSDUL LHDOHLQWHUYDOHORUHJDOHVDXQHHJDOH

c)

GHP ULPHDHJDO VDXQHHJDO DLQWHUYDOHORUGHYDULD LH

d)

GHOLPLWDLQIHULRDU DLQWHUYDOXOXLPRGDO

e)

GHOLPLWDLQIHULRDU GHIUHFYHQ HOHLQWHUYDOXOXLPRGDOSUHPRGDOúLSRVWPRGDO

3) Într-XQ VSLWDO  GLQ SDFLHQ LL LQWHUQD L P

QkQF  UHJLP I U  VDUH $OF WXLQG JUXSXUL GH FkWH 

SDFLHQ LSUREDELOLWDWHDFDH[DFWSDFLHQ LV  LQ UHJLPI U VDUHHVWH

a) b) c) d) e) 4)

0,015625; 0,2344; 0,9375; 0,50; 0,0468.

3UHFL]D LFDUHQXHVWHSULQFLSDO IXQF LHDLQGLFDWRULORUVWDWLVWLFL

a) GHP VXUDUH b) GHDQDOL] VDXVLQWH]  c) GHYHULILFDUHDLSRWH]HORUúLVDXGHWHVWDUHDVHPQLILFD LHLSDUDPHWULORUXWLOL]D L d) de fundamentare a deciziilor; e) de estimare. 5)

3URGXVXO JOREDO EUXW FUHúWH vQWU R SHULRDG  FX  LDU SRQGHUHD FRQVXPXOXL LQWHUPHGLDU vQ

produsul global brut scade de la 64% la 60%. Produsul intern brut: a) FUHúWHFX b) scade cu 28,8%; c) FUHúWHFX d) FUHúWHFX e) FUHúWHFX

6)

ÌQWHVWDUHDLSRWH]HLVWDWLVWLFHSULYLWRDUHODSDUDPHWUXO³PHGLDSRSXOD LHL´

H0 : m = m0 Ha : m < m0

FkQGGDWHOHSURYLQGHODXQHúDQWLRQGHYROXPUHGXVUHJLXQHDFULWLF HVWHGDW GH

a) z < − zα ; b) z < − zα / 2 ; c) t < − tα , n ; d) t < − tα / 2, n ; e) t < − tα , n − 1 . 7)

&DUHGLQXUP WRDUHOHDILUPD LLSULYLQGPHGLDDULWPHWLF HVWHDGHY UDW 

a)

VXPD S WUDWHORU WXWXURU DEDWHULORU LQGLYLGXDOH DOH WHUPHQLOR

r seriei de la media lor

DULWPHWLF HVWH]HUR

b)

P ULPHD PHGLHL DULWPHWLFH HVWH FXSULQV  vQWUH [min úL [max GRDU GDF  VHULD SUH]LQW  R WHQGLQ

c)

FODU GHVLPHWULH

SHQWUXRVHULHGHGLVWULEX LHGHIUHFYHQ HPHGLDDULWPHWLF FDOFXODW SHED]DIUHFYHQ HORU

reGXVHGHFRULHVWHPDLPLF d)

GHFkWPHGLDVHULHLLQL LDOHGHFRUL

PHGLD SURGXVXOXL D GRX  YDULDELOH DOHDWRDUH  HVWH HJDO  FX SURGXVXO PHGLLORU FHORU GRX 

variabile; e)

SHQWUX R VHULH GH GLVWULEX LH GH IUHFYHQ H PHGLD FDOFXODW  SH ED]D IUHFYHQ HORU UHODWLYH

eVWHHJDO 8)

FXPHGLDDULWPHWLF GHWHUPLQDW SHED]DIUHFYHQ HORUDEVROXWH

$QDOL]D IHQRPHQXOXL GH FRQFHQWUDUH  GLYHUVLILFDUH QX DUH VHQV DWXQFL FkQG JUXSDUHD XQLW FROHFWLYLW

LORU

LLV

-a efectuat:

a) pe variante; b) SHLQWHUYDOHHJDOHGHYDULD LH c) GXS RFDUDFWHULVWLF GHVSD LX d) GXS RFDUDFWHULVWLF DOWHUQDWLY  e) GXS RFDUDFWHULVWLF QHQXPHULF  9)

7LPSXOREVHUY ULLVDXDOFXOHJHULLGDWHORUVHDOHJH

a) b)

vQWRWGHDXQDvQSHULRDGDvQFDUHSRSXOD LDVWDWLVWLF SUH]LQW XQPDUHJUDGGHVWDELOLWDWH vQIXQF LHGHVFRSXOFHUFHW ULLúLDOREVHUY ULLVWDWLVWLFHGXS FD]FkQGSRSXOD LDVWDWLVWLF  SUH]LQW  VDX QX XQ JUDG PDUH GH VWDELOLWDWH GH H[HPSOX UHFHQV PkQWXO SRSXOD LHL REVHUYDUHDFRWD LLORUODEXUV DXQRUDF LXQLHWF 

c) vQIXQF LHGHSRVLELOLW LOHLQIRUPDWLFHGH prelucrare a datelor culese; d) DWXQFLFkQGVHGRUHúWHV VHMXVWLILFHRDQXPLW DF LXQHGHMDGHFODQúDW  e) ODvQWkPSODUHI U FULWHULLSUHFL]DWHúLDQDOL]DWHDSULRULF 10) Într-R FROHFWLYLWDWH VWDWLVWLF  GDF  GLYHUVLILFDUHD HVWH PD[LP  úL HYLGHQW FRQFHQWUDUHD este PLQLP DWXQFLFRHILFLHQWXOGHFRQFHQWUDUH&RUUDGR-Gini este:

a) G=1;

1 ; n 1 c) G = ; n b) G =

d) G=0; e) G =

n.

11) ÌQFRQWXOPDFURHFRQRPLF³9HQLWXUL´UHVXUVHOHVHIRUPHD]

GLQ

a) $PRUWL]DUHúL3,1pp; b) PIBppúLVXEYHQ iile de exploatare; c) PIBppúLLPSR]LWHOHLQGLUHFWH d) Amortizare, PIBppúLVXEYHQ LLOHGHH[SORDWDUH e) $PRUWL]DUHDLPSR]LWHLQGLUHFWHúLLPSR]LWHSHLPSRUWXUL 12) 6

VHSUHFL]H]HFDUHGLQXUP WRDUHOHDILUPD LLQXHVWHDGHY UDW 

a) b) c) d) e)

x = Me = Mo ; într-RUHSDUWL LHXQLPRGDO XúRUDVLPHWULF PHGLDQDVHSODVHD] vQWUHPHGLHúLPRG într-RUHSDUWL LHXQLPRGDO XúRUDVLPHWULF PHGLDVHSODVHD] vQWUHPRGúLPHGLDQ  într-RUHSDUWL LHXQLPRGDO SR]LWLYvQFOLQDW F tre valorile mici x < Me < Mo ; într-R UHSDUWL LH XQLPRGDO  SR]LWLY vQFOLQDW  F WUH YDORULOH PDUL PRGXO VH VLWXHD] vQRULFHUHSDUWL LHVLPHWULF XQLPRGDO 

 OD

VWkQJDPHGLDQHLúLDPHGLHL

13) 8Q DQDOLVW HFRQRPLF VWXGLD]  GLVWULEX LD ILUPHORU GXS cercetare-GH]YROWDUH 3HQWUX D YHULILFD LSRWH]D QRUPDOLW χ2úLRE LQHSHQWUXXQQXP

UGHJUDGHGHOLEHUWDWHO

 SURFHQWXO GLQ YHQLWXUL FKHOWXLW SHQWUX LL HPSLULFH RE LQXWH HO XWLOL]HD]  WHVWXO

YDORDUHD

χ 2calc = 18,30 . Probabilitatea

PD[LP FXFDUHVHJDUDQWHD] UH]XOWDWXOHVWH

a) b) c) d) e)

75%; 90%; 95%; 99%; 97,5%.

14) &DUHGLQXUP WRDUHOHDILUPD LLUHIHULWRDUHODFRHILFLHQWXOGHYDULD LHQXHVWHDGHY UDW  a) HVWHXQLQGLFDWRUVLQWHWLFDOvPSU úWLHULL b) HVWHH[SUHVLDUHODWLY DDEDWHULLPHGLLS WUDWLFH c) YDORUL PLFL DOH FRHILFLHQWXOXL GH YDULD LH VHPQLILF  XQ JUDG PDUH GH UHSUH]HQWDWLYLWDWH D mediei caracteristicii studiate; d) YDORULPLFLDOHFRHILFLHQWXOXLGHYDULD LHUHIOHFW RWHQGLQ DFFHQWXDW GHVLPHWULHDGLVWULEX LHL e) YDORUL PLFL DOH FRHILFLHQWXOXL GH YDULD LH UHIOHFW  RPRJHQLWDWHD FROHFWLYLW LL GLQ SXQFWXO de vedere al caracteristicii studiate. 15) 2 FDUDFWHULVWLF

 LPSRUWDQW  GH FDOLWDWH SHQWUX VXFXULOH GH IUXFWH vPEXWHOLDWH HVWH SURSRU LD GH

FRQFHQWUDW QDWXUDO SH FDUH R FRQ LQ ÌQWU XQ SURFHV GH IDEULFD LH D XQHL P UFL GH VXFXUL

-

presupunem c

SURFHQWXOGHFRQFHQWUDWQDWXUDOHVWHDSUR[LPDWLYQRUPDOGLVWULEXLWFXPHGLD

úL FRHILFLHQWXO GH YDULD LH  6WLFOHOH FDUH FRQ LQ PDL SX LQ GH   FRQFHQWUDW QDWXUDO VXQW

UHVSLQVH FDOLWDWLY 'DF   GH VWLFOH VXQW YHULILFDWH OD FRQWUROXO FDOLWD

tiv pot fi respinse

aproximativ: a) b) c) d) e)

2112 sticle; 4224 sticle; 1056 sticle; 124 sticle; 248 sticle.

16) 3HQWUXFDUDFWHUL]DUHDSURFHVHORUGHSURGXF LHVXELHFWHOHHFRQRPLFHVHDJUHJ



a) SHVHFWRDUHLQVWLWX LRQDOH b) GXS IRUPDMXULGLF  c) pe ramuri; d) QXHVWHQHFHVDU RDJUHJDUHVSHFLDO SHQWUXDFHVWVFRS e) DWkWSHVHFWRDUHLQVWLWX LRQDOHFkWúLSHUDPXUL 17) 0HGLDDULWPHWLF

DS WUDWHORUDEDWHULORULQGLYLGXDOHGHODWHQGLQ DORUFHQWUDO VHQXPHúWH

a) DEDWHUHPHGLHDEVROXW  b) DEDWHUHPHGLHS WUDWLF  c) dispersie; d) PHGLDO  e) moment centrat de ordin trei. 18) Într-R úFRDO

 JHQHUDO  VH RUJDQL]HD]  XQ WHVW GH YHULILFDUH D DSWLWXGLQLORU HOHYLORU SHQWUX

LQIRUPDWLF 'LVWULEX LDHOHYLORUGXS SXQFWDMXORE LQXWHVWHDSUR[LPDWLYQRUPDO 3ULPLLGLQ FHL PDL SX LQ vQFOLQD L VSUH DFHDVW  GLVFLSOLQ  RE LQ SkQ  OD  SXQFWH LDU FHL PDL SHUIRUPDQ L  RE LQ  úL SHVWH  GH SXQFWH 'DF  YDORDUHD PHGLDQ  HVWH GH  GH SXQFWH LDU FHL PDL PXO LGLQWUHHOHYLRE LQGHSXQFWHFRHILFLHQWXOOXL%RZOH\HVWH

a) b) c) d) e)

0,4; 0,53; 0,07; - 0,4; - 0,53.

19) PenWUXVWXGLXOFDOLW

LLSURGXF LHLIDEULFDWHvQVHULHvQWU RXQLWDWHHFRQRPLF VHREVHUY SHULRGLF

-

XQORWGHH[HPSODUHSUHOHYDWHGLQSURGXVHOHDIODWHODVIkUúLWXOODQ XOXLGHIDEULFD LH3RSXOD LD VWDWLVWLF LQYHVWLJDW HVWH

a) SURGXF LDWRWDO UHDOL]DW  b) ansamblul loturilor de produse; c) lotul format prin prelevare; d) SURGXF LDQHWHUPLQDW  e) SURGXF LDUHDOL]DW IDFWXUDW úLOLYUDW 20) 'DF

EHQHILFLDULORU

 VH XUP UHúWH FXQRDúWHUHD FRPSRUWDPHQWXOXL vQ GRPHQLXO YHQLWXULORU FKHOWXLHOLORU úL

RSHUD LXQLORUILQDQFLDUHVXELHFWHOHHFRQRPLFHVHDJUHJ GXS FULWHULXO

a) b) c)

DFWLYLW

LLGHSXVH

LQVWLWX LRQDO GHUDPXU 

d) IRUPDMXULGLF e) a)+b)+c)+d).

GHRUJDQL]DUH

21) 6DODULD LL XQHL ILUPHDX VDODULXO PHGLX  PLL OHLFX R DEDWHUHPHGLH S WUDWLF  D VDODULLORU  mii lei. PatroQXO ILUPHL KRW U úWH V  P UHDVF  ILHFDUH VDODULX LQGLYLGXDO GH  RUL 'LVSHUVLD QRLORUVDODULLID

GHVDODULXOPHGLXYDIL

a) 150; b) 22500; c) 29250; d) 253,5; e) 38025. 22) ÌQ PRGHOXO GH DQDOL]

 GLVSHUVLRQDO  XQLIDFWRULDO  GLVSHUVLD FRUHFWDW  GLQWUH JUXSH VH RE LQH

UDSRUWkQGYDULDQ DVLVWHPDWLF GLQWUHFHOHUJUXSH ODQXP UXOJUDGHORUGHOLEHUWDWHQRWDWFX³O´

Acest num r este: a) b) c) d) e)

l=n-1; l=n-r; l=r-1; l=n-r-1; l=n-2.

23) ÌQFD]XOLQGLFDWRULORUGHWLSFDOLWDWLYDJUHJDUHDVHUHDOL]HD]

SULQWU

-o:

a) RSHUD LHGHDGXQDUH b) oSHUD LHGHDGXQDUHVDXVF GHUH c) numai printr-RPHGLHDULWPHWLF  d) numai prin calculul unei medii armonice; e) SULQFDOFXOXOXQHLP ULPLPHGLL 24) ,GHQWLILFD LFDUHGLQWUHDILUPD LLOHXUP a)

WRDUHUHIHULWRDUHODRELHFWXOREVHUY ULLHVWHIDOV 

2ELHFWXO REVHUY ULL HVWH PXO LPHD GH IHQRPHQH GH PDV  GHVSUH FDUH XUPHD]  V  VH FXOHDJ GDWHOHVWDWLVWLFH

b) c)

2ELHFWXOREVHUY ULLHVWHRPXO LPHGHXQLW

LVLPSOHVDXFRPSOH[HGHREVHUYDUH

3RSXOD LD VXSXV  REVHUY ULL WUHEXLH GHOLPLWDW  FD YROXP vQ WLPS úL vQ VSD LX LQGLIHUHQW GDF HDHVWHVWDWLF VDXGLQDPLF 

d) e)

1XvQWRWGHDXQDRELHFWXOREVHUY ULLFRLQFLGHFXRELHFWXOFHUFHW ULL &KLDUGDF RELHFWXOREVHUY ULLHVWHELQHGHILQLWGXS FULWHULLFODUHHVHQ LDOHVWDELOHQXVH SRDWHDVLJXUDVXEQLFLRIRUP FRPSDUDELOLWDWHDGDWHORUG

25) &RUHF LDOXL6KHSSDUGVHDSOLF

e la o observare la alta.

GLVSHUVLHLFkQG

a) seria este pe variante; b) VHULDHVWHSHLQWHUYDOHQHHJDOHGHYDULD LH c) VHULDHVWHSHLQWHUYDOHHJDOHGHYDULD LH d) FkQGGLVWULEX LDHVWHDSUR[LPDWLYQRUPDO úLSUH]LQW e) FkQGVHULDHVWHELPRGDO 

XQQXP UPDUH

de intervale egale;

26) 3UHFL]D LFDUHHOHPHQWHGLQFHOHSUH]HQWDWHPDLMRVQXHVWHRIXQF LHVSHFLILF

PHWRGHLJUXS ULL

FODVLILF ULLvQDFWLYLWDWHDVWDWLVWLF 

a)

VLVWHPDWL]DUHD GDWHORU LQGLYLGXDOH SULQ UHVWUkQJHUHD QXP UXOXL GH

variante ale variabilei

de grupare; b) c) d) e)

IDFLOLWDUHDFDOFXOXOXLWXWXURULQGLFDWRULORUSULPDULúLGHULYD L VWUXFWXUDUHDSRSXOD LHLVWDWLVWLFHvQFODVHJUXSHRPRJHQH SUH]HQWDUHDúLGHVFULHUHDVWUXFWXULLSRSXOD LHLVWDWLVWLFH FDUDFWHUL]DUHDOHJ WXULORUVWDWL

27) Programul propriu-]LV DO REVHUY

stice dintre variabilele analizate.

ULL HVWH IRUPDW GLQ WRWDOLWDWHD FDUDFWHULVWLFLORU YDULDELOHORU 

SHQWUXFDUHXUPHD] V VHFXOHDJ GDWHOHGHODXQLW

a)

vQ vQWUHE UL FDUH VX

LOHSRSXOD LHLVWDWLVWLFH(OVHFRQFUHWL]HD] 

nt înscrise în formulare statistice la care se primesc obligatoriu

U VSXQVXULFXSULYLUHODQLYHOXOGHGH]YROWDUHVDXIRUPDORUGHPDQLIHVWDUH

b) într-R OLVW

 GH YDULDELOH GHVSUH FDUH VH FXOHJ GDWHOH GLQ GRFXPHQWHOH SH FDUH XQLW

LOH GH

REVHUYDUHGRUHVFV OHSXQ ODGLVSR]L LH

c)

vQ vQWUHE UL vQVFULVH vQ FKHVWLRQDUH VDX DOWH IRUPXODUH VWDWLVWLFH DGUHVDWH OD WRDWH VDX OD R SDUWH GLQ XQLW

LOH SRSXOD LHL úL DOH F URU SRVLELOH U VSXQVXUL UHIOHFW  IRUPHOH LQGLYLGXDOH

de manifestare ale fenomenelor; d) vQWUHE ULLQFOuse în chestionare sau în alte formulare statistice numai atunci când ele sunt DGUHVDWH GLUHFW WXWXURU XQLW

LORU GH REVHUYDUH VDX OD R SDUWH GLQ DFHVWHD úL DOH F URU

SRVLELOHU VSXQVXULUHIOHFW IRUPHOHLQGLYLGXDOHDOHIHQRPHQHORUGHPDV LQYHVWLJDWH

e) în variantele variabilelor precizate. 28) 3HQWUXGLVWULEX LDXQHLYDULDELOHDOHDWRDUH;VHFXQRDúWHYDORDUHDGLVSHUVLHLúLYDORDUHD momentului centrat de ordinul 4: 20876491. &RHILFLHQWXOOXL)LVFKHUSHQWUXP VXUDUHDEROWLULLDUHYDORDUHD

γ2 γ2 γ2 γ2 e) γ 2

a) b) c) d)

= −0,782 ; = 2,218 ; = 5,218 ; = 0,45 ; = −2,218 .

29) 6HH[FOXGGLQFDOFXOXOLQGLFDWRULORUPDFURHFRQRPLFLGHUH]XOWDWHWUDQ]DF LLOH a) b) c) d) e)

intersectoriale; bilaterale; unilaterale; intrasectoriale; de SLD 

30) &RQWXOPDFURHFRQRPLF3URGXF LHDUHFDVROG a) b) c) d) e)

PINpp; PIBpf; PIBpp; VN; PNBpf.

31) 'LVWULEX LD HOHYLORU GLQ FODVD , D XQHL úFROL JHQHUDOH GXS media zece este: Nr. materii Nr. elevi VaORDUHDPHGLDQ a) b) c) d) e)

0 10

1 30

2 80

3 70

 QXP UXO PDWHULLORU OD FDUH DX DYXW

4 50

5 20

DVHULHLHVWH

2 materii; 2,5 materii; 3 materii; 2,7 materii; 70 elevi.

32) 'LVWULEX LD XQHL YDULDELOH DOHDWRDUH ; HVWH SHUIHFW VLPHWULF  GH PHGLH x = 20  'DF  VH DGDXJ GRX XQLW LVWDWLVWLFHFXYDORULOHYDULDELOHLVWXGLDWe x1 úL[2 DWXQFLQRXDGLVWULEX LH a) b) c) d) e)



DUHDVLPHWULHSR]LWLY  HVWHSHUIHFWVLPHWULF  DUHDVLPHWULHQHJDWLY  DUHILHDVLPHWULHSR]LWLY ILHDVLPHWULHQHJDWLY  QXSUH]LQW DVLPHWULH

33) 1XVXQWFXSULQVHvQYDORDUHDSURGXF LHL a) serviciile statului; b) EXQXULOHGHFDSLWDOGLQSURGXF LHSURSULH c) autoconsumul; d) FKLULDDXWRLPSXV LSRWHWLF  e) EXQXULOHSURGXVHúLFRQVXPDWHSHQWUXSURGXFHUHDDOWRUEXQXULúLVHUYLFLL 34) Atunci când datele provin dintr-XQ HúDQWLRQ GH YROXP UHGXV Q  úL VH WHVWHD] prLYLQGSDUDPHWUXOPHGLDvQWUHJLLFROHFWLYLW L

 LSRWH]D QXO 

H0 : m = m0 Ha : m > m0

UHJLXQHDFULWLF HVWHGDW GH

a) z > zα ; b) z > zα / 2 ; c) t > tα ; n − 1 ; d) t > tα / 2 ; e) t > − tα − 2; n − 1 . 35) Aplicând modelul analizei

GLVSHULVRQDOH XQLIDFWRULDOH VH DFFHSW  LSRWH]D FRQIRUP F UHLD

αVHvQGHSOLQHúWHFRQGL LD

IDFWRUXOGHJUXSDUHHVWHVHPQLILFDWLYGDF ODXQSUDJGHVHPQLILFD LH

a) Fcalc < Fα , n − 1, r − 1 ; b) Fcalc < Fα , r − 1, n − r ; c) Fcalc < Fα , r − 1, n − 1 ; d) Fcalc > Fα , r − 1, n − 1 ;

e) Fcalc > Fα , r − 1, n − r .

36) 2JUXS GHGHVWXGHQ LVXV LQHODGRX GLVFLSOLQHFkWHXQWHVWSHQWUXYHULILFDUHDFXQRúWLQ HORU Testele au punctaje diferite, iar rezultatele sunt: 25

- la testul A:

- la testul B:

∑ x 2Ai = 9000;

25

∑ x Ai = 450;

i =1 25

i =1 25

i =1

i =1

∑ x Bi2 = 425;

∑ x Bi = 100;

*UXSDGHVWXGHQ LHVWHPDLRPRJHQ GLQSXQFWXOGHYHGHUHDOFXQRúWLQ HORUDFXPXODWH

a) la disciplina A; b) la disciplina B; c) ODDPEHOHGLVFLSOLQHSUH]LQW DFHODúLJUDGGHRPRJHQLWDWH d) nu sunt sufLFLHQWHGDWHSHQWUXDILVWXGLDW RPRJHQLWDWHVHULLORU e) QXVHSRWFRPSDUDRPRJHQLW LOHODFHOHGRX GLVFLSOLQHGHRDUHFFHSXQFWDMHOHWHVWHORUDX fost diferite. 37) 3UREDELOLWDWHD FD R FRPSDQLH GH DVLJXU

UL V  ILH LQXW  V  SO WHDVF  R SROL

 SHQWUX R SUREOHP 

PHGLFDO  PDMRU  HVWH  'DF  XQ JUXS GH  GH SHUVRDQH DVLJXUDWH VXQW VHOHFWDWH vQWkPSO WRU SUREDELOLWDWHD FD DFHDVW  FRPSDQLH V  SO WHDVF  FHO SX LQ R SROL

 SHUVRDQHORU

selectate este: a) b) c) d) e)

0,8196; 0,1804; 0,1353; 0,8647; 0,001.

38) Valoarea individual pe scala:

³]HUR´DYDULDELOHL³P ULPHDH[WUDVXOXLGHFRQW´DUHVHPQLILFD LHFRQFUHW 

a) RUGLQDO  b) de rapoarte; c) de intervale; d) GLVFUHW  e) FRQWLQX  39) 3HQWUX SDWUX ILOLDOH DOH XQHL VRFLHW L FRPHUFLDOH VWUXFWXUD FLIUHL GH DIDFHUL UHDOL]DWH úL LQGLFLL UHDOL] ULL programului la cifra de afaceri au fost:

Filiala A B C D

Structura cifrei de afaceri realizate (%) 20 40 30 10

,QGLFHOHUHDOL]

ULL

programului cifrei de afaceri 1,1 1,2 1,25 1,5

,QGLFHOHUHDOL] ULLSURJUDPXOXLFLIUHLGHDIDFHULSHvQWUHDJDVRFLHWDWHFRPHUFLDO DIRVW

a) b) c) d) e)

1,2625; 1,225; 1,2542; 1,2168; 1,2465.

TESTUL 7

1)

([SUHVLD VLQWHWL] ULL YDORULORU LQGLYLGXDOH DOH XQHL YDULDELOH VWDWLVWLFH vQWU

-un singur nivel estarea fenomenelor

UHSUH]HQWDWLYDWRWFHHDFHHVWHHVHQ LDORELHFWLYúLVWDELOvQDSDUL LDúLPDQLI GHPDV HVWHGDW GH

a) YDORDUHDORUPHGLDQ  b) valoarea lor medial ; c) valoarea lor medie; d) FRHILFLHQWXOORUGHYDULD LH e) FDOFXOXOXQHLP ULPLUHODWLYHGHLQWHQVLWDWH 2)

3HULRDGDGHWLPSFkWIXQF LRQHD]  XQDQXPLWWLSGHEDWHULL HVWHQRUPDO GLVWULEXLW FXRPHGLHGH GHRUHúLRGHYLD LHVWDQGDUGGHRUH3UREDELOLWDWHDFDREDWHULHV IXQF LRQH]HvQWUHúL

de ore este: a) b) c) d) e) 3)

0,5918; 0,4082; 0,8164; 0,1836; 0,7959.

'DF  vQWU R VHULH GH GLVWULEX LH YDORULOH LQGLYLGXDOH VH VLPSOLILF  GH N RU

serii este:

i, atunci dispersia noii

a) de k2RULPDLPLF ID GHGLVSHUVLDVHULHLLQL LDOH b) GHNRULPDLPDUHGHFkWGLVSHUVLDVHULHLLQL LDOH c) HJDO FXGLVSHUVLDVHULHLLQL LDOH d) de k2RULPDLPDUHID GHGLVSHUVLDVHULHLLQL LDOH e) GHNRULPDLPLF GHFkWGLVSHUVLDVHULHLLQL LDOH 4)

ÌQPRGHOXOGHDQDOL] GLVSHUVLRQDO XQLIDFWRULDO VHXWLOL]HD] WHVWXO³)´GDWGHUHOD LD

∑ (y i − y) r

=1 a) Fcalc = i

2

ni :

r −1

∑ ( y i − y) r

b) Fcalc =

∑ ∑ (yij − y i ) r

2

i =1 r m

m

2

i = 1 j =1

;

n−r

ni

∑ ∑ ( yij − y)

; 2

i =1 j =1

∑( r

c) Fcalc =

i =1

yi − y r −1

)

2

∑ ∑ (y j − y) r

ni :

m

i =1 j =1

n −1

2

;

∑ (y i − y) r

d) Fcalc = i =1

2

∑ ∑ ( yij − y i ) r

ni :

r −1

∑ ∑ ( yij − y i ) r

e) Fcalc =

m

i =1 j =1

m

2

i =1 j =1

2

;

n −1

∑ (y i − y) r

ni :

n−r

i =1

r −1

2

ni .

5) În teVWDUHD LSRWH]HL VWDWLVWLFH SULYLQG PHGLD SRSXOD LHL FkQG GDWHOH SURYLQ GH OD XQ HúDQWLRQ GH YROXPUHGXVQ úL

H 0 : m = m0 H a : m ≠ m0

UHJLXQHDFULWLF HVWHGDW GH

a) z < − zα sau z > zα ; b) z < − zα / 2 sau z > zα /2 ; c) t < − tα / 2, n sau t > t α / 2 ,n ;

d) t < − tα , n − 1 sau t > t α ,n −1 ; e) t < − t α / 2,n −1 sau t > t α / 2,n −1

6)

ÌQFDGUXOXQXLVWXGLXGHSLD

HIHFWXDWvQOXQDLDQXDULHV DXUP ULWSULQWUH

GH FRQVXPDWRUL DVXSUD FDOLW YDULDELODRSLQLHúLFX[i

-

altele opinia a 100

LL XQXL DQXPLW SURGXV XWLOL]DW vQ PRG FXUHQW 6H QRWHD]  FX ;

opinia consumatorului i ( i = 1,100 ) intervievat. P HVWHIRUPDW GLQ:

3RSXOD LDVWDWLVWLF QRWDW FX

a) WR LFRQVXPDWRULL b) consumatorii români; c) FHLGHFRQVXPDWRULLQWHUYLHYD L d) FRQVXPDWRULLSRWHQ LDOL e) consumatorii din zona de sud-HVWD

ULL

 9DULDELOD;GHILQLW vQSUREOHPD HVWH

a) FDOLWDWLY b) FDOLWDWLY c) QRPLQDO d) de timp; e) QXPHULF 8)

FRQWLQX  GLVFUHW   

&DUHGLQXUP WRDUHOHDILUPD LLQXHVWHDGHY UDW SHQWUXRVHULHVWDWLVWLF 

a) b) c) d) e)

vQWUHTXDUWLODúLTXDUWLODVHJ VHVFGLQREVHUYD LLVLWXDWHvQFHQWUXOGLVWULEX LHL YDORDUHDTXDUWLOHLHVWHHJDO FXPHGLDQDGRDUSHQWUXRVHULHVLPHWULF  YDORDUHDPHGLDQHLHVWHvQWRWGHDXQDHJDO FXYDORDUHDTXDUWLOHL SHQWUXRVHULHVLPHWULF DEDWHUHDLQWHUTXDUWLOLF HVWHQXO  SHQWUXRVHULHVLPHWULF DEDWHUHDLQWHUTXDUWLOLF FXSULQGHGLQREVHUYD LL

9)

3HQWUXRGLVWULEX LHVLPHWULF 

a) abaterileLQGLYLGXDOHVHFRPSHQVHD] GRDUODQLYHOXOvQWUHJLLFROHFWLYLW L b) abaterile individuale sunt nule; c) DEDWHUHDPD[LP SR]LWLY HVWHHJDO FXDEDWHUHDPD[LP QHJDWLY  d) DEDWHULOHLQGLYLGXDOHVHFRPSHQVHD] DWkWSHWRWDOFkWúLODQLYHOXOFHQWUDOL]DWDOXQLW e) VXPDDEDWHULORULQGLYLGXDOHHVWHHJDO FXDPSOLWXGLQHDYDULD LHL 10) *UDGXOGHOLEHUWDWHHVWHXQFRQFHSWVWDWLVWLFFHGHVHPQHD]

LORU



a) QXP UXOGHHOHPHQWHGLQWU-o colectivitate; b) num rul de elemente dintr-o colectivitate minus unul; c) num rul de elemente necesare pentru a defini starea unui ansamblu; d) num rul de elemente independente necesare pentru a defini starea unui ansamblu; e) QXP UXOGHUHOD LLLQGHSHQGHQWHFDUHOHDJ HOHPHQWHOHXQXLDQVDPEOX 11) 'RX

 YDULDELOH VWDWLVWLFH DX IRVW PRGHODWH vQWU R SRSXOD LH VWDWLVWLF  FX Q XQLW

HFXD LHLOLQLDUHGHIRUPD

∑ (xi − x) n

2

y = 5 + 64 x ùWLLQGF

n

∑ (yi − y)

= 30;

i =1

2

-

L FX DMXWRUXO



= 1960  SHQWUX Q

 XQLW

L VWDWLVWLFH DWXQFL LQWHUYDOXO GH

i =1

încredere pentru panta liniei de regresie, la o probabilitate de 95% este: a) b) c) d) e)

(63,53 ; 64,47); (4,53 ; 5,47); (58,92 ; 66,65); (61,35 ; 66,65); (58,92 ; 69,08).

12) 'LVSHUVLDXQHLFDUDFWHULVWLFLGHWLSDOWHUQDWLYHVWHPD[LP

FkQG

a) QXP UXOGHU VSXQVXULDILUPDWLYHHVWHHJDOFXQXP UXOGHU VSXQVXULQHJDWLYH b) WRDWHXQLW LOHFROHFWLYLW LLvQUHJLVWUHD] U VSXQVXULDILUPDWLYH c) WRDWHXQLW LOHFROHFWLYLW LLvQUHJLVWUHD] U VSXQVXULQHJDWLYH d) WRDWHXQLW LOHFROHFWLYLW LLvQUHJLVWUHD] ILHU VSXQVXULQHJDWLYHILHU VSXQVXULSR]LWLYH e) nu se poate preciza în ce caz dispersia unei caracteristiFLDOWHUQDWLYHHVWHPD[LP  13) 'HQVLWDWHDGHUHSDUWL LHDYDULDELOHLDOHDWRDUHQRUPDOHGHPHGLH x = 20,9 úLGLVSHUVLHHVWHGHVFULV a) f ( xi ) = b) f ( xi ) = c) f ( xi ) = d) f ( xi ) = e) f ( xi ) =

1 2π

⋅e

−

1 17,5 2π 1 17,5 2π

1 4,18 2π 1 4,18 2π

20,9 35

⋅e ⋅e

⋅e ⋅e

2

−

−

; 1 2⋅17,5

2

( xi − 20,9 )2

1 ( xi − 20,9 )2 2⋅17 ,5

;

;

−

1 ( xi − 20,9 )2 2⋅4,18 ;

−

1 ( xi − 20,9 )2 2⋅17,5

.

GH

14) 0HGLDDUPRQLF a) b) c)

VHGHILQHúWHFD

PHGLDDULWPHWLF FDOFXODW GLQLQYHUVHOHYDORULORULQGLYLGXDOHvQUHJLVWUDWH YDORDUHDLQYHUV DPHGLHLDULWPHWLFHDWHUPHQLORUVHULHL YDORDUHD

LQYHUV 

D

PHGLHL

DULWPHWLFH

FDOFXODW 

GLQ

LQYHUVHOH

S WUDWHORU

YDORULORU

individuale înregistrate; d) e)

YDORDUHDLQYHUV DPHGLHLDULWPHWLFHFDOFXODW GLQLQYHUVHOHYDORULORULQGLYLGXDOH YDORDUHDFDUHGDF DUvQORFXLWHUPHQLLVHULHLQXDUPRGLILFDVXPDORU

15) ,QGLFDWRUXO ³HQHUJLD caracterizarea:

LQIRUPD LRQDO 

2QLFHVFX´

HVWH

XWLOL]DW

vQ

DQDOL]D

VWDWLVWLF 

SHQWUX

a) asimetriei; b) dispersiei; c) QRUPDOLW LLGLVWULEX LHL d) FRQFHQWU ULL e) WHQGLQ HLFHQWUDOH 16) 'LUHFWRUXOXQXLSRVWGHUDGLRFRPDQG

RFHUFHWDUH VWDWLVWLF vQVFRSXOGHWHUPLQ ULL DXGLHQ HLGH

FDUHVHEXFXU SRVWXOV X&HUFHW WRUXOFXOHJHSHXQHúDQWLRQGDWHSULYLQGQXP UXOGHRUHDXGLDWH úL DIO  F   GLQ SHUVRDQH DVFXOW  SRVWXO GH UDGLR PDL SX LQ GH GRX  RUH  vQWUH  úL  RUH vQWUHúLRUHvQWUHúLRUHLDUUHVWXOSHVWHRUH1XP UXOPHGLXGHRUHGHDXGL LH SHRSHUVRDQ GLQHúDQWLRQHVWH

a) b) c) d) e)

4,8 ore; 4,7 ore; 6 ore; 4,2 ore; 4,6 ore.

17) 6  VH SUHFL]H]H FDUH GLQ XUP Poisson: a) pi = b) pi =

WRDUHOH GLVWULEX LL GH SUREDELOLWDWH GHVFULH R YDULDELO  DOHDWRDUH

10! 0,9 xi 0,110− xi (xi=0, 1, 2, … , 10); xi !⋅ (10 − x i )!

(0,5) xi e −0,5

(xi=0, 1, 2, 3, … );

xi !

c) pi = C6xi ⋅ 0,2 ⋅ 0,8 6− xi d) pi =

(xi=0, 1, 2, … , 6);

x i ! e − xi

(xi=0, 1, 2, 3, … )

(0,5) xi

e) f ( xi ) =

1 31 , 2π

⋅e

−

( xi − 20,9)2 2⋅9 , 61

.

18) 3HQWUX R FROHFWLYLWDWH GH Q XQLW L VLVWHPDWL]DWH FRQFRPLWHQW vQ U JUXSH GXS  YDORULOH caracteriVWLFLL ; FRQVLGHUDW  FDUDFWHULVWLF  HVHQ LDO  GH LQIOXHQ  úL vQ P JUXSH GXS  YDORULOH FDUDFWHULVWLFLLDQDOL]DWH<LQIOXHQ DIDFWRUXOXL;HVWHP VXUDW GH

a) b) c)

vPSU úWLHUHDYDORULORULQGLYLGXDOHGLQILHFDUHJUXS vQMXUXOPHGLHLGHJUXS  vPSU úWLHUHDYDORULORULQGLYLGXDOHGLQILHFDUHJUXS vQMXUXOPHGLHLJHQHUDOHDFROHFWLYLW vPSU úWLHUHDPHGLLORUGHJUXS vQMXUXOPHGLHLJHQHUDOHDFROHFWLYLW

LL

LL

d) e)

vPSU úWLHUHDYDORULORULQGLYLGXDOHvQMXUXOPHGLHLPHGLLORUGHJUXS  vPSU úWLHUHDPHGLHLPHGLLORUGHJUXS ID

19) ÌQPRGHOXOGHDQDOL] a)

m

i =1 j =1 r

b)

∑ ( y i − y)

i =1 r

2

∑ (y i − y)

c) i =1

2

d)

;

r −1

e)

m

2

;

n −1

∑ ∑ ( yij − y ) m

;

ni

i =1 j =1 r

2

ni ;

∑ ∑ ( yij − y ) r

LL

GLVSHUVLRQDO XQLIDFWRULDO YDULDQ DIDFWRULDO VLVWHPDWLF HVWH

∑ ∑ ( yij − y i ) r

GHPHGLDJHQHUDO DFROHFWLYLW

2

.

i =1 j =1

20) În testarea ipotezei statistice

H 0 : m ≥ 100

H a : m < 100

XWLOL]kQGWHVWXO]VHRE LQHYDORDUHDWHVWXOXL]

a) b) c) d) e)

-1,11. Nivelul de încredere al testului este:

86,65%; 36,65%; 13,35%; 26,70%; 73,30%.

21) Într-un proces de testare a ipotezelor statistice, eroarea de genul al doilea este: a) HURDUHDSHFDUHRIDFHPDFFHSWkQGLSRWH]DQXO FkQGHDHVWHDGHY UDW  b) HURDUHDSHFDUHRIDFHPDFFHSWkQGLSRWH]DDOWHUQDWLY FkQGHDHVWHIDOV  c) HURDUHDSHFDUHRIDFHPDFFHSWkQGLSRWH]DQXO FkQGHDHVWHIDOV  d) eroarea pe FDUHRIDFHPHOLPLQkQGLSRWH]DQXO FkQGHDHVWHDGHY UDW  e) HURDUHDSHFDUHRIDFHPHOLPLQkQGLSRWH]DDOWHUQDWLY DWXQFLFkQGHDHVWHIDOV



22) ÌQ XWLOL]DUHD PHWRGHL UHJUHVLHL SHQWUX VWXGLXO GHSHQGHQ HL GLQWUH YDULDELOH PRGHOXO GH IRUPD

y=α + a) b) c) d) e)

1 β + ε este un model: x

liniar; H[SRQHQ LDO

logaritmic; hiperbolic; parabolic.

23) 'LVSHUVLDYDORULORUXQHLYDULDELOHDOHDWRDUH;ID a) b) c) d) e) 24) Un

GHRFRQVWDQW DHVWHPLQLP FkQG

a = 0;

a = x; pentru orice a; a = ∑ xi ; a = xmax.

VLVWHP DO XQXL YHKLFXO VSD LDO WUHEXLH V  IXQF LRQH]H FRQWLQXX SHQWUX FD QDYD V  UHLQWUH vQ

VSD LX 2 FRPSRQHQW  D VLVWHPXOXL IXQF LRQHD]  FRUHVSXQ] WRU  GLQ WLPS 3HQWUX D DVLJXUD EXQD IXQF LRQDUH D VLVWHPXOXL VXQWPRQWDWH SDWUX FRPSRQHQWH VLPLODUH vQ DúDIHO vQFkW VLVWHPXO IXQF LRQHD]  GDF  FHO SX LQ R FRPSRQHQW  OXFUHD]  &RPSRQHQWHOH RSHUHD]  LQGHSHQGHQW 3UREDELOLWDWHDFDVLVWHPXOV FDG HVWH

a) 0,05%; b) 5%; c) 15%; d) 52,20%; e) 0,5220%. 25) 3HQWUXRVHULHGHUHSDUWL LHGHIUHFYHQ HPHGLDS r

a) x p =

∑ (x n )

2

i i

i =1

;

r

∑n

i

i =1

r

b) x p =

∑x n

2 i i

i =1 r

;

∑n

i

i =1 r

c) x p =

∑ (x n )

2

i i

i =1

r

∑ ni i =1

r

d) x p =

∑x n i =1 r

2 i i

;

∑n

i

i =1

r

e) x p =

∑x n i =1 r

i

∑n i =1

i

. i

;

WUDWLF VHFDOFXOHD] FD

26) 'RX

 JUXSH GH VWXGHQ L FX HIHFWLYH GH  úL UHVSHFWLY  GH SHUVRDQH DX VXV LQXW XQ WHVW GH

FXOWXU JHQHUDO 3ULPDJUXS DRE LQXWPHGLDLDUDGRXD1RWDPHGLHSHDQVDPEOXOFHORU GRX JUXSHHVWH

a) b) c) d) e)

8,14; 8,10; 8,12; 8,00; 8,09.

27) Într-R FROHFWLYLWDWHD VWDWLVWLF

 VLVWHPDWL]DW  vQ U JUXSH GXS  YDULD LD FDUDFWHULVWLFLL GH JUXSDUH ;

úLvQPJUXSHGXS YDORULOHYDULDELOHLDQDOL]DWH<H[LVW vQWRWGHDXQDUHOD LD

2

a) σ = σ i2 + δ 2 ; 2

b) σ ≥ δ 2 ; σ i2 2 ∑ c) σ = ; r 2

d) σ ≤ σ 2 ;

∑∑ (y r

e) σ 2 =

m

i =1 j =1

r

)

2

j

− y i nij

.

m

∑∑ n i =1 j =1

ij

28) Într-R FROHFWLYLWDWHD GH  VDODULD L VLVWHPDWL]DW

 GXS  IDFWRUXO GH JUXSDUH ; QXP UXO RUHORU

OXFUDWH  vQ  JUXSH úL GXS  YDULDELOD GHSHQGHQW  VDODULXO vQ  JUXSH DSOLFkQGX DQDOL] 

ST

GLVSHUVLRQDO 

V D

-

RE LQXW

YDULDQ D

VLVWHPDWLF 

61



úL

-se modelul de

YDULDQ D

WRWDO 

9DORDUHDFDOFXODW DUDSRUWXOXL)SHQWUXXWLOL]DUHDWHVWXOXLFXDFHODúLQXPHHVWH

a)Fcalc=81,875; b) Fcalc=73,23; c) Fcalc=1,25; d) Fcalc=61,09; e) Fcalc=36,94. 29) În testarea ipotezei statistice

H 0 : m ≥ 100

H a : m < 100

VHRE LQHYDORDUHDWHVWXOXLVWDWLVWLF]

-1,11. 3UDJXOGHVHPQLILFD LHDOWHVWului este: a)0,3665; b) 0,1335; c) 0,267 ; d) 0,06675; e) 0,43325.

30) Într-un proces de testare a ipotezelor statistice, eroarea de genul întâi este: a) HURDUHDSHFDUHRIDFHPDFFHSWkQGLSRWH]DQXO FkQGHDHVWHDGHY UDW  b) eroarea pe care o facem acceptând ipoteza nXO DWXQFLFkQGHDHVWHIDOV  c) HURDUHDSHFDUHRIDFFHPDFFHSWkQGLSRWH]DDOWHUQDWLY FkQGHDHVWHDGHY UDW  d) HURDUHDSHFDUHRIDFHPHOLPLQkQGLSRWH]DQXO DWXQFLFkQGHDHVWHDGHY UDW  e) HURDUHDSHFDUHRIDFHPHOLPLQkQGLSRWH]DDOWHUQDWLY DWXQFLFkQGHDHVWHDGHY 31) 6

UDW 

 VH SUHFL]H]H FDUH GLQ XUP WRDUHOH PHWRGH GH FDUDFWHUL]DUH D OHJ WXULORU GLQWUH YDULDELOHOH

VWDWLVWLFHQXVHvQFDGUHD] vQFDWHJRULD³PHWRGHORUVLPSOH´

a) metoda seriilor interdependente; b) PHWRGDJUXS ULORU c) PHWRGDJUDILF  d) PHWRGDFRUHOD iei; e) PHWRGDWDEHOXOXLGHFRUHOD LH

TESTUL 8 1) Prin AUDIT-ul financiar efectuat în luna ianuarie 1998 la S.C. “ICS” SRL s-D FRQVWDWDW F  vQ IDFWXULOH HODERUDWH vQ  H[LVW  DQXPLWH HURUL vQ FDOFXOXO 79$-XOXL FDUH DX DYXW GUHSW VXUV  QHFXQRDúWHUHD PHWRdologiei de calcul a TVA-XOXL OD XQHOH SURGXVH DSUR[LP UL HURQDWH GHIHF LXQLDOHPLMORFXOXLWHKQLFGHFDOFXOHWF 3RSXOD LDVWDWLVWLF VWXGLDW HVWH

a) ansamblul facturilor elaborate de S.C. “ICS” SRL; b) DQVDPEOXOSURGXVHORUúLVHUYLFLLORUUHDOL]DWHGH6&³,&6´65/SkQ OD;,, c) DQVDPEOXO SURGXVHORU úL VHUYLFLLORU UHDOL]DWH GH 6& ³,&6´ 65/ GHVI FXWH SH SLD

 úL

IDFWXUDWHSkQ OD;,,

d)

DQVDPEOXO SURGXVHORU úL VHUYLFLLORU UHDOL]DWH SHQWUX D IL GHVI FXWH SH SLD

SRL, facturateSkQ e)

DQVDPEOXO IDFWXULORU HODERUDWH GH 6& ³,&6´ 65/ SkQ  OD ;,, SHQWUX SURGXVHOH úLVHUYLFLLOHUHDOL]DWHúLGHVI FXWHSHSLD

2)

 GH 6& ³,&6´

OD;,,úLODFDUHVHSHUFHSH79$ 

&DOFXOXODPSOLWXGLQLLYDULD LHLYDORULORULQGLYLGXDOHDUHVHQVSHQWUX

a) serii statistice numerice formate pe variante; b) VHULLVWDWLVWLFHIRUPDWHGXS RYDULDELO DOWHUQDWLY  c) VHULLVWDWLVWLFHIRUPDWHSHLQWHUYDOHHJDOHGHYDULD LH d) VHULLVWDWLVWLFHIRUPDWHSHLQWHUYDOHQHHJDOHGHYDULD LH e) orice tip de serie. 3) Pentru o colectivitDWH GH Q XQLW L FDUH DX IRVW VWUXFWXUDWH FRQFRPLWHQW vQ r JUXSH GXS  YDORULOH FDUDFWHULVWLFLL ; úL vQ mJUXSH GXS  YDORULOH FDUDFWHULVWLFLL < PHGLD FDUDFWHULVWLFLL < SH vQWUHDJD colectivitate ( y QXVHFDOFXOHD] m

a) y =

∑y n j =1 m

j .j

;

∑n

.j

j =1

r

b) y =

∑y n i =1 r

i. i .

;

∑n

i.

i =1 r m

∑∑ y n

j =1 c) y = i =1r m

ij

ij

;

∑∑ n

ij

i =1 j =1 r

m

∑∑ y n

j =1 d) y = i=1 n

ij

ij

;

r

e) y =

∑y n i =1 r

i. i .

∑n i =1

i.

.

FD

4)

ÌQ DQXO  LQGLFHOH PHGLX OXQDU DO SUH XULORU GH FRQVXP OD VHUYLFLL D IRVW SHQWUX SHULRDGD

ianuarie-DXJXVWúLSHQWUXSHULRDGDDXJXVW-decembrie 1,0319. Indicele mediu lunar pe anul 1994 a fost: a) b) c) d) e) 5)

1,0505; 1,0474; 1,0435; 1,0436; 104,35%.

3HQWUX GRX  YDULDELOH VWDWLVWLFH ; úL < vQWUH FDUH H[LVW  R GHSHQGHQ JUDILF V

 OLQLDU  XWLOL]kQG PHWRGD

-au calculat:

σ 2x = 9043;

cov( x , y ) = −2392 ,8;

y = 37;

x = 364.

(FXD LDGHUHJUHVLHFDUHPRGHOHD] GHSHQGHQ DGLQWUHFHOHGRX YDULDELOHHVWH

a) b) c) d) e) 6)

y = 133,3 + 0,2646x ; yˆ = 133,3 − 0,2646 x ; yˆ = 0,2646 + 133,3 x ; yˆ = 1412,92 − 3,78 x ; yˆ = −1338,92 − 3,78 x .

ÌQ UHSDUWL LD ELQRPLDO  FX Q REVHUYD LL S

- probabilitatea succesului, q - probabilitatea

LQVXFFHVXOXLIUHFYHQ DDNVXFFHVHvQ1VHULLHVWH

a) q n − k p k ; b) Cnk q n − k p k ; c) Cnk p n − k q k ; d) N ⋅ C nk q n − k p k ; e) N ⋅ q n − k p k . 7)

ÌQVWXGLXOPLúF ULLQDWXUDOHDSRSXOD LHLVHDQDOL]HD] SULQWUHDOWHOHúLYDULDELOD³UDQJXOQ VFXWXOXL YLX´ÌQLDQXDULHvQ5RPkQLDUHSDUWL LDGXS DFHDVW YDULDELO VHSUH]LQW DVWIHO

5DQJXOQ

VFXWXOXLYLX

1XP

UGHQRXQ

Primul

VFX L

139958

Al doilea

64897

Al treilea

19812

Al patrulea

9657

Al cincilea

5650

$OúDVHOHD

3966

$OúDSWHOHD

2322

Al 8-OHDúLSHVWH

3722

Sursa: Anuarul statistic al României, CNS, 1994, p.126

Datele prezentate mai sus sunt: a) b) c) d) e) 8)

individuale; grupate; de stoc; de flux; agregate.

3HQWUX GRX  YDULDELOH VWDWLVWLFH GHSHQGHQWH ; úL < FX \ XQLW

 I[  DX IRVW FXOHVH GDWH GH OD  GH

LVWDWLVWLFHúLvQXUPDSUHOXFU ULLGDWHORUV DRE LQXWFRHILFLHQWXOGHFRUHOD LHU

-

-0,82.

&RHILFLHQWXOGHFRUHOD LHU

a) HVWHVHPQLILFDWLYVWDWLVWLFODXQSUDJGHVHPQLILFD LHα=0,0005; b) nu este semnificativ statistic; c) este semnificativ statistic doar pentru cel mult un nivel de încredere de 1-α=0,90; d) QXHVWHVHPQLILFDWLYVWDWLVWLFODXQSUDJGHVHPQLILFD LHα=0,010; e) DUHRYDORDUHFDUHQXSRDWHILWHVWDW SHQWUXQLFLXQSUDJGHVHPQLILFD LH 9)

)UHFYHQ HOHUHGXVHODXQLWDWHVHFDOFXOHD] 

a) vQFD]XOUHSDUWL LLORUSHLQWHUYDOHQHHJDOHSHQWUXDVLJXUDUHDFRPSDUDELOLW LLIUHFYHQ HORU b) SHQWUXDVWXGLDSRQGHUHDXQLW LORUVWDWLVWLFHGLQWU-RJUXS vQWRWDOXOFROHFWLYLW LLVWXGLDWH c) pentru a detHUPLQD QXP UXO XQLW LORU FDUH DX YDORDUHD LQGLYLGXDO  VLWXDW  SkQ  OD XQ anumit nivel al caracteristicii; d) SHQWUXDVWXGLDVWUXFWXUDXQHLVHULLGHGLVWULEX LH e) SHQWUX D VWXGLD QXP UXO XQLW LORU VWDWLVWLFH FDU DX YDORULOH LQGLYLGXDOH VLWXDWH SHVWH XQ anumit nivel al caracteristicii. 10) 3UHVXSXQHP F SHUHFKL

12

VXPD

∑ ( yi − y i )

i =1

a) b) c) d) e)

 vQ XUPD DSOLF ULL PHWRGHL GH UHJUHVLH OLQLDU  V

2

S WUDWHORU

DEDWHULORU

YD

lorilor

-a calculat, pentru 12 valori empirice de la valorile ajustate

= 0,507 . Atunci, s e2 HVWLPDWRUXOGLVSHUVLHLDEDWHULORUvQWkPSO

ε, este:

WRDUH

0,0507; 0,04225; 0,04609; 0,2252; 0,2055.

11) 'LVSHUVLDFDOFXODW

ID

GHRFRQVWDQW 

a este, comparatLYFXGLVSHUVLDFDOFXODW

a) de aRULPDLPLF  b) mai mare de a2 ori; c) PDLPLF FXS WUDWXOGLVWDQ HLGLQWUHPHGLHúLFRQVWDQWDa; d) mai mare cu a2; e) PDLPDUHFXS WUDWXOGLVWDQ HLGLQWUHPHGLHúLFRQVWDQWDa.

ID

GHPHGLH

12) 2YDULDELO DOHDWRDUH;DUHRGLVWULEX LHQRUPDO care P ( x ≤ x 0 ) = 0,8413 este: a) 54,23; b) 45,77; c) 53; d) 59; e) 46. 13) 3HQWUX YHULILFDUHD QRUPDOLW variabilei χ2 are forma: r

2 a) χ calc =

b) χ

∑ (n i =1

2 c) χ calc

, pentru

LL UHSDUWL LLORU HPSLULFH XWLOL]kQG WHVWXO

χ2  YDORDUHD FDOFXODW

 D

− npi )

2

i

npi

; 2

 n − npi   ; = ∑  i npi  i =1  r n − npi =∑ i ; npi i =1 r

2 calc

GHPHGLHúLGLVSHUVLH9DORUHD[0

r

2 d) χ calc =∑ i =1 r

2 e) χ calc =∑ i =1

ni − npi ; (npi )2

(ni − npi )2 . npi

14) ÌQ FDGUXO PHWRGHORU JHQHUDOH GH DERUGDUH úWLLQ LILF

 D IHQRPHQHORU HFRQRPLFR

-sociale, un loc

LPSRUWDQWvORFXS DEVWUDFWL]DUHDVXFFHVLY LQGXF LDúLGHGXF LD$FHVWHPHWRGH

a) nu pot fi utilizate într-XQ GHPHUV VWDWLVWLF GHRDUHFH RSHUHD]

 FX GDWH FRQFUHWH RE LQXWH

SULQREVHUY ULWRWDOHúLSDU LDOH

b)

VXQWXWLOL]DWHvQVWXGLXOVWDWLVWLFDOIHQRPHQHORUGHPDV vQWUXFkWSHQWUXDVHUH LQHQXPD

i

FHHD FH HVWH HVHQ LDO úL WLSLF WUHEXLH V  VH HOLPLQH DVSHFWHOH vQWkPSO WRDUH úL QHHVHQ LDOH GH OD SDUWLFXODUXO RE LQXW SULQ REVHUYDUHD vQUHJLVWUDUHD  YDORULORU HPSLULFH VH WUHFH

inductiv spre ceea ce este în general valabil pentru întregul ansamblu, etc.; c)

QXSRWILXWLOL]DWHGHVWDWLVWLF vQWUXFkWvQRULFHFHUFHWDUHQXVHSRUQHúWHGHODLSRWH]HFDUH

ar trebui verificate; d) e)

VXQWXWLOL]DWHQXPDLvQVWXGLXOUHSDUWL LLORUVWDWLVWLFHXQL úLPXOWLGLPHQVLRQDOH VXQWXWLOL]DWHQXPDLGDF VXQWRUJDQL]DWHVRQGDMH

statistice.

15) Analizate la nivelul unui ansamblu, formele individuale de manifestare ale fenomenelor de PDV  SDU DVHP Q WRDUH vQWUH HOH ILLQG JHQHUDWH GH FDX]H HVHQ LDOH FRPXQH VH VXSXQ DFHOHLDúL OHJLGHDSDUL LHúLGH]YROWDUH$FHDVW OHJHDF LRQHD] 

a) stDWLFFkQGIHQRPHQHOHVXQWFLUFXPVFULVHODDFHODúLVSD LXúLDFHHDúLIRUP

GHRUJDQL]DUH

GDUvQFRQGL LLGHWLPSGLIHULWH

b) GLQDPLFFkQGIHQRPHQHOHVXQWGHOLPLWDWHvQDFHODúLVSD LXVXQWvQUHJLVWUDWHvQDFHOHDúLXQLW LGHWLPS c) atât static, când fenomenHOH GH PDV  VXQWFLUFXPVFULVHvQDFHOHDúL FRQGL LLGH WLPS FkWúL GLQDPLF FkQG IHQRPHQHOH VXQW GHOLPLWDWH vQ VSD LX úL RUJDQL]DWRULF GDU vQUHJLVWUDWH vQ XQLW

LGHWLPSGLIHULWH

d) exclusiv dinamic, când se face ipoteza c fenomenele au fost înregistrate lD DFHOHDúL PRPHQWHGHWLPSYDULDELOHILLQGVSD LXOúLIRUPDGHRUJDQL]DUH

e)

VWDWLF GHRDUHFH GLQDPLF QX SRDWH DF LRQD vQWUXFkW UHOD LLOH GH FDX]DOLWDWH GLQWUH

fenomenele sociale nu au un caracter dinamic.

16) 2 YDULDELO

 DOHDWRDUH ; GLVWULEXLW  QRUPDO úL FX REOLFLWDWH PRGHUDW DUH  GLQ YDORUL VLWXDWH

vQ FHQWUXOGLVWULEX LHLFXSULQVHvQWUH úLFRHILFLHQWXOGHYDULD LHHVWH LDUYDORDUHD PRGDO $VLPHWULDHVWH

a) PRGHUDWSR]LWLY  b) PRGHUDWQHJDWLY  c) HJDO FX]HUR d) nu se poate preciza felXOúLP ULPHDDVLPHWULHL e) HJDO FXDPSOLWXGLQHDVHPLLQWHUTXDUWLOLF  17) $EDWHUHDPHGLHLQWHUTXDUWLOLF

VHFDOFXOHD] FD

a) Q3 − Q1 ; Q − Q1 b) 3 ; 2 Q − Q1 c) 2 ; 2 (Q3 − Me )+ (Q1 − Me ) ; d) 2 e) 2(Q2 − Q1 ). 18) Pentru dou

YDULDELOHVWDWLVWLFHDF URUWHQGLQ

SULQ HFXD LD GH UHJUHVLH

DGHSHQGHQ HLVWDWLVWLFH\

I[ DIRVWPRGHODW 

y = 25 − 0,7 x , se cunosc dispersiile σ 2x = 2603,04  úL σ 2y = 1896,6 .

&RHILFLHQWXOGHFRUHOD LHDUHYDORDUHD

a) b) c) d) e)

0,82; 0,96; -0,96; -0,82; -0,597.

19) 3UREDELOLWDWHDFDYDORULOHXQHLYDULDELOHDOHDWRDUHQRUPDOHV RULDEDWHUHDPHGLHS WUDWLF GHRSDUWHúLGHDOWDID

a) b) c) d) e)

VHVLWXH]HODRGLVWDQ

5%; 0,05%; 2,5%; 47,50%; 97,5%.

20) Un grup de  DQJDMD L HVWHDOHV GLQWU-R FRPSDQLH vQ VFRSXO GH D GHWHUPLQD QXP VXV LQVLQGLFDWXOFRPSDQLHL3UHVXSXQHPF GLQWR LDQJDMD LLVXV LQVLQGLFDWXO 3UREDELOLWDWHDFDPDLSX LQGHDQJDMD LGLQFHLV VXV LQ VLQGLFDWXOHVWH

a) b) c) d) e)

PDLPDUHGH

GHPHGLHHVWH

61,78%; 38,22%; 83,28%; 21,50%; 16,72%.

UXO FHORUFDUH

21) 'DF

YDORULOHXQHLFDUDFWHULVWLFLVXQWPLFúRUDWHFXFRQVWDQWD

a) b) c) d) e)

a, atunci dispersia noii serii este:

HJDO FXGLVSHUVLDVHULHLLQL LDOH PDLPDUHGHFkWGLVSHUVLDVHULHLLQL LDOHFXS WUDWXOGLVWDQ HLGLQWUHPHGLHúLFRQ

stanta a;

PDLPLF GHFkWGLVSHUVLDVHULHLLQL LDOHFXS WUDWXOGLQWUHPHGLHúLFRQVWDQWD

a;

PDLPLF GHFkWGLVSHUVLDVHULHLLQ LDOHFXFRQVWDQWD

a; PDLPDUHGHFkWGLVSHUVLDVHULHLLQL LDOHFXFRQVWDQWDa.

22) Patronul unei firme ce vinde autoturisme presupune F  UHOD LD GLQWUH QXP UXO GH DXWRWXULVPH vândute într-R]L< úLQXP UXOGHYkQ] WRULFHOXFUHD] vQVDORQXOGHSUH]HQWDUHúLvQVHFWRUXOGH SXEOLFLWDWH D SURGXVXOXL ;  SRDWH IL PRGHODW  SULQWU-R OLQLH GUHDSW  'DWHOH FXOHVH SHQWUX  ]LOH sunt: xi yi

6 20

6 18

4 10

2 6

3 11

Atunci: a)

OHJ WXUD

GLQWUH

FHOH

GRX 

YDULDELOH

SRDWH

IL

PRGHODW 

SULQ

HFXD LD

GH

UHJUHVLH

yˆ = 0,125 + 3,125 x ;

b) FRYDULDQ DGLQWUH[úL\DUDW ROHJ WXU SXWHUQLF LQYHUV vQWUHFHOHGRX YDULDELOH c) panta linie drepte de regresiHHVWHLDUSXQFWXOGHLQWHUFHS LHFXD[D2\HVWH-0,125; d) FRHILFLHQWXOGHFRUHOD LHHVWHVHPQLILFDWLYVWDWLVWLFSHQWUXRSUREDELOLWDWHGH e)

DSUR[LPDWLY  GLQ YDULD LD YDORULORU FDUDFWHULVWLFLL < vQ MXUXO PHGLHL

y este explLFDW



SULQOHJ WXUDOLQLDU GLQWUH;úL<

23) 3HQWUX LGHQWLILFDUHD úL GLPLQXDUHD HURULORU GH REVHUYDUH HVWH QHFHVDU FRQWUROXO GDWHORU FXOHVH Acest control nu presupune: a)

FDSULQVRQGDMV VHUHIDF DQXPLWHFDOFXOHGHRE LQHUHDYDORULORUXQRULQGLFDWRUL

însFULúL

în formulare; b)

FDODFHQWUHOHGHSUHOXFUDUHV VHYHULILFHGDF DXVRVLWWRDWHIRUPXODUHOHFXWRDWHUXEULFLOH

completate; c)

XWLOL]DUHDXQRUPRGHOHGHYHULILFDUHDLSRWH]HORUVWDWLVWLFHúLDSOLFDUHGHWHVWHGHYHULILFDUH DVHPQLILFD LLORUYDORULORULQGL

catorilor;

d) e)

HIHFWXDUHDGHFRPSDU UL VXEQLFLRIRUP XWLOL]DUHDXQRUSURJUDPHLQIRUPDWLFHVSHFLDOHODERUDWH

24) Pentru calculul mediei aritmetice într-RVHULHQXPHULF GHGLVWULEX LHGHIUHFYHQ HSHLQWHUYDOHVH iau în considerare: a) limitele inferioare; b) mijloDFHOHLQWHUYDOHORULQGLIHUHQWGHUHSDUWL LLOHGLQLQWHUYDOH c) limitele superioare; d) OLPLWHOHVXSHULRDUHGDF IUHFYHQ HOHVXQWUHODWLYH e) PLMORDFHOHLQWHUYDOHORUvQLSRWH]DDSULRULF DQRUPDOLW LLUHSDUWL LLORUGLQLQWHUYDOH

25) &RHILFLHQWXO GH GHWHUPLQD LH R2, calculat pe baza regulii de adunare a dispersiilor, are întotdeauna valoarea: a) R 2 = 1 ;

b) R 2 ∈[0,1] ; c) R 2 ∈ (0,1);

d) R 2 ≤ 35% ; e) R 2 > 50% . 26) Inegalitatea dintre abaterile standard ale unei vaULDELOH ; QRUPDO UHSDUWL]DWH vQ SRSXOD LLOH VWDWLVWLFH    GH DFHODúL YROXP úL DFHHDúL PHGLH

x , σ 1 > σ 2 > σ 3  HVWH YL]XDOL]DW

varianta:

a)

b) 3

3 2

1 2

1

c)

d) 1

2 3 2

1

3

e)

2

1 3

 vQ

27) 3HQWUX FHOH GRX

 YDULDELOH VWDWLVWLFH vQWUH FDUH H[LVW  R GHSHQGHQ

 OLQLDU  V

-au înregistrat o

PXO LPHGHGDWHVWDWLVWLFHÌQXUPDSUHOXFU ULLDFHVWRUDV DXRE LQXWLQGLFDWRULL

-

∑ y = 968; ∑ x = 183,91; ∑ y ∑ x y = 19485,9; i = 1,11 i

i

i

2 i

= 96299,6;

∑x

2 i

= 4099,8;

i

'HVSUHGHSHQGHQ DGLQWUHFHOHGRX YDULDELOHVHSRDWHDILUPD

a) b) c) d) e)

GHSHQGHQ DHVWHLQYHUV  HVWLPDUHDFRYDULDQ HLHVWH

yˆ = 88 + 3,2213 x ; ˆ = 34,14 + 3,2213 x . HFXD LDGHUHJUHVLHHVWH y HFXD LDGHUHJUHVLHHVWH

28) 3HQWUXXUP

WRDUHOHYDORULDOHXQHLYDULDELOHDOHDWRDUH;

{7,11,1414,12,20}

a) b) c) d) e)

cov(x,y)=130,82;

FRHILFLHQWXOGHFRUHOD LHHVWH

FDUHGLQXUP WRDUHOHDILUPD LLHVWHDGHY UDW 

Me = 14; 0R

úL0H



x = 13 úL0H  x = 14 úL0R ; x = Mo = Me = 14 .

29) &RQVLGHUkQGXUP

WRDUHOHYDORULDOHXQHLYDULDELOHDOHDWRDUH;

{5,7,4,5,20,6,4} , indicatorul cel

PDLSRWULYLWSHQWUXDFDUDFWHUL]DWHQGLQ DFHQWUDO HVWH

a) PHGLDDUPRQLF  b) media; c) modul; d) PHGLDS WUDWLF  e) mediana. 30) Un meteoURORJ GRUHúWH V

 úWLH vQ FH P VXU  SUHYL]LXQLOH VDOH VXQW IRQGDWH ÌQ DFHVW VHQV HO

DQDOL]HD] YDULDELODQXPLW SUHYL]LXQH$FHDVW YDULDELO LDGRX YDORUL

0, daca previziunea a fost incorecta x= 1, daca previziunea este corecta 0HWHRURORJXOUHVSHFWLYDXUP ULWSUHYL]LXQLOHHIHFWXDWHvQFHOH GH]LOHFRQVHFXWLYHúLDFRQVWDWDW F DXIRVWFRUHFWHLDUDXIRVWLQFRUHFWH3HED]DDFHVWRUGDWHHOWHVWHD] LSRWH]D

H0SURSRU LDSUHYL]LXQLORUHIHFWXDWHúLFRUHFWHHVWHGHúL H1SURSRU LDHVWHGLIHULW GHúL cu testul χ2:

χ =∑ 2

a)

=

c) d) e)

2

=

= 203,9 > χ 12;0,95 = 3,84

25 ⇒ se respinge ipoteza H0;

χ =∑ =

+ frecventa teoretica)

frecventa teoretica

(32 + 25)2 + (18 + 25)2

2

b)

(frecventelor observate

(frecventelor observate

- frecventa teoretica )

2

frecventa teoretica

(32 − 25)2 + (18 − 25)2

=

= 3,92 > χ 12;0,95 = 3,84

25 ⇒ se respinge ipoteza H0;

χ2vQYDULDQWDE úLVHDOHJHDWXQFLLSRWH]D+0; 2 χ vQYDULDQWDD úLVHDOHJHDWXQci ipoteza H1;

VHFDOFXOHD]  VHFDOFXOHD]

 (frecventelor observate)2  = χ = ∑  ∑ frecventelor teoretice  2

32 2 + 18 2 = = 269,6 > χ 12;0,95 = 3,84 25 + 25 ⇒ se respinge ipoteza H0. 31) 1RWHOH RE LQXWH GH  VWXGHQ L GLQ DFHHDúL JUXS

 vQ VHVLXQHD GH YDU  OD SDWUX GLVFLSOLQH VH

SUH]LQW DVWIHO

1XPHúL

prenume A.B. C.D. E.F. G.H. M.V.

DISCIPLINA NR. 2 NR. 3 6 7 7 9 8 8 9 10 7 4

NR. 1 9 6 7 10 5

3HQWUX FDUDFWHUL]DUHD GLVLPLODULW

NR. 4 8 9 6 8 5

LL VWXGHQ LORU GXS  QRWHOH RE LQXWH VH FDOFXOHD]  PDWULFHD

GLVWDQ HORUDEVROXWH$FHDVWDHVWH

a)

AB AB 0 CD 7 EF 7 GH 7 MV 11

CD 7 0 6 8 10

EF 7 6 0 8 8

GH MV 7 11 8 10 8 8 0 15 15 0

b)

AB AB 0 CD 7 EF 7 GH 7 MV 0

CD 7 0 6 0 8

EF 7 6 0 8 10

GH 7 0 8 0 15

MV 0 8 10 15 0

c) NR1 NR2 NR3 NR4

NR1 NR2 NR3 NR4 0 7 7 11 7 0 6 8 7 6 0 15 11 8 15 0 e) AB CD EF GH MV

AB 0 -7 -7 11 7

d)

CD -7 0 -6 8 -10

EF -7 -6 0 8 8

AB NR1 0 NR2 7 NR3 7 NR4 11

CD 7 0 6 10

GH 11 8 8 0 15

MV 7 -10 8 15 0

EF 7 6 0 8

GH 7 8 8 0

MV 11 10 8 15

TESTUL 9

1)

ÌQ VWXGLXO UHSDUWL LHL QRUPDOH VH IRORVHúWH úL QR LXQHD  UHSDUWL LHL

-α) - punct percentilic α ∈[0,1] al

N(0,1). Acesta:

a. este valoarea Cα pentru care Φ( Cα ) = 1 − α ; b. este cuantila de ordin 1-α; c. este cuantila de ordin α; d. este cuantila de ordin

1 ; α

e. este valoarea pentru care Φ(Cα ) = 1 + α . 2)

'LVSHUVLDXQHLVXPHGHYDULDELOHQRWDW 

σ 2x

1 + x2 + ..+ x n

: n

a)

HVWH HJDO  FX VXPD GLVSHUVLLORU YDULDELOHORU H[LVW RGHSHQGHQ

b)

∑ σ 2xi

GDF  vQWUH YDULDELOHOH

x1, x2, …, xn

i =1

OLQLDU 

HVWHHJDO FXVXPDGLVSHUVLLORUYDULDELOHORUPDMRUDW FXGXEOXOVXPHLFRYDULDQ HORUGLQWUH

n

YDULDELOHOXDWHVXFFHVLYGRX FkWHGRX 

∑σ

i =1

2 xi

n

+ 2∑ ∑ Cov ( x i , x j ) ; i =1 j > i

c) HVWHHJDO FXVXPDFRYDULDQ HORUGLQWUHYDULDELOHOXDWHVXFFHVLYGRX FkWHGRX d) nu se poate calcula; e) HVWHOLSVLW GHVHQVGHRDUHFHvQSUDFWLF QXVHSRWvQWkOQLDVWIHOGHFD]XUL 3)



'DF  SH ED]D GDWHORU XQHL VHULL VWDWLVWLFH YDORDUHD PHGLH D FDUDFWHULVWLFLL V

-a calculat ca medie

DUPRQLF DWXQFLvQFDOFXOXOGLVSHUVLHLSHQWUXFDUDFWHUL]DUHDvPSU úWLHULLVHXWLOL]HD] 

a) PHGLDDULWPHWLF  b) mediaJHRPHWULF  c) PHGLDDUPRQLF  d) PHGLDFURQRORJLF  e) mediana; f) PHGLDS WUDWLF  g) cuartila a treia. 4)

ÌQUHSUH]HQW ULOHJUDILFHDOHGDWHORUVWDWLVWLFHVHXWLOL]HD] 

a) b)

vQH[FOXVLYLWDWHVFDUDDULWPHWLF 

c)

vQ IXQF LH GH RUGLQXO GH P ULPH DO GDWHORU VFDOD QRPLQDO  RUGLQDO  GH LQWHUYDOH GH

vQ IXQF LH GH RUGLQXO GH P ULPH DO GDWHORU VH XWLOL]HD]  GXS  FD] VFDUD DULWPHWLF  ORJDULWPLF VHPLORJDULWPLF GXEOXORJDULWPLF HWF UDSRDUWHFRQWLQX VDXGLVFUHW 

d) e)

RULFHVFDU QXPDLJUDILFXOV ILHWUDVDWvQWU RULFHVFDU QXPDLJUDILFXOV ILHWUDVDWvQWU

-un sistem de axe rectangulare; -un sistem de axe polare.

5)

5HSDUWL LD PXQFLWRULORU GLQWU R XQLWDWH LQGXVWULDO  GXS  VDODULXO ORU PHGLX OXQDU QHW VH SUH]LQW 

-

astfel: Clase salariale (u.m.) [800; 1000] [1000; 1100] [1100; 1200] [1200; 1300] [1300; 1500]

Nr. persoane 26 33 64 7 10

Procentul muncitorilor cu salariile medii lunare mai mici sau egale cu 1200 u.m. este: a) 64%; b) 45,8%; c) 87,9%; d) 12,1%; e) 23,5%. 6)

6FRSXOXQHLREVHUY ULVWDWLVWLFH

a) b)

vQPRGREOLJDWRULXWUHEXLHV FRUHVSXQG FXVFRSXOFHUFHW ULLVWDWLVWLFHHIHFWXDWH VHSUHFL]HD] vQIXQF LHGHQHFHVLW

LOHVSHFLILFHGHLQIRUPD LLSHQWUXGRPHQLXOvQFDUHVH

RUJDQL]HD] FHUFHWDUHDúLFDUHVHvQFDGUHD] vQVFRSXOJHQHUDODODFHVWHLD

c)

QX WUHEXLH SUHFL]DW GHRDUHFH QX LQIOXHQ HD]  YROXPXO úL FDOLWDWHD GDWHORU QHFHVDUH GHPHUVXOXLúWLLQ LILF

d)

QX WUHEXLH SUHFL]DW GHRDUHFH QX SUH]LQW  LPSRUWDQ

 SHQWUX UH]ROYDUHD SUDFWLF  D XQRU

SUREOHPHFXPDUILGHOLPLWDUHDRELHFWXOXLGHREVHUYDUHGHILQLUHDXQLW

stabilirea programului propriu-]LVDOREVHUY e)

LORUGHREVHUYDUH

ULL

WUHEXLH FODU SUHFL]DW GHRDUHFH vQ IXQF LH GH DFHVWD VH UHDOL]HD]  QXPDL LQVWUXLUHD

personalului care culege datele. ÌQ FRQFHS LD GH DVW ]L VWDWLVWLFD IDFH SDUWH GLQ FDGUXO úWLLQ HORU FDUH VWXGLD]  VXE DVSHFW

cantitatiYIHQRPHQHOHúLSURFHVHOHvQWU-RYL]LXQHVLVWHPLF

ODQLYHOPLFURúLPDFURHFRQRPLF LQkQG

VHDPDGHGLQDPLVPXOVWUXFWXULORUH[LVWHQWHúLGHIDFWRULLFDUHDF LRQHD] YDULDELOvQWLPSúLVSD LX  ÌQFRQVHFLQ

VFRSXOXQXLGHPHUVVWDWLVWLFHVWH

a) excluVLYGHFXQRDúWHUHDIHQRPHQHORUúLSURFHVHORULQYHVWLJDWH b) GHFXQRDúWHUHúLIXQGDPHQWDUHDYDULDQWHORUGHFL]LLORUGHDF LXQH c) GH FXQRDúWHUH GH GHVSULQGHUHD OHJLW LORU VXE FDUH VH PDQLIHVW  IHQRPHQHOH úL SURFHVHOH LQYHVWLJDWHúLGHIXQGDPHQWDUHDDFWLYLW

d) e) 8)

LLPDQDJHULDOH

GHFRQVHPQDUHDPDQLIHVW ULLIHQRPHQHORULQYHVWLJDWHODXQPRPHQWGDW VLPLODUFXFHODOXQHLDFWLYLW

LFRQWDELOH

3HQWUXDvQ HOHJHFDUDFWHUXODFHVWRUIHQRPHQHWUHEXLHSRUQLWGHOD

a) b) c) d) e)

natura raporturilor de cauzalitate a acestora; scopXOFHUFHW ULL VFRSXOREVHUY ULL

prelucrarea datelor culese; identitatea formelor lor individuale de manifestare.

9)

8QLW

LOHFRPSOH[HGHREVHUYDUH

a) VXQWUH]XOWDWHDOHRUJDQL] ULLVRFLDOHúLHFRQRPLFHDSRSXOD LHLFROHFWLYLW LL VWDWLVWLFH b) pot fi de exemplu: angajatul într-R vQWUHSULQGHUH MXF WRUXO vQWU-R HFKLS  GH IRWEDO persoana unei familii; c) VXQW QXPDL XQLW LOH UDSRUWRDUH FDUH SRWULYLW OHJLVOD LHL vQ YLJRDUH LQIRUPHD]  VLVWHPDWLF LLXQLW

DVXSUDDFWLYLW

d)

LORUDIODWHvQVWUXFWXUDORURJDQL]DWRULF 

VXQWHOHPHQWHOHVLPSOHFRQVWLWXWLYHDOHSRSXOD LHLVWDWLVWLFHFDUHVXQWGLVSXVHV U VSXQG  ODvQWUHE ULOHGLQFKHVWLRQDUGHH[HPSOXVWXGHQWXOSHUVRDQDFXGUHSWGHYRWHWF 

e)

VXQWGHWLSXOPXO LPHDvQWUHSULQGHULORUPLFLúLPLMORFLLPXO LPHDF V

10) 3UHFL]D LúLDUJXPHQWD LGDF a) b) c) d) e)

toriilor,etc.

DILUPD LD³RULFHQXP UHVWHRGDW VWDWLVWLF ´HVWH

DGHY UDW  IDOV  HVWHDGHY UDW GDF QXP UXOHVWHQDWXUDO HVWHDGHY UDW GHRDUHFHVWDWLVWLFDVWXGLD] IHQRPHQHOHGHPDV GLQSXQFWGHYHGHUHFDQWLWDWLY QX HVWH DGHY UDW  GHRDUHFH VWDWLVWLFD VWXGLD]  úL YDULDELOH DOH F URU YDULDQWH VXQW

nenumerice. 11) /D H[DPHQXO GH %D]HOH 6WDWLVWLFLL GLQ  SULPLL  VWXGHQ L GLQ FDWDORJXO JUXSHL  DXRE LQXWXUP WRDUHOHQRWH

Nr. crt Nota

1 10

2 7

3 4

4 8

5 9

6 9

7 7

8 3

9 6

10 2

Datele prezentat în tabel sunt: a) b) c) d) e)

individuale; agregate; de stoc; de flux; grupate.

12) 0HGLDDULWPHWLF

∑ (xi − x) n

a)

HVWHDFHDYDORDUHDQXPHULF DYDULDELOHLVWXGLDWHFDUHPLQLPL]HD] 

2

;

i =1

b) max x i − x ; n

c)

∑

i , j =1 i≠ j

∑ (x i − x ) n

d)

xi − x x j − x ; 3

;

i =1 n

∑ (xi − x )(x j − x )

e)

i , j =1

σx

.

13) 3HQWUX

GRX  VHULL GH GLVWULEX LH GH IUHFYHQ H LQGLFDWRUXO ³DPSOLWXGLQHD vPSU úWLHULL´ HVWH

FRPSDUDELOGDF 

a) b) c) d) e) 14)

FHOHGRX VHULLVHUHIHU ODDFHHDúLFDUDFWHULVWLF  FHOHGRX VHULLVHUHIHU ODDFHHDúLFROHFWLYLWDWH FHOHGRX VHULLVHUHIHU ODFDUDFWHULVWLFLGLIHULWHGDUFXDFHHDúLXQLWDWHGHP VXU  FHOHGRX VHULLDXDFHODúLJUDGGHDVLPHWULH FHOHGRX VHULLVHUHIHU ODFROHFWLYLW

LGHDFFHODúLYROXP

3XQFWXO$VHPQLILF 

 x ’− x  ;  σ 

a) P ( X < x ’) = Φ 

1,0

A 0,5

x − 3σ

-3

x − 2σ

x −σ

x

-2

-1

0

x’ x + σ 1

x + 2σ

2

x + 3σ

3

 x ’− x  ;  σ 

b) P ( X > x ’) = Φ 

 x ’− x  ;  σ 

c) P ( X = x ’) = Φ 

 x ’− x  ;  σ 

d) P ( X < x ’) > Φ 

 x ’− x  .  σ 

e) P ( X < x ’) < Φ 

15)  GH HOHYL GLQ GRX

 RUDúH SDUWLFLS  OD XQ FRQFXUV GH FXOWXU  JHQHUDO  &HL  GH HOHYL GLQ

SULPXORUDúRE LQXQSXQFWDMPHGLXGHSXQFWHFXXQFRHILFLHQWGHYDULD LHGHLDUFHLGLQ DO GRLOHD RUDú RE LQ XQ SXQFWDM PHGLX GH  SXQFWH FX R DEDWHUH PHGLH S WUDWLF  GH  SXQFWH )DFWRUXOGHJUXSDUHRUDúXO FRQWULEXLHODYDULD LDSXQFWDMHORURE LQXWHGHHOHYLvQSURSRU LHGH

a) 23,46%; b) 10,28%; c) 76,54%;

d) 48,44%; e) 24,48%. 16) 3ULQFLSDOD SURSULHWDWH D IHQRPHQHORU GH PDV OHJHD GH DSDUL LH D DFHVWRUD VH PDQLIHVW DFHDVW

FDX]

IHQRPHQHOHGHPDV

 HVWH YDULDELOLWDWHD vQ WLPS úL vQ VSD LX úL

 FD WHQGLQ

 úL QX vQ ILHFDUH FD] vQ SDUWH 'LQ

VXQWQXPLWHúLIHQRPHQHQHGHWHUPLQLVWHVDXVWRFKDVWLFH

LDULQWHUSUHWDUHDúLDQDOL]DORUWUHEXLHV

FDG

VXELQFLGHQ DQXPHUHORUPDUL3RWULYLWDFHVWHL

legi: a)

YDULD LLOH vQWkPSO WRDUH GH OD WHQGLQ D JHQHUDO  SURYRFDWH GHIDFWRULL RELHFWLYL úL HVHQ LDOL VHFRPSHQVHD] UHFLSURFGDF H[LVW XQQXP UPDUHGHFD]XULLQGLYLGXDOH

b) c)

QXPDLvQWkPSO WRUYDULD LLOHGHODWHQGLQ DJHQHUDO VHFRPSHQVHD]  QXHVWHSRVLELO WUHFHUHDGHODQXPHURDVHOHGDWHLQGLYLGXDOHODLQGLFDWRULVLQWHWLFLVSHFLILFL

ansamblului investigat; d)

YDULD LLOH vQWkPSO WRDUH GH OD WHQGLQ D JHQHUDO  SURYRFDWH GHIDFWRULLDOHDWRUL GH LQIOXHQ

se compeQVHD] HVHQ

e)

OXDWHvQVWXGLX

WHQGLQ DGHPDQLIHVWDUHWUHEXLHV VHYHULILFHODQLYHOXOILHF UHLXQLW

17) 3URFHVXOGHFXQRDúWHUHVWDWLVWLF a) b) c) d) e)



 UHFLSURF GDF  H[LVW  XQ QXP U PDUH GH FD]XUL LQGLYLGXDOH GH DFHHDúL LGHREVHUYDUH

VHvQFKHLHFX

observarea total VDXSDU LDO DIHQRPHQHORUGHPDV prelucrarea datelor înregistrate; interpretarea rezultatelor; prezentarea datelor în tabele, serii sau grafice;

GHOLPLWDWH

DQDOL]D úL LQWHUSUHWDUHD UH]XOWDWHORU úL FX IRUPXODUHD FRQFOX]LLORU VWDWLVWLFH FDUH

obligatoriu WUHEXLH V în viitor.

 FXSULQG  YDULDQWH SUREDELOH GH DSDUL LH DOH DFHORUDúL IHQRPHQH

18) 3HQWUX VWDELOLUHD JUHXW LL VSHFLILFH D SURGXF LHL UHEXWDWH vQWU-un lot de volum N=3000 produse s-DX SUHOHYDW vQWkPSO WRU úL QHUHSHWDW  GH SURGXVH ÌQ XUPD HIHFWX ULL controlului acestora 9 produse au fost depistate rebuturi. Pentru o probabilitate de 0,975 (zα=1,96) procentul de rebut estimat pentru întregul lot este: a) (0,015; 0,06); b) (0,012; 0,048; c) (0,15; 0,20); d) (0,02; 0,05); e) (0,18; 0,25). 19) 2PHGLHFDOFXODW

GLQWU

-un úLUGHYDORULLQGLYLGXDOHHVWHUHSUH]HQWDWLY

GDF 

a) s-DXXWLOL]DWIUHFYHQ HOHDEVROXWHGHDSDUL LHDYDORULORULQGLYLGXDOH b) úLUXOGHYDORULLQGLYLGXDOHHVWHRPRJHQ c) XQXOGLQFRHILFLHQ LLGHDVLPHWULHLDYDORULvQLQWHUYDOXO>-1, 1]; d) úLUXOGHYDORULHVWHVtructurat pe intervale de grupare egale; e) s-DXWLOL]DWPHGLDDULWPHWLF 

20) &DUHHVWHUHOD LDFRUHFW a) ryx = b) ryx =

xy − x ⋅ y ; σ xσ y

∑ (x − x )(y − y)

c) ryx = b d) ryx =

GHFDOFXODFRHILFLHQWXOXLGHFRUHOD LHOLQLDU VLPSO 

nσ x σ y

;

σx ; σy n∑ xy − ∑ x ∑ y  n x − ( x ) n y − ( y) ∑   ∑ ∑   ∑ 2 

2

∑ ( yi − Y ) 1− 2 ∑ ( yi − y)

2

2

;

2

e) ryx =

.

21) 2 FRPSDQLH FDUH SURGXFH XQ QRX WLS GH vQJU

ú PkQW DJULFRO HVWH LQWHUHVDW  GH VWXGLHUHD

FRUHOD LHL GLQWUH SURGXF LD GH URúLL <  úL FDQWLWDWHD GH vQJU ú PkQW DSOLFDW ;  2 VXSUDID GLYL]DW  vQ RSW SDUFHOH GH P ULPL HJDOH SH FDUH VXQW DSOLFDWH FDQWLW 3URGXF LLOH GH URúLL NJ  úL FDQWLW

 HVWH

L GLIHULWH GH vQJU ú PkQW

LOH GH vQJU ú PkQW DSOLFDW NJ  vQUHJLVWUDWH SHQWUX ILHFDUH

SDUFHO VXQW

xi yi

1 25

&RHILFLHQWXOGHFRUHOD LHDUH

a) b) c) d) e)

1,5 31

2 27

2,5 28

3 36

3,5 35

4 32

4,5 34

valoarea:

0,37; 0,98; 0,73; -0,84; 1,00.

22) Într-XQ úLU GH YDORUL LQGLYLGXDOH UHIHULWRDUH OD DFHHDúL YDULDELO

 úL REVHUYDW  vQWU R SRSXOD LH

-

VWDWLVWLF GHOLPLWDW vQWLPSúLvQVSD LXYDORDUHDPRGDO HVWH

a) YDORDUHDLQGLYLGXDO SR]LWLY FHDPDLPDUH b) valoaUHDLQGLYLGXDO QHJDWLY PD[LP vQYDORDUHDEVROXW  c) YDORDUHDLQGLYLGXDO SR]LWLY VDXQHJDWLY FXFHDPDLPDUHIUHFYHQ GHDSDUL LH d) DFHDYDORDUHFDUHvQUHJLVWUHD] FHDPDLPDUHDEDWHUHDEVROXW ID GHPHGLH e) YDORDUHDFDUHPLQLPL]HD] GLVSHUVLD 23) PentrXDQDOL]DGHSHQGHQ HORUVWDWLVWLFHGLQWUHYDULDELOHPHWRGDJUDILF a) b) c) d) e)

LQWHUSUHWDUHDLQWHQVLW

SHUPLWH

LLOHJ WXULORUGLQWUHYDULDELOH

FRQVWDWDUHDH[LVWHQ HLOHJ WXULLVWDWLVWLFH LGHQWLILFDUHDH[LVWHQ HLGLUHF LHLúLIRUPHLOHJ WXULLGLQWUHGRX YDULDELOH

statistice;

HVWLPDUHDSDUDPHWULORUIXQF LHLGHUHJUHVLH HVWLPDUHDUDSRUWXOXLGHFRUHOD LHGDUQXúLDFRHILFLHQWXOXLGHFRUHOD LHVDXGHDVRFLHUH

24) )LHRVHULHVWDWLVWLF IRUPDW GLQQ SYDORULLQGLYLGXDOH[1, x2, …, xnúL51, R2, …, Rn rangurile ordonate ale celor n valori. Mediana (Me) este:

1 n ∑ xi ; n i =1 1 b) F ( Me) = ; 2 c) Me = R p+1 ;

a) Me =

 n + 1

d) Me = x  ;  2 

n   n + 1 x  + x 2   2  e) Me = . 2 25) Într-RVHULHGHUHSDUWL LHGHLQWHUYDOHLQWHUYDOXOPHGLDQHVWH a) acela care vPSDUWHvQGRX

S U LHJDOHQXP UXOGHLQWHUYDOHDOHVHULHL

r

∑ ni

b)

FRUHVSXQ] WRUSULPHLIUHFYHQ HFXPXODWHFDUHGHS úHúWH

i =1

;

2 r

∑ ni + 1

c)

FRUHVSXQ] WRUSULPHLIUHFYHQ HFXPXODWHFDUHGHS úHúWH

d) e)

FRUHVSXQ] WRULQWHUYDOXOXLFXIUHFYHQ DFHDPDLPDUH

26) 'DF

i =1

2

;

FRUHVSXQ] WRULQWHUYDOXOXLvQFDUHHVWHSODVDW PHGLD

 vQWU RVHULHGHUHSDUWL LHGHIUHFYHQ H

-

FXPXODWH FUHVF WRU

(Fa i )i =1,r

x i    ni  i =1,r

r

,

∑ ni

= n VHFDOFXOHD]

i =1

 úL IUHFYHQ HOH FXPXODWH GHVFUHVF WRU

(Fd i )i =1,r , atunci între ele

H[LVW UHOD LD

a) Fai + Fd i = n ; b) Fai = Fd i + n ; c) Fai + Fd ( i +1) = n ; d) Fai + Fd i = 100 ; e) Fai + Fd (i +1) = 100 . 27) )UHFYHQ DDEVROXW

FXPXODW FUHVF WRUDXOWLPHLJUXSHHVWHvQWRWGHXQDHJDO FX

a) QXP UXOGHXQLW LGLQFROHFWLYLWDWH b) QXP UXOGHXQLW LGLQXOWLPDJUXS  c) 100%; d) IUHFYHQ DDEVROXW FXPXODW GHVFUHVF WRUDXOWLPHLJUXSH e) IUHFYHQ DDEVROXW DXOWLPHLJUXSHSOXVYROXPXOFROHFWLYLW

LL

IUHFYHQ HOH

28) În general, în cadrul

VRFLHW

LL GDU úL vQ QDWXU  IHQRPHQHOH SRW V  DSDU  FD UH]XOWDW DO XQHL

VLQJXUHFDX]HVDXFDUH]XOWDWDOPDLPXOWRUFDX]HFDUHVHPDQLIHVW L]RODWVDXvQLQWHUGHSHQGHQ



vQWUH HOH ÌQ SULPXO FD] VXQW IHQRPHQH XQLYRF GHWHUPLQDWH úL GH UHJXO  HOH VH SUH]LQW  FD IHQRPHQHVLPSOHLGHQWLFHvQWUHHOHGHQXPLWHúLIHQRPHQHWLSLFHÌQFHOGH

-al doilea caz, apar ca

IHQRPHQH PXOWLFDX]DOH DO F URU SURFHV GH IRUPDUH SRDWH V  SUH]LQWH JUDGH GLIHULWH GH FRPSOH[LWDWH FX UHOD LL PXOWLSOH GH LQWHUGHSHQGHQ

 IRUPkQG  vPSUHXQ  XQ DQVDPEOX D F UXL

GLPHQVLXQH úL VWUXFWXU  SRW IL GHOLPLWDWH vQ WLPS vQ VSD LX úL RUJDQL]DWRULF 6WDWLVWLFD VWXGLD] 

fenomenele din: a) b) c) d) e)

primul caz; cazul al doilea; ambele cazuri; DOW FDWHJRULHGHFkWFHOHSUHFL]DWH

cazul al doilea, dar numai cele cuantificabile.

29) 0HGLDDULWPHWLF a) b) c) d) e)

DVXPHLGLQWUHGRX YDULDELOHHVWHHJDO FXVXPDPHGLLORUFHORUGRX YDULDELOHFkQG

FHOHGRX YDULDELOHVHDIO vQWU RUHOD LHGHLQWHUGHSHQGHQ

-



FHOGRX YDULDELOHVHDIO vQWU RUHOD LHGHLQYHUV SURSRU LRQDOLWDWH

-

FHOHGRX YDULDELOHVHUHIHU ODDFHHDúLFROHFWLYLWDWH FHOHGRX YDULDELOHVXQWLQGHSHQGHQWH FHOHGRX YDULDELOHVXQWGLUHFWSURSRU LRQDOH

30) 6WXGLD LXUP WRDUHOHDILUPD LL )HQRPHQHOHGHPDV vQJHQHUDODSDUFDRPXO LPHGHIRUPH individuale diferiWH DSDUHQW I U  QLFL R OHJ WXU  GH OD R IRUP  OD DOWD GDU FDUH DQDOL]DWH FRPSDUDWLYVHFRQVWDW F DXDFHHDúLHVHQ

 $FHDVWDVHH[SOLF vQSULQFLSDOSULQIDSWXOF HOH

VXQW JHQHUDWH GH R VHULH GH FDX]H FRPXQH FDUH VH PDQLIHVW  GH UHJXO  vQ FRQGL LL

diferite; 3) La

IHQRPHQHOH GH PDV  GLQ VRFLHWDWH UHOD LLOH GH PXOWLFDX]DOLWDWH GLUHFW  VDX LQGLUHFW  FDUH OH GHWHUPLQ  IDF LPSRVLELO  FXQRDúWHUHD OHJLORU FDUH OH SURGXF úL JXYHUQHD]  GDF  VH LDX vQ VWXGLX

izolat doar câteva din formele lor de manifestare, ignorând ansamblul din care fac parte; 4) În SUDFWLF IRUPHOHLQGLYLGXDOHGHPDQLIHVWDUHGLIHU GHODRXQLWDWHODDOWDvQIXQF LHGHPRGXOFXP VHDVRFLD] úLVHFRPELQ IDFWRULLGHLQIOXHQ

de manifHVWDUH GLQ FDGUXO DQVDPEOXOXL I

GHQDWXU GLIHULW O VkQGLPSUHVLDF ILHFDUHIRUP 

U  V  H[LVWH R FDX]DOLWDWH FHUW    $QDOL]DWH IRUPHOH

LQGLYLGXDOHGHPDQLIHVWDUHDOHIHQRPHQHORUGHPDV SDUDVHP Q WRDUHvQWUHHOHILLQGJHQHUDWHGH FDX]HHVHQ LDOHFRPXQHVXSXQkQGX VHDFHOHLDúLOHJLGHDSDUL LHúLGH]Y

-

&DUHGLQDILUPD LLOHGHPDLVXVVXQWIDOVH

a) úL b) úL c) úL d) WRDWHFXH[FHS LD  e) nici una.

oltare.

TESTUL 10

1)

3HQWUXYHULILFDUHDQRUPDOLW

LLGLVWULEX LHLHPSLULFHvQWU RFROHFWLYLWDWHGHQXQLW

pe r intHUYDOH GH JUXSDUH GDF  VH XWLOL]HD] valoarea χ2WDEHODUFRUHVSXQ] WRDUHXQXLQXP a) b) c) d) e) 2)

 WHVWXO

χ2 YDORDUHD FDOFXODW

LVLVWHPDWL]DWH

 HVWH FRPSDUDW  FX

UGHJUDGHGHOLEHUWDWHHJDOFX

n-r; n-1; r-1; r-3; n-3.

'LVSHUVLDXQHLUHSDUWL LELQRPLDOHFXS

- probabilitatea succesului, q - probabilitatea insuccesului

úLQQXP UXOGHREVHUYD LLHVWH

a) np; b) nq; c) npq ; d) npq(q-p); e) npq. 3)

&RQVLGHU P XUP WRDUHOH SHUHFKL GH REVHUYD LL SHQWUX YDULDELOHOH ; úL < vQWUH FDUH H[LVW  R GHSHQGHQ

GHIRUPD\

xi yi

I[ 

1 1

4 3

3 3

2 1

5 4

6 7

0 2

6 VHDUDWHFDUHGLQXUP WRDUHOHDILUPD LLHVWHDGHY UDW 

a)

HFXD LDGHUHJUHVLHOLQLDU HVWH

yˆ = 0,536 − 0,821x ;

SHQWUX XQ SUDJ GH VHPQLILFD LH α=0,05, coeficientul de regresie nu este semnificativ statistic; c) intervalul de încredere pentru coeficientul de regresie este (0,243, 1,399); d) HFXD LDGHUHJUHVLHOLQLDU HVWH yˆ = 0,536 + 0,821x ; e) FRHILFLHQWXOGHFRUHOD LHHVWHU -0,92.

b)

4)

3HQWUXRVHULHGHUHSDUWL LHGHIUHFYHQ HFXWHQGLQ

a) b) c) d) e)

GHQRUPDOLWDWHDEDWHUHDPHGLHOLQLDU 

HVWHDSUR[LPDWLYGLQDEDWHUHDLQWHUTXDUWLOLF  HVWHPDLPLF VDXHJDO FX HVWHDSUR[LPDWLYGLQYDORDUHDDEDWHULLPHGLLS WUDWLFH HVWHHJDO FX]HUR FXSULQGHGLQXQLW

LOHVWDWLVWLFHGLQFHQWUXOGLVWULEX LHL

5) Pentru verificarea norPDOLW

χ 2tabelar FRUHVSXQ]

FRPSDU FXYDORDUHD

a) b) c) d) e)

LL UHSDUWL LLORU HPSLULFH XWLOL]kQG WHVWXO

χ2, valoarea χ 2calculat se

WRUXQXLQXP UGHJUDGHGHOLEHUWDWHHJDOFX

QXP UXOXQLW

LORUVWDWLVWLFHGLQFROHFWLYLWDWHPLQXVXQX

QXP UXOXQLW

LORUVWDWLVWLFHGLQFROHFWLYLWDWHPLQXVGRL

QXP UXOLQWHUYDOHORUGHYDULD LHPLQXVXQX

χ2 ;

QXP UXOLQWHUYDOHORUGHYDULD LHPLQXVQXP UXOGHSDUDPHWULDLOHJLLGHUHSDUWL LH

QXP UXO LQWHUYDOHORU GH YDULD LH PLQXV QXP UXO GH SDUDPHWUL DL OHJLL GH UHSDUWL LH

χ2 ,

minus unu. 6)

&DUHGLQXUP WRDUHOHDILUPD LLHVWHDGHY UDW 

a) PHGLDJHRPHWULF VHFDOFXOHD] FDRPHGLHDULWPHWLF DORJDULWPLORUYDORULORULQGLYLGXDOH b) SURGXVXODEDWHULORUWHUPHQLORUVHULHLGHODPHGLDORUJHRPHWULF HVWH c) suma abaterilor WHUPHQLORUVHULHLGHODPHGLDORUJHRPHWULF HVWH d) SURGXVXODEDWHULORUWHUPHQLORUVHULHLGHODPHGLDORUJHRPHWULF HVWH e) PHGLD JHRPHWULF HVWHDFHD YDORDUHFDUHvQORFXLQGWHUPHQLLVHULHLQXPRGLILF SURGXVXO S WUDWHORUORU

7) Într-o colectivitate staWLVWLF

IHQRPHQXOGHFRQFHQWUDUHvQVHDPQ 

a) RYDULD LHVF ]XW DYDORULORUFDUDFWHULVWLFLLvQMXUXOPHGLHL b) RGLVWULEX LHvQIRUP GH³-´ c) RDVLPHWULHVF ]XW DGLVWULEX LHL d) RGLVWULEX LHvQIRUP GH³8´ e) cumularea valorilor caracteristicii în cadrul uneLJUXSHFODVHDOHFROHFWLYLW 8)

'DF  vQWUH FXDUWLOHOH FDOFXODWH SHQWUX R VHULH GH UHSDUWL LH H[LVW  UHOD LD

Q2 =

UHSDUWL LDHVWH

a) b) c) d) e) f)

Q1 + Q3 atunci 2

DVLPHWULF ODGUHDSWD DVLPHWULF ODVWkQJD QRUPDO  KLSHUEROLF  ELGLPHQVLRQDO  ELPRGDO 

9) PriQFHWHVWVHYHULILF a) b) c) d) e)

LL

FRUHVSRQGHQ DGLQWUHUHSDUWL LLOHWHRUHWLFHúLFHOHHPSLULFH"

χ2 ; F (R.A.Fisher); t (Student); Kolmogorov-Smirnov; Wald.

10) )LH VHULD VWDWLVWLF



{x1 , x 2 ,... , x n }

 RE LQXW  SULQ REVHUYDUHD XQHL YDULDELOH QXPHULFH ; úL

pentru care s-au calculat media x  úL GLVSHUVLD  σ 2 . Controlându-se calitatea datelor culese, se x

FRQVWDW F ILHFDUHGLQDFHVWHDDXIRVWPDMRUDWH OD vQUHJLVWUDUHFXGHXQLW

L6HULDFRUHFW DU

x x  x fi fost:  1 , 2 , ..., n  . Calculându-se din nou dispersia pentru valorile corecte se 100 100

FRQVWDW F DFHDVWDHVWH

100 

a)

HJDO FXGLVSHUVLDLQL LDO "

b)

PDLPLF GHFkW

σ 2 de 10.000 ori?

c)

PDLPLF GHFkW

σ 2 cu

x x

d) mai mare decât σ 2 x

1 ? 100 1 ? cu 100

e) mai mare decât σ 2 de 100 de ori? x

11) 3HQWUXGRX YDULDELOHVWDWLVWLFHGHSHQGHQWH[úL\FX\ au calculat indicatorii:

I[ V DXFXOHVGDWHGHODXQLW

-

LúLV

-

, ;∑xi2 = 0957118 , ;∑xi yi = 296734 , ∑yi =1133;∑yi2 = 92703;∑xi = 3658 i

i

i

i

i

ÌQ LSRWH]D XQHL GHSHQGHQ H OLQLDUH HFXD LD GH UHJUHVLH FDUH PRGHOHD]  OHJ WXUD GLQWUH FHOH GRX YDULDELOHHVWH

a) b) c) d) e)

yˆ = 55,55 + 522,35 x ; yˆ = −522,35 + 55,55 x ; yˆ = 522,35 − 55,55 x ; yˆ = −522,35 x + 55,55 ; yˆ = −55,55 + 522,35 x ;

12) Se precizeaz

XUP WRDUHOHSRSXOD LLVWDWLVWLFH

 SRSXOD LD%XFXUHúWLXOXLODRFWRPEULH  SRSXOD LDGLQ5RPkQLDGLQPHGLXOXUEDQODLXOLH  PXO LPHDIDFWXULORUHODERUDWHGH6&³,&6´65/vQWULP,

4) 5)

PXO LPHDF V WRULLORUvQFKHLDWHvQ5RPkQLDv

n anul 1997;

VWRFXULOHGHP UIXULDOHvQWUHSULQGHULORUPLFLúLPLMORFLLODVIkUúLWXODQXOXL

3RSXOD LLVWDWLVWLFHGLQDPLFHVXQW

a)

úL

b)

úL

c)

úL

d)

úL

e)

úL

13) ÌQFD]XOXQHLREVHUY

ULVWDWLVWLFHDOF UHLVFRSHVWH³IRWRJUDILHUHD]LOHLGHO

ucru a unui muncitor”:

a) WLPSXOREVHUY ULLFRLQFLGHFXWLPSXOODFDUHVHvQUHJLVWUHD] GDWHOH b) WLPSXOREVHUY ULLQXFRLQFLGHFXWLPSXOODFDUHVHvQUHJLVWUHD] GDWHOH c) WLPSXOREVHUY ULLVHUHIHU ODGXUDWDV SW PkQLLGHOXFUXDPXQFLWRUXOXL d) precizarea timpXOXLREVHUY ULLHVWHOLSVLW GHVHQV e) WLPSXOREVHUY ULLHVWHPRPHQWXOFULWLF³RUD]HUR´D]LOHLvQFDUHPXQFLWRUXOVHSUH]LQW

ODOXFUX

14) Coeficientul de concentrare al lui Corrado-*LQLVHFDOFXOHD] a) G =

FD

n

∑x i =1

2 i

;

  x b) G = ∑  n i  i =1  ∑ xi  i =1 n

  ;    2

  n x c) G = n∑  n i  i =1  ∑ xi  i =1

     

  n x d) G = ∑  n i  i =1  ∑ xi  i =1

   ;   

2

  n  xi ∑  n i =1  ∑ xi  i =1 e) G = n

      .

15) 0HGLDDULWPHWLF

−1

;

2

DXQHLYDULDELOHDOHDWRDUH;UHSUH]LQW 

a) momentul simplu de ordinul întâi; b) momentul centrat de ordinul întâi; c) momentul centrat de ordinul al doilea; d) momentul simplu de ordinul al doilea; e)

PRPHQWXOVLPSOXGHRUGLQXODOGRLOHDPLQXVPRPHQWXOVLPSOXGHRUGLQXOvQWkLODS WUDW

16) /DWHVWDUHDQRUPDOLW a)

VH DFFHSW  LSRWH]D F  vQWUH GLVWULEX LD HPSLULF  úL FHD QRUPDO  WHRUHWLF  QX H[LVW  FRQFRUGDQ

b)



VH UHVSLQJH LSRWH]D FRQIRUP F UHLD vQWUH GLVWULEX LD HPSLULF  úL FHD WHRUHWLF  H[LVW 

concordDQ d)



VH DFFHSW  LSRWH]D F  vQWUH GLVWULEX LD HPSLULF  úL FHD QRUPDO  WHRUHWLF  H[LVW  FRQFRUGDQ

c)

χ2GDF  χ 2calc < χ 2tab , atunci:

LLUHSDUWL LLORUHPSLULFHXWLOL]kQGWHVWXO



VHDFFHSW LSRWH]DFRQIRUPF UHLDGLVWULEX LDHPSLULF GLIHU VHPQLILFDWLYGHFHDQRUPDO  WHRUHWLF 

e)

QXH[LVW PRWLYHVXILFLHQWHSHQWUXDDFFHSWDLSRWH]DQRUPDOLW

LLGLVWULEX LHLHPSLULFH

17) $PSOLWXGLQHDUHODWLY a) b) c) d) e)

x max − x min ; 100 x max − x min 100 ; x min x max − x min 100 ; x max x max − x min 100 ; x x max − x 100 . x

18) 5HSDUWL LDELQRPLDO a) b) c)

DYDULD LHLVHFDOFXOHD] FD

WLQGHF WUHUHSDUWL LDQRUPDO 

GDF QLFLSSUREDELOLWDWHDVXFFHVXOXL úLQLFLTSUREDELOLWDWHDLQVXFFHVXOX GDF S

T

i) nu sunt nule;



GDF  XQD GLQWUH SUREDELOLW

L GHYLQH IRDUWH PLF  úL Q QXP UXO GH REVHUYD LL  FUHúWH

VXILFLHQWSHQWUXDS VWUDQSILQLW

d) e)

GDF RSUREDELOLWDWHSVDXT GHYLQHQXO  GDF QLFLSúLQLFLTQXVXQWPLFLLDUQDUHYDORULPDUL

19) ÌQ PRGHOXO GH DQDOL]

 GLVSHUVLRQDO  XQLIDFWRULDO  GLVSHUVLD FRUHFWDW  GLQ LQWHULRUXO JUXSHORU VH

RE LQH UDSRUWkQG VXPD S WUDWHORU DEDWHULORU GLQ LQWHULRUXO FHORU U JUXSH OD QXP UXO JUDGHORU GH OLEHUWDWHO $FHVWQXP U

a) b) c) d) e)

l=n; l=n-1; l=r-1; l=n-2; l=n-r.

20) 3HQWUX XQ VWXGLX VRFLRORJLF FX WHPD ³,PSOLFD LL DOH IHQRPHQXOXL GH úRPDM vQ 5RPkQLD´ V-a IRUPDW XQ HúDQWLRQ GH  GH SHUVRDQH LQFOXVH vQ ³VIHUD IRU HL GH PXQF ´ ÌQ FKHVWLRQDUXO

special elaborat s-DX

FXSULQV úL vQWUHE UL UHIHULWRDUH OD VWDUHD FLYLO  úL

categoria socio-

SURIHVLRQDO &HOHGRX YDULDELOHVXQWGHDFHHDúLQDWXU FXYDORULVLWXDWHSHRVFDO 

a) FRQWLQX  b) GLVFUHW  c) RUGLQDO  d) QRPLQDO  e) de intervale. 21) Într-R SRSXOD LH VWDWLVWLF \

 VH XUP UHVF YDULDELOHOH QXPHULFH [ \ úL ] vQWUH FDUH H[LVW  UHOD LD

:

[] 0HGLD DULWPHWLF  D YDULDELOHL [ HVWH HJDO  FX SURGXVXO PHGLLORU YDULDELOHORU \ úL ] DWXQFL

când: a)

\úL]VHDIO vQWU RDQXPLW GHSHQGHQ

-



b) c) d) e)

\úL]VXQWLQGHSHQGHQWHvQWUHHOH \úL]VXQWYDULDELOHQRUPDOL]DWHGDUGHSHQGHQWH \úL]VXQWOLQLDUG

ependente;

\úL]DXFRYDULDQ DGLIHULW GH]HUR

22) 'HVSUHVWRFXOGHP UIXUL H[LVWHQWODRVRFLHWDWHFRPHUFLDO în urma inventarierii:

VH FXQRVFXUP WRDUHOH GDWHRE LQXWH

Data inventarierii 1.01.1997 1.02.1997 15.03.1997 10.05.1997 1.07.1997 Stocul existent (mil. lei) 50 58 68 70 75 6WRFXOPHGLXGHP UIXULDOVRFLHW

a) b) c) d) e)

LLFRPHUFLDOHGLQSHULRDGD

- 1.07.197 a fost de:

66 mil. lei; 60 mil. lei; 64,2 mil. lei; 50 mil. lei; 75 mil. lei.

23) 2PDúLQ

XWLOL]DW SHQWUXDGR]DFDQWLWDWHDGHFXORDUHvQYRSVHDGR]HD] vQPHGLH

m ml pe cutie

GH YRSVHD &DQWLWDWHD GHFXORDUH GR]DW HVWHFXQRVFXW  D DYHD R GLVWULEX LH QRUPDO  FX GLVSHUVLD HJDO  FX  'DF  PDL PXOW GH  PO GH FXORDUH HVWH DPHVWHFDW  vQ RE LQHUHD XQHL QXDQ H GH

albastru, vopseaua este respins din cutii este: a) b) c) d) e)

 9DORDUHD OXL

m DVWIHO vQFkW V

 QX ILH UHVSLQVH PDL PXOW GH 

5,072; 5,6272; 5,536; 5,068; 5,6288.

24) 3HQWUX FRQVWUXLUHD LQGLFLORU GH JUXS VH XWLOL]HD]  PDL PXOWH VLVWHPH GH SRQGHUDUH ,QIOXHQ D sistemului de ponderare utilizat poate fi SXV vQHYLGHQ XWLOL]kQG a)

H[FOXVLY FRHILFLHQWXO GH FRUHOD LH DO LQGLFLORU LQGLYLGXDOL DL IDFWRUXOXL FDQWLWDWLY úL DL

factorului calitativ ( r x

);

i if

b)

DQDOL]kQGFRHILFLHQ LLGHYDULD LHDLFHORUGRX FDWHJRULLGHLQGLFLLQGLYLGXDOL

c) produsul Vi x ⋅ Vi f ⋅ ri xi f = I

x ( f1 ) 1/ 0

:I

x ( f0 ) 1/ 0

;

d)

UHOD LD

I x ( f1 ) : I x ( f0 ) = 1 + ri xi f ⋅ Vi x ⋅ Vi f ;

e)

UHOD LD

I x ( f1 ) ⋅ I x ( f0 ) = 1 + ri xi f ⋅ Vi x ⋅ Vi f .

25) &DUHHVWHPXO LPHDYDORULORUFRHILFLHQWXOXLGHFRUHOD LHvQFDGUXOOHJ a) b) c) d) e)

Vi x ; Vi f );

WXULORUGLUHFWH

[ -1, 1 ]; [ -1, 0 ]; ( 0, 1 ]; PXO LPHDQXPHU

elor reale;

[ -3, 3 ].

26) 3HQWUXRFROHFWLYLWDWHVWUXFWXUDW

vQ UJUXSHGXS YDORULOHFDUDFWHULVWLFLL ;IDFWRUGHJUXSDUH úL

vQPJUXSHGXS YDORULOHYDULDELOHLDQDOL]DWH<UHJXODGHDGXQDUHDGLVSHUVLLORUVHSRDWHDSOLFD XWLOL]D úL GDF  DYHP OD GLVSR]L LH IUHFYHQ HOH UHODWLYH vQ ORFXO IUHFYHQ HORU DEVROXWH FX FRQGL LD

ca: m

a)

∑

r

f . j = 1 úL ∑ f i. = 1 ;

j =1 r m

b)

i =1

∑ ∑ f ij

= 1;

i =1 j =1 r

c)

∑ f i. = 1 ;

i =1 m

d)

∑

j =1 m

e)

r

f ij = 1 úL ∑ f i. = 1 ;

∑ f ij

i =1

= 1.

j =1

27) Coeficientul lui Pearson β 2 =

µ4 µ 22

VHXWLOL]HD] SHQWUXDQDOL]DVWDWLVWLF D

a) asimetriei; b) YDULD LHL c) boltiri; d) WHQGLQ HLFHQWUDOH e) LQGLFDWRULORUPHGLLGHSR]L LH 28) ÌQ WHVWDUHD LSRWH]HL VWDWLVWLFH SULYLWRDUH OD SDUDPHWUXO ³PHGLD SRSXOD LHL´ UHJLXQHD FULWLF GDW GH t < − t α ;n −1 când:

 HVWH

a) datele provin dintr-XQHúDQWLRQGHYROXPUHGXVúLVHHIHFWXHD] WHVWXQLODWHUDOVWkQJD b) datele provin dintr-XQHúDQWLRQGHYROXPUHGXVúLVHHIHFWXHD] WHVWXQLODWHUDOGUHDSWD c) datele provin dintr-XQ HúDQWLRQ GH YROXP QRUPDO VH FXQRDúWH GLVSHUVLD SRSXOD LHL úL V-a efectuat test unilateral stânga; d) datele provin dintr-XQHúDQWLRQGHYROXPUHGXVúLV-a efectuat test bilateral; e) datele provin dintr-XQHúDQWLRQGHYROXPQRUPDOúLV-a efectuat test bilateral. 29) Într-R VHULH GH GLWULEX LH QRUPDO

 GXS  R DQXPLW  YDULDELO  QXPHULF  vQWUH YDORDUHD PHGLDQ 

PRGDO úLPHGLHHVWHDGHY UDW UHOD LD

a) b) c) d) e)

x < Mo < Me ; Me < x < Mo ; x = Mo = Me ; x < Me < Mo ; Mo < Me < x .

Unde x PHGLDDULWPHWLF Me = mediana; Mo YDORDUHDPRGDO 30) 3HQWUXRUHSDUWL LHGHIUHFYHQ HFXWHQGLQ GHQRUPDOLWDWHV VHSUHFL]H]HFDUHGLQXUP DILUPD LLSULYLWRDUHODPHGLDVDQXHVWHDGHY UDW 

a)

UHSUH]LQW SXQFWXOIRFDOGHSHVFDO vQMXUXOF UXLDYDORULOHVHEDODQVHD] SHUIHFW

WRDUHOH

n

b)

PLQLPL]HD] IXQF LDGHGLVWDQ

GHWLSXO

∑ (a − xi )

2

;

i =1

c) d) e)

HVWHSX LQVHQVLELO ODIOXFWXD LLOHGHVHOHF LH vQSURFHVXOLQIHUHQ HLVWDWLVWLFHHVWHGHRELFHLSUHIHUDW DOWRULQGLFDWRULDLWHQGLQ HLFHQWUDOH HVWHPDLSX LQDIHFWDW GHYDORULOHH[WUHPHGHFkWPHGLDQDúLPRGXO

31) 6HFXQRVFXUP WRDUHOHGDWHSULYLQGQXP noiembrie 1997:

UXOGHIDFWRULvQWRFPLWHGH6&$QRQLPXV65/vQOXQD

3RSXOD LDVWDWLVWLF VWXGLDW HVWHVWUXFWXUDW úLSUH]HQWDW vQ

a) Tabelul I; b) Tabelul II; c)Tabelul III; d) Tabelul IV; e) Tabelul V. Data 1 2 3 4 5 6 7 8 9 10

Nr. facturi 6 10 12 10 8 9 10 11 12 9

I Grupe de ]LOHGXS

QU

de facturi 0-5 6 - 11 11 - 15 16 - 20

Nr. zile

GXS

QUGH

facturi 0 -5 6 - 10 11 - 15 16 - 20

Nr. de zile

UXOXL]LOQLFGH

facturi (0-5] ( 5 - 10 ] (10 - 15 ] ( 15 - 20 ]

Nr. facturi 10 14 6 18 13 9 14 12 17 12

II Grupe de zile

1 13 13 3

IV Intervale ale QXP

Data 11 12 13 14 15 16 17 18 19 20

Nr. zile 1 16 10 3

Nr. facturi 14 12 11 10 8 4 12 9 12 16

III Intervale Nr. de timp facturi 0-6 7 - 14 15 - 22 23 - 30

V Intervale ale QXP

1 13 13 3

Data 21 22 23 24 25 26 27 28 29 30

55 90 103 82

Nr. de zile

UXOXLGH

facturi zilnice [0-5) [ 5 - 10 ) [10 - 15 ) [ 15 - 20 )

1 9 17 3

TESTUL 11

1)

1RW PFX

σ 2REV úLFX σ 2FREV  GLVSHUVLLOHPHGLHLGH VHOHF LHvQFD]XULOH IRUP

ULLHúDQWLRDQHORU

vQYDULDQWHOHFXUHYHQLUHúLI U UHYHQLUH&RPSDUkQGFHOHGRX GLVSHUVLLV VHDSUHFLH]HFDUHGLQ

variantele de mai jos sunt corecte: 2 2 a) σ REV < σ FREV ; 2 2 b) σ REV > σ FREV ; 2 2 c) σ FREV = σ REV ; σ2 N −n d) FREV > ; 2 σ REV N −1 σ2 N −n e) FREV = . 2 σ REV N −1

2)

6HFRQVLGHU RSRSXOD LHVWDWLVWLF GHYROXP1 XQ QXP U QDWXUDO QHQXO /D XQLW

cu N = n ⋅ k ; unde n -YROXPXOHúDQWLRQXOXLúLN-

LOH GH REVHUYDUH V D XUP ULW YDULDELOD ; DOH F UHL YDORUL

individuale sunt x i = i (cu i=1,2,…,N).

'LVSHUVLDPHGLHLGHVHOHF LHvQFD]XOIRUP ULLHúDQWLRQXOXLvQYDULDQWDI U UHYHQLUHHVWH

a) b)

N +1 ; 2 N ( N + 1)

12

;

N ; 2 (k − 1)(N + 1)

c) (k − 1) d) e) 3)

12 (k − 1) 12

;

.

6HFRQVLGHU RSRSXOD LHVWDWLVWLF GHYROXP1FX XQ QXP U QDWXUDO QHQXO /D XQLW

N = n ⋅ k ; unde n -YROXPXOHúDQWLRQXOXLúLN-

LOH GH REVHUYDUH V-D XUP ULW YDULDELOD ; DOH F UHL YDORUL individuale sunt x i = i (cu i=1,2,…,N   3UHVXSXQHP F  VH H[WUDJH OD vQWkPSODUH XQ QXP U ³a” vQWUH  úL k ( a ∈ (1, k )  (IHFWX P R H[WUDJHUH PHFDQLF  D HúDQWLRQXOXL FHHD FH vQVHDPQ  F  HúDQWLRQXOHVWHIRUPDWGLQXQLW LOH a , a + k ,.., a + ( n − 1) k . 'LVSHUVLDPHGLHLGHVHOHF LHHVWH

a)

(k − 1)(N + 1)

12 2 k −1 b) ; 12

;

k 2 − 1)N ( c) ; d) e)

12 (k − 1)N

;

12 N ( N + 1) 12

.

6 FRQVLGHU PFD]XOXQXLVRQGDMFXUHYHQLUH úLSUREDELOLW

în fiecare din cele n SUHOHY ( i = 1, N 3UHFL]

 /D XQLW

UL XQLW

LOH

Ui ( i = 1, N

LOHLQHJDOH$FHDVWDvQVHDPQ F 

 VH UHJ VHVF vQ HúDQWLRQ FX SUREDELOLW

LOH GH REVHUYDUH V D XUP ULW YDULDELOD ; DOH F UHL YDORUL VXQW

-

ile Ai

xi ( i = 1, N ).

ULSHQWUXSUREOHPHOH úL

4) Suma T =

N

∑ Xi

HVWHHVWLPDW 

i =1

[]

1 n xi  a) nedeplasat de T = ∑ deoarece M Tˆ = T , unde cu M [] ⋅ s-a notat media; n i =1 Ai 1 n x b) deplasat de T = ∑ i deoarece M T − T ≠ 0 ; n i =1 Ai

[]

1 n x c) nedeplasat de T = ∑ i deoarece T = T ; n i =1 Ai 1 n x d) deplasat de T = ∑ i deoarece M 2 T − T 2 ≠ 0 ; n i =1 Ai

[]

1 n x e) nedeplasat de T = ∑ i deoarece M 2 T − T 2 = 0 . n i =1 Ai

[]

2

x  5) 1RW P FX D(x i / Ai ) = ∑ Ai  i − T  dispersia valorilor xi /Ai cu i = 1, N . Dispersia  i =1  Ai estimatorului T este: N

x  1 N a) D T = ∑ Ai  i − T  n i =1  Ai 

2

 x 1 N b) D T = ∑ Ai  i − T  n i =1  Ai 

2

() ()

≠

1 ∑ n  i

=

2  1  xi − T2 ; ∑ n  i Ai 

2

 xi2 −T2; Ai 

x xj  1 2 x2  = ∑ i − 2T 2 ; c) D T = ∑ ∑ Ai A j  i − ni j n i Ai  Ai A j  i< j

()

xi2 2  d) D T = ∑ + 2T 2 ; n i Ai

()

 1 Nx e) D T = ∑  i − T  n i =1  Ai 

()

6)

2

=

2  1  N xi −T2. ∑ n i =1 Ai 

$QDOL]kQGFRQGL LLOHIRUPXODWHOD úL VHFRQVWDW F HVWHDGHY UDW UHOD LD

x  n a) D i  = D T ;  Ai  N

()

 b) D 

xi  n − N D T ; = Ai  N − 1

()

x  c) D i  = nD T ;  Ai 

()

x  d) D i  = D T ;  Ai 

()

 e) D 

xi  1  = D T . Ai  n

()

()

7) Un estimator nedeplasat pentru D T este: 2

()

n x  1 i − T  ;  ∑ n (n − 1) i =1  Ai 

()

1 n  ∑ n − 1 i =1 

a) D T = b) D T =

2

 xi − T  ; Ai  2

N x  1 i c) D T = − T  ;  ∑ n( n − 1) i =1  Ai 

()

()

n n x  i

2

xj   ; d) SUH]HQWDWvQYDULDQWDD úLvQSOXV D T = − ∑ ∑ A  2 A n (n − 1) i j  i j 1

i< j

()

e) SUH]HQWDWvQYDULDQWDF úLvQSOXV D T =

N N x  i

2

xj  − ∑ ∑  A A  . j i j  i i< j

8)

&RPSDUkQG GLVSHUVLD HVWLPDWRUXOXL GLQ FD]XO VHOHF LHL FX SUREDELOLW SUREDELOLW

L LQHJDOH 'I

LHJDOH'EFRQVWDW PF UHOD LDDGHY UDW GLQXUP WRDUHOHYDULDQWHHVWH

a) DI > DEvQRULFHVLWXD LH

:

cu cel cu

b) DI < DE

∑

⇔

Nx i2 >

i

c) DI < DE

⇔

d) DI < DE

⇔

x i2 ∑A ; i i

1 GDF N 1 A i < GDF N Ai >



xi2 HVWHPDUHDGLF xi este corelat pozitiv cu Ai);



xi2 HVWHPLFDGLF xi este corelat pozitiv cu Ai);

e) DI = DE. 6  FRQVLGHU P FD]XO vQ FDUH ILHFDUH XQLWDWH VHOHFWDW  vQ HúDQWLRQ PRGLILF  FRQGL LLOH XUP WRDUHORU H[WUDJHUL DOH XQLW

primei unit XQLW

LORU vQ HúDQWLRQ 'HFL

L vQ HúDQWLRQ WUHEXLH V  FXQRDúWHP DWXQFL

Ai1 HVWH GDF

 SUREDELOLWDWHD GH H[WUDJHUH D

Ai2( j ) SUREDELOLWDWHD GH LHúLUH vQ HúDQWLRQ D

LORU 8i vQ D GRXD H[WUDJHUH GXS  FH vQ SULPD H[WUDJHUH D DS UXW XQLWDWHD 8j

, etc. De exemplu,

GDF  8j HVWH VHOHF LRQDW OD SULPD H[WUDJHUH DWXQFL

Ai2( j ) =

Ai1

∑ Aα1

α≠ j

=

(

Ai1

1 − A1j

)

. Problema aceasta,

GHVWXO GH FRPSOLFDW  D IRVW VWXGLDW  WHKQLF úL SUDFWLF vQ  GH +RURYLW] úL 7KRPSVRQ $VWIHO DX IL[DWGRX JUXSHGHQXPHUHSi

Uj úL 8j V

- probabilitatea ca UjV

ILJXUH]HvQHúDQWLRQúLSij

 ILJXUH]H VLPXOWDQ vQ HúDQWLRQ $FHVWH SUREDELOLW

- probabilitatea ca

L VXQW QXPHUH VXEXQLWDUH úL vQ SOXV

UHVSHFW FRQGL LLOHXUP WRDUH

∑ pi

= n úL

∑ ∑ pij

= n ( n − 1) 

ÌQ DFHVWH FRQGL LL HVWLPDWRUXO XQXL 7RWDO

N x THT = ∑ i i =1 pi

 QXPLW úL HVWLPDWRUXO OXL +RURYLW]

- Thompson.

3UHFL]

ÌQFRQGL LLOHSUH]HQWDWHSUHFL]D LYDORDUHDGHDGHY UDDILUPD LLORUXUP WRDUH

a) THT este un estimator nedeplasat;

1 b) THT este un estimator deplasat cu THT ; 2

[ ] d) M [THT ] − THT = pi ; e) M [THT ] − THT = pij . c) M THT = THT ;

∑ x i este

UL SHQWUX SUREOHPHOH   úL

10)). 9)

T=

i =1

i j i≠ j

i

N

10)ÌQFRQGL LLOHSUH]HQWDWHGLVSHUVLDHVWLPDWRUXOXL THT este: N p (1 − p ) pij − pi p j i a) D THT = ∑ i X i2 − ∑ ∑ Xi X j ; pi p j pi2 i =1 i j

[

]

i≠ j

N p (1 − p ) pij − pi p j i b) D THT = ∑ i X i2 + ∑ ∑ Xi X j ; 2 p p p i j i =1 i j i

[ ]

i≠ j

2

x xj  1  ; c) D THT = ∑ ∑ pi p j − pij  i −  2i p p  i j j

(

[ ]

)

i≠ j

[ ]

d) D THT =

[ ]

e) D THT =

N p (1 − p ) pij − pi p j i i X i2 : Xi X j ; 2 p p p i j i =1 i j i i≠ j 2 1 n n  pi p j − pij   xi x j 

∑

∑ ∑ 

2i

i≠ j

11)1RW

P FX

∑∑

j 

 −  .  p  p  i j

pij

σ 2S  úL FX σ 2STRAT  GLVSHUVLD PHGLLORU GH VHOHF LH SHQWUX FD]XO VHOHF LHL VLPSOH úL

UHVSHFWLY SHQWUXFD]XO VHOHF LHL VWUDWLILFDWH &RPSDUkQGFHL GRL LQGLFDWRULFRQVWDW P YDORDUHD GH DGHY UDDILUPD LLORUXUP WRDUH

a) σ 2STRAT < σ 2S , deoarece media dispersiilor straturilor este mai mare decât dispersia JHQHUDO 

b) σ 2STRAT < σ 2S , deoarece media dispersiilor straWXULORU vQ RULFH VLWXD LH HVWH PDL PLF



GHFkWGLVSHUVLDJHQHUDO FXFRQGL LDFDGLVSHUVLDGLQWUHVWUDWXULV ILHQHQXO 

c) σ 2STRAT = σ 2S   GHRDUHFH PHGLD GLVSHUVLLORU VWUDWXULORU HVWH HJDO

 FX GLVSHUVLD GLQWUH

straturi;

d) σ 2STRAT − σ 2S V ILHPDLPLF GHFkWGLVSHUVLDGLQWUHVWUDWXUL e) FRPSDUDUHDFHORUGRX GLVSHUVLLHVWHOLSVLW GHVHQV 12)6H FRQVLGHU

 F 

σ 2STRAT  HVWH GLVSHUVLD PHGLHL GH VHOHF LH vQ FD]XO VHOHF LHL VWUDWLILFDWH SH

straturile “h” (cu h = 1, m ). SHQRWHD] VLWXD LHGLVSHUVLDHVWHPD[LP 

a) b)

h

FX

nh volumul stratului h

 GDF 

n1 = n 2 = ... = n h = ... = n m ; n1 ≠ n 2 ≠... ≠ n h ≠... ≠ n m ;

⇒n=

m

∑ nh

h =1

ÌQDFHDVW 

Nh c) n h = pentru (∀)h = 1, m ; m ∑ Nh h =1

d) n1 ≠ n 2 úL n 3 = n 4 =... = nh =... = n m ; e) N 1 = N 2 =... = N h =... = N m .

TESTUL 12*)

1) Estimatorul unui parametru θ

a)

VHQRWHD] FX

θ $FHVWHVWLPDWRUHVWHQHGHSODVDWGDF



GLIHUHQ D GLQWUH PHGLD VD úL YDORDUHD SDUDPHWUXOXL HVWH GLIHULW  GH ]HUR GDU DFHDVW  GLIHUHQ

QXGHS úHúWHGLQYDORDUHDSDUDPHWUXOXL

b) GLVSHUVLD VD HVWH PLQLP

 

()

D θ → 0 FkQG YROXPXO HúDQWLRQXOXL WLQGH F

WUH YROXPXO

SURGXF LHL n → N ); c) GLVSHUVLDVDHVWHPLQLP SHQWUXRULFHYROXPIL[DWDOHúDQWLRQXOXL d) mHGLDVDHVWHHJDO FXYDORDUHDSDUDPHWUXOXL M θ → θ );

()

e) 2)

GLVSHUVLDVDHVWHPD[LP 

6  VH SUHFL]H]H FDUH GLQ VHULLOH GH UHSDUWL LH FDUDFWHUL]DWH SULQ XUP WRDUHOH VHWXUL GH YDORUL SUH]LQW RDVLPHWULHSR]LWLY 

a) b) c) d) e)

x = 40 u.m ; Me = 40 u.m.; Mo = 40 u.m.; x = 2500 u.m ; Me = 3000 u.m.; Mo = 3300 u.m.; x = 151,25 u. m ; Me = 138,75 u.m.; Mo = 112,58 u.m.; x = 180 u.m 0H

XP0R

XPúLXP

x = Me = Mo = 0

3) Scala de interval:

a) DUHWRDWHFDUDFWHULVWLFLOHVFDOHORURUGLQDOHúLGHUDSRUW b) DUH WRDWHFDUDFWHULVWLFLOH VFDOHL RUGLQDOH úL vQ SOXV GLVWDQ D GLQWUH GRX

 QXPHUH DOH VFDOHL

DUHRVHPQLILFD LHFRQFUHW 

c)

HVWH R VFDO  QXPHULF  úL vQ SOXV UDSRUWXO GLQWUH GRX  SXQFWH DOH

scalei este independent

GHXQLWDWHDGHP VXU 

d) SUH]LQW PXOWHGLQFDUDFWHULVWLFLOHVFDOHLRUGLQDOH e) PDLHVWHGHQXPLW úLVFDO GHUDSRUWVDXVFDO GLVFUHW 4)



3HQWUX FRQVWUXLUHD LQGLFLORU GH JUXS VH XWLOL]HD]  PDL PXOWH VLVWHPH GH SRQGHUDUH ,QIOXHQ D

sistePXOXLGHSRQGHUDUHXWLOL]DWSRDWHILSXVvQHYLGHQ



a) XWLOL]kQGH[FOXVLYFRHILFLHQWXOGHFRUHOD LHDOLQGLFLORULQGLYLGXDOLDLIDFWRULORU[úLI b) DQDOL]kQGFRHILFLHQ LLGHYDULD LHDLFHORUGRX FDWHJRULLGHLQGLFLLQGLYLGXDOLV x ; V f );

i i x ( f1 ) x ( f 0 ) c) utilizând valorile raportului I 1/ 0 : I 1/ 0 = V x V f r x f , unde r x f este coeficientul i i i i i i GHFRUHOD LH

x( f )

x( f )

d) XWLOL]kQGUHOD LD I 1/ 0 1 : I 1/ 0 0 = 1 + r x f V x V f ; i i i i e)

XWLOL]kQGUHOD LD

x( f )

 6XELHFW OD H[DPHQXO GH OLFHQ

*)

x( f )

I 1/ 0 1 + I 1/ 0 0 = 1 + r x f V x V f . i i i i

 OD GLVFLSOLQD ³7HRULD VWDWLVWLFLL´ OD IDFXOWDWHD GH &LEHUQDWLF  6WDWLVWLF  úL

,QIRUPDWLF (FRQRPLF  VSHFLDOL]DUHD6WDWLVWLF 6HVLXQHD0DL

-

5)

6HFRQVLGHU XQWDEHOGHFRQWLQJHQ

{[(x , y )n ]; j ∈ J , k ∈ K} j

k

jk

reduse U j =

xj − x

σx

úL

Vk =

FRUHOD LH vQIRUPDVDJHQHUDO 

 'DF  SH ED]D WDEHOXOXL FRQVLGHUDW FDOFXO P YDORULOH FHQWUDWH úL

yk − y ( cu x úL y mediile variabLOHORU;úL<LDU σ x úL σ y abaterile σy

VWDQGDUG DOH YDULDELOHORU ; úL <  DWXQFL FRYDULDQ D GLQWUH YDULDELOHOH ; úL < QRWDW  FX &RY;< 

este: a) Cov ( X , Y ) ≠ σ x σ y Cov (U ,V ) ; b) Cov ( X , Y ) =

Cov (U ,V ) ; σ xσ y

c) Cov ( X , Y ) = σ x σ y Cov (U ,V ) ; d) Cov ( X , Y ) − Cov (U ,V ) = σ xσ y ; e) Cov ( X , Y ) = σ U σ V Cov (U ,V ) . 6)

5HIHULWRUODDFWLYLWDWHDHFRQRPLF DXQHLVRFLHW

Unitatea

LFRPHUFLDOHVHFXQRVFXUP WRDUHOHGDWH

9DORDUHDSURGXF LHL PLOOHLSUH XULFXUHQWH

Perioada ED]

A B

1200 875

Perioada

Modificarea valorii SHVHDPDPRGLILF SUH XULORU

ULL

(mil. lei)

FXUHQW

1850 1600

350 275

0RGLILFDUHD UHODWLY  D YDORULL SURGXF LHL OD QLYHOXO vQWUHJLL VRFLHW

L FDX]DW  GH PRGLILFDUHD

YROXPXOXLIL]LFDOSURGXF LHLvQWUHFHOHGRX SHULRDGHDIRVWHJDO FX

a) -12,5%; b) +100,0%; c) +36,1%; d) +136,1%; e) -112,5%. 7)

ÌQFD]XOXQHLREVHUY ULVWDWLVWLFHDOF UXLVFRSHVWH³IRWRJUDILHUHD´]LOHLGHOXFUXDXQXLOXFU WRU

a) WLPSXOREVHUY ULLFRLQFLGHFXWLPSXOODFDUHVHvQUHJLVWUHD] GDWHOH b) WLPSXOREVHUY ULLQXFRLQFLGHFXWLPSXOODFDUHVHvQUHJLVWUHD] GDWHOH c) WLPSXOREVHUY ULLVHUHIHU ODGXUDWDV SW PkQLLGHOXFUXDOXFU WRUXOXL d) SUHFL]DUHDWLPSXOXLREVHUY ULLQXDUHVHQV e) WLPSXO REVHUY ULL HVWH PRPHQWXO FULWLF ³RUD ]HUR´ D ]LOHL vQ FDUH OXFU WRUXO VH SUH]LQW

 OD

lucru. 8)

$QDOL]D LXUP WRDUHOHSRSXOD LLVWDWLVWLFH SRSXOD LD%XFXUHúWLXOXLODLXOLH SRSXOD LD GLQ5RPkQLDGLQPHGLXOXUEDQOD LXOLH PXO LPHD IDFWXULORUHODERUDWH GH6&³,&6´ 65/vQWULP, PXO LPHDF V WRULLORUvQFKHLDWHvQ5RPkQLDvQ P UIXULDOvQWUHSULQGHULORUPLFLúLPLMORFLLODVIkUúLWXODQXOXL

anul 1997; 5) stocurile de

3RSXOD LLVWDWLVWLFHGLQDPLFHVXQW

a) úL b) úL c) úL d) úL e) úL 9)

6H

úWLH

F 

σ 2y =

Yi = b0 + b1 xi 'DF

(

c) σ 2y.x > σ 2y d) σ 2y.x > σ 2y e) σ 2y.x < σ 2y 10) 2 YDULDELO

(

)

úL

σ Y2 =

(

)

2 1 Yi − y ∑ n i

unde

UHVWHFRHILFLHQWXOGHFRUHOD LHGLQWUHYDULDELOHOH<úL;DWXQFL

( (1 − r (1 − r (1 − r (1 − r

a) σ 2y.x = σ 2y 1 − r 2 b) σ 2y .x = σ 2y

)

2 2 1 1 yi − y ;σ 2y.x = ∑ yi − Yi ∑ r i n i

2 2

2 2

) ) ) ) )

úL

úL

σ 2y = σ 2y .x + σ Y2 ;

σ 2y < σ 2y .x + σ Y2 ;

úL

σ 2y = σ 2y .x + σ Y2 ;

úL

σ 2y < σ 2y .x + σ Y2 ;

úL

σ 2y > σ 2y .x + σ Y2 .

 FRPSOH[  < HVWH H[SULPDW  vQ IXQF LH GH IDFWRULL [ ] X Y J K Z S DOH F URU

LQIOXHQ HWUHEXLH L]RODWH5HOD LDRELHFWLY  GLQWUH< úLIDFWRULL V LILLQGPXOWLSOLFDWLY SHUPLWHR

descompunere în trepte de forma: Y

Â]

= x

u

v

g

p

w

h

cu y = x ⋅ z = u ⋅ v ⋅ z = u ⋅ v ⋅ g ⋅ p = u ⋅ v ⋅ g ⋅ w ⋅ h ÌQWUH LQGLFHOH YDULDELOHL < úL LQGLFLL YDULDELOHORU IDFWRULDOH GDF  VH XWLOL]HD]  WHKQLFD VXEVWLWXLULLvQO Q XLWHQXH[LVW UHOD LD

a) I y = I y ( x) ⋅ I y ( z) ; b) I y = I y ( z) ⋅ I y ( u) ⋅ I y ( v ) ; c) I y = I y ( u) ⋅ I y ( v ) ⋅ I y ( g ) ⋅ I y ( w) ⋅ I y ( h ) ; d) I y = I y ( x ) ⋅ I y ( g ) ⋅ I y ( w) ⋅ I y ( h ) ; e) I y − I y ( u) ⋅ I y ( v ) ⋅ I y ( g ) ⋅ I y ( w) ⋅ I y ( h) ≠ 0 .

11) (YROX LD3URGXVXOXL,QWHUQ%UXWSHORFXLWRUvQSHULRDGD-VHSUH]LQW Anii ID

GHDQXOSUHFHGHQW

1994 14,0

1995 +7,3

1996 +4,4

DVWIHO

1997 -6,3

0HGLDDQXDO DHYROX LHLSURFHQWXDOHHVWHGH

a) -0,09%; b) 102,0%; c) 201,3%; d) +2,21%; e) +4,35%. 12) 1RW

P FX

σ 2R  úL FX σ 2F  GLVSHUVLLOH PHGLLORU GH VHOHF LH SHQWUX SURFHGHHOH GH IRUPDUH D

HúDQWLRDQHORU vQ YDULDQWHOH FX UHYHQLUH úL I U  UHYHQLUH &RPSDUkQG FHL GRL LQGLFDWRUL UHOD LD FRUHFW HVWH

a) σ 2R > σ 2F ; b) σ 2F > σ 2R ; c) σ 2R = σ 2F ;

1 d) σ 2F = σ 2R ; 2 e) σ 2F = σ 2R

YROXPXOHúDQWLRQXOXL

13) Inegalitatea dintre aEDWHULOH VWDQGDUG DOH XQHL YDULDELOH ; QRUPDO UHSDUWL]DWH vQ SRSXOD LLOH VWDWLVWLFH    GH DFHODúL YROXP úL DFHHHDúL PHGLH

varianta: a)

x , σ 1 > σ 2 > σ 3  HVWH YL]XDOL]DW b)

3

3 2

1 2

1

c)

d) 1

2 3 2 3

1

 vQ

e) 2

1 3

14) 6H FXQRDúWH IDSWXO F  6& ³,&6´ 65/ D UHDOL]DW vQ OXQD ,$1 ¶ R FLIU  GH DIDFHUL GH  POG lei, iar în perioada IAN ’97 - APR ’98 a cunoscut o modificarePHGLHOXQDU GHPOGOHLÌQ ipoteza în care în perioada MAI ’98 - ,81 ¶ vQUHJLVWUHD]  DFHHDúL HYROX LH FD DFHHD GLQ ,$1 ’97 -$35¶YDORULOHHVWLPDWHDOHFLIUHLGHDIDFHULvQOXQLOHPDLLXQLHúLLXOLHVXQW

a) POGOHLPOGOHLúL mld. lei; b) POGOHLPOGOHLúLPOGOHL c) POGOHLPOGOHLúLPOGOHL d) POGOHLPOGOHLúLPOGOHL e) POGOHLPOGOHLúLPOGOHL 15) 'DF

 vQWUH GRX  YDULDELOH < úL ; QX H[LVW  QLFL R OHJ WXU  YDULDEL

lele sunt independente)

FRHILFLHQWXOGHFRUHOD LHHVWHHJDOFX]HUR5HFLSURFDDFHVWHLDILUPD LL

a) HVWHIDOV  b) HVWHDGHY UDW  c) HVWHDGHY UDW GRDUGDF GLVSHUVLLOHFHORUGRX YDULDELOHVXQWHJDOH d) HVWHDGHY UDW GRDUGDF FHOHGRX GLVWULEX LLIRUPDOHGXS ;úL<VXQWQRUPDOH e) HVWH DGHY UDW  GRDU GDF  GDWHOH FHORU GRX  YDULDELOH VXQW VLVWHPDWL]DWH vQWU-un tabel de FRQWLQJHQ

FRUHOD LH 

16) La un punct comercial din vânzarea unui produs s-a realizat în luna APR ’98 o încasare de 8 mil. lei. Ca urmare a major ULL SUH XOXL ID  GH OXQD $35 ¶ vQFDV ULOH GLQ OXQD $35 ¶ DX FXQRVFXWRFUHúWHUHGHOHL&DUHDUILIRVWvQFDV ULOHOXQLL$35¶GDF SUH XOQXV-ar fi modificat?

a) 7,7 mil. lei; b) 7,3 mil. lei; c) 5 mil. lei; d) 6 mil. lei; e) 7 mil. lei. 17) ÌQHYROX LDVDvQGHOXQJDW

VWDWLVWLFDV

-a dezvoltat continuu atât sub aspectul obiectului de studiu

GDU PDL DOHV DO SHUIHF LRQ ULL úL GLYHUVLILF ULL PHWRGHORU GH DERUGDUH D DFHVWXL RELHFW ÌQ WRDWH PRPHQWHOHGH]YROW ULLVDOHVWDWLVWLFDVHRFXS GH

a) fenomene care se proGXFODRDQXPLW XQLWDWHGHREVHUYDUH b) IHQRPHQHFDUHVHUHSURGXFvQPRGLGHQWLFODXQLW LOHGHREVHUYDUH c) fenomene care se produc într-XQ QXP U PDUH GH FD]XUL úL DOH F URU IRUPH LQGLYLGXDOH PDQLIHVW DQXPLWHUHJXODULW

L

d) fenomene exclusiv economice; e) fenoPHQHFDUHDXODRULJLQHDSURGXFHULLORUXQVLQJXUIDFWRUGHLQIOXHQ



18) $QDOL]D L

XUP WRDUHOH

QR LXQL

 

$XWRQRPLH

 

FRQILGHQ LDOLWDWH

 

WUDQVSDUHQ

VSHFLDOL]DUH    SURSRU LRQDOLWDWH    GHRQWRORJLH SURIHVLRQDO    LQGHSHQGHQ

elDERUDUHDGHFL]LLORU DUJXPHQWDUHDDF LXQLORUGXS 11) observare.



 

 SROLWLF   

GHFODQúDUHDORU SUHOXFUDUHDGDWHORU

$FWLYLWDWHDVWDWLVWLFLLSXEOLFHWUHEXLHV VHGHVI úRDUHUHVSHFWkQGXUP WRDUHOHSULQFLSLL

a) úL b) úL c) 3, úL d) úL e) úL 19) 6WDELOL L YDULDQWD GH DGHY

U D DILUPD LHL XUP WRDUH 5HFHQV PkQWXO FD PHWRG  GH REVHUYDUH

VWDWLVWLF 

a) QXSUHVXSXQHFXOHJHUHDGDWHORUGHODWRDWHXQLW LOHSRSXOD LHLVWDWLVWLFHELQHGHOLPLWDW  b) are exclusiv un caracter demografic; c) VHvQFDGUHD] vQVIHUDREVHUY ULORUFXFDUDFWHUSHUPDQHQW d) VHRUJDQL]HD] FXRDQXPLW SHULRGLFLWDWH e) VH RUJDQL]HD]  RUL GH FkWH RUL 6WDWLVWLFD 218 GHFODQúHD]  DF LXQHD GH HIHFWXDUH D UHFHQV PLQWHORUvQ

ULOH

membre.

20) *UDILFHOHVWDWLVWLFHWUDVDWHvQFRRUGRQDWHSRODUHVHXWLOL]HD]

vQPRGFXUHQWSHQWUXYL]XDOL]DUHD

a) RULF UHLVHULLGHGDWHVWDWLVWLFH b) VHULLORUGHUHSDUWL LH c) WUHQGXOXLWHQGLQ HL GLQHYROX LDvQWLPSDXQXLIHQRPHQ d) HYROX LDvQWLPSDXQXLIHQRPHQDIHFWDW GHRVFLOD LLVH]RQLHUH e) WHQGLQ HLOHJ WXULLGLQWUHYDULDELOHúLSHQWUXDOHJHUHDPRGHOHORUGHUHJUHVLH 21) 6H FXQRDúWH IDSWXO F

 vQWU R UDPXU  GH DFWLYLWDWH YDULDELOD ³VDODULXO PHGLX EUXW´ <  HVWH

-

GHSHQGHQW  SULQWUH DOWHOH GH ³JUDGXO PHGLX DO vQGHSOLQLULL QRUPHORU´ ;  úL ³JUDGXO PHGLX GH vQ]HVWUDUH WHKQLF  D PXQFLL´ ;  &RQWULEX LD FHORU GRL IDFWRUL ; úL ; OD YDULD LD VDODULXOXL PHGLXEUXW\ HVWHHVWLPDW SULQ

a) R y2/ x x = ry2/ x + ry2/ x ; 1 2 1 2 b) R y / x x = 1 2

r y2/ x + r y2/ x − 2ry / x ry / x rx1x2 1 2 1 2 1 − rx2 x 1 2

;

c) R y / x x = r y2/ x + ry2/ x − 2ry / x ry / x rx1x2 ; 1 2 1 2 1 2 d) rx1x2 = 0 ; e) R y / x x = 1 2

r y2/ x + ry2/ x 1 2 1 − rx2 x

.

1 2

127



r -FRHILFLHQWXOGHFRUHOD LHOLQLDU



22) Prin AUDIT-ul financiar efectuat în luna ianuarie 1998 la S.C. “ICS” SRL s-D FRQVWDWDW F  vQ IDFWXULOH HODERUDWH vQ  H[LVW  DQXPLWH HURUL vQ FDOFXOXO 79$-ului FDUH DX DYXW GUHSW VXUV  QHFXQRDúWHUHD PHWRGRORJLHL GH FDOFXO D 79$-XOXL OD XQHOH SURGXVH DSUR[LP UL HURQDWH GHIHF LXQLDOHPLMORFXOXLWHKQLFGHFDOFXOHWF 3RSXOD LDVWDWLVWLF VWXGLDW HVWH

a) ansamblul facturilor elaborate de S.C. “ICS” SRL; b) ansambOXOSURGXVHORUúLVHUYLFLLORUUHDOL]DWHGH6&³,&6´65/SkQ OD;,, c) DQVDPEOXO SURGXVHORU úL VHUYLFLLORU UHDOL]DWH GH 6& ³,&6´ 65/ GHVI FXWH SH SLD

 úL

IDFWXUDWHSkQ OD;,,

d)

DQVDPEOXO SURGXVHORU úL VHUYLFLLORU UHDOL]DWH SHQWUX D IL GHVI FXWH SH SLD

 GH 6& ³,&6´

65/IDFWXUDWHSkQ OD;,,úLODFDUHVHSHUFHSH79$

e)

DQVDPEOXO IDFWXULORU HODERUDWH GH 6& ³,&6´ 65/ SkQ  OD ;,, SHQWUX SURGXVHOH úLVHUYLFLLOHUHDOL]DWHúLGHVI FXWHSHSLD

23) G.U<XOH

úLODFDUHVHSHUFHSH79$

  SUHFL]HD]  F  LQGLFDWRULL UHSDUWL LLORU VWDWLVWLFH WUHEXLH V  vQGHSOLQHDVF 

XUP WRDUHOHFRQGL LL V ILHGHILQL LvQPRGRELHFWLY V GHSLQG GHWRDWHGDWHOHGLQVHUL V  DLE  VHPQLILFD LL FRQFUHWH   V  ILH VLPSOX GH FDOFXODW   V  ILH SX LQ VHQVLELOL OD IOXFWXD LLOH GH VHOHF LH V VHSUHWH]HXúRUODFDOFXOHDOJHEULFH $FHVWHFRQGL LLvQWRWDOLWDWH

a) sunt respectate de medie; b) sunt respectate de dispersie; c) VXQWUHVSHFWDWHGHFRYDULDQ  d) VXQWUHVSHFWDWHGHYDORDUHDPRGDO  e) nu sunt rHVSHFWDWHGHQLFLXQLQGLFDWRUDOWHQGLQ HLFHQWUDOHVDXDOYDULD LHL 24) /X

PvQFRQVLGHUDUHXQWDEHOGHFRQWLQJHQ

OXL<FRQGL LRQDWHGH;

{(y , n ), j k

jk

dispersiile:

y (x j ) =

1 n j.

unde n j . = ∑ n jk

∑y n k

k

jk úL

( )

σ 2y x j =

FRUHOD LH 

{[(x , y ), n ]j ∈ J , k ∈ K } j

k

jk

fixat , k ∈ K}3HQWUXDFHVWHDGLQXUP

[

úLGLVWULEX LLOH

VHFXQRVFPHGLLOHúL

( )]

2 1 yk − y x j n jk ∑ n j. k

 HVWH HIHFWLYXO IUHFYHQ D  PDUJLQDO  DVRFLDW  YDULDQWHL [M D YDULDELOHL ; ÌQ

k

IXQF LH GH HOHPHQWHOH SUH]HQWDWH vQ LSRWH]  GLVSHUVLD YDULDELOHL < 

varianta:

( )

[( ) ]

2 1 1 n j .σ 2y x j + ∑ n j . y x j − y ; ∑ n j n j 2 1 b) σ 2y < ∑ n j. y x j − y ; n j

a) σ 2y =

[( ) ] ( )

c) σ 2y <

1 ∑ n j.σ 2y x j ; n j

d) σ 2y =

2 1 1 n j.σ 2y x j − ∑ n j. y x j − y ; ∑ n j n j

( )

[( ) ]

σ 2y  VH SUH]LQW

 FRUHFW vQ

e) σ 2y >

[( ) ]

( )

2 1 1 n j .σ 2y x j + ∑ n j . y x j − y . ∑ n j n j

FXFRYDULDQ DGLQWUH<úLFHLODO LIDFWRULGHLQIOXHQ

25) 3HQWUX GRX HFXD LD

FXH[FHS LDIDFWRUXOXL;

 YDULDELOH VWDWLVWLFH D F URU WHQGLQ

GH

UHJUHVLH

y i = 25 − 0,7 x i 

úL

 D GHSHQGHQ HL VWDWLVWLFH D IRVW PRGHODW  SULQ

VH

PDL

FXQRVF

GLVSHUVLLOH

σ 2x = 2603,04 úL

σ 2y = 1896,6 &RHILFLHQWXOGHFRUHOD LHDUHYDOoarea: a) 0,82; b) 0,96; c) -0,96; d) -0,59; e) -0,82. 26) 'DF

 vQWUH FXDUWLOHOH FDOFXODWH SHQWUX R VHULH GH UHSDUWL LH H[LVW  UHOD LD

Q2 = (Q1 + Q3 ) / 2

DWXQFLUHSDUWL LDHVWH

a) DVLPHWULF VSUHYDORULOHPDUL b) DVLPHWULF VSUHYDORULOHPLFL c) QRUPDO  d) KLSHUEROLF  e) bidimHQVLRQDO  27) 9HULILFDUHDFRQFRUGDQ HLGLQWUHUHSDUWL LDHPSLULF

RE LQXW vQWU RFHUFHWDUHFRQFUHW úLUHSDUWL LD

-

WHRUHWLF  SUHVXSXV  VH HIHFWXHD]  FX DMXWRUXO PDL PXOWRU WHVWH ([SUHVLD

k

(ni − npi )2

i =1

np i

∑

UHSUH]LQW VWDWLVWLFDWHVWXOXL

a) Shapiro-Wilk; b) Lilliefors; c) Hi-S WUDW χ 2 ); d) Kolmogorov - Smirnov; e) Gnedenko. 28) 2JUXS

GHGHVWXGHQ LVXV LQHODGRX GLVFLSOLQHFkWHXQWHVWSHQWUXYHULILFDUHDFXQRúWLQ HORU

7HVWHOHDXSXQFWDMHGLIHULWHLDUSHED]DORUVHFXQRDúWHF 

25

2 - la testul A: ∑ xiA = 9000

25

∑ xiA = 450

i =1 25

i =1 25

i =1

i =1

2 - la testul B: ∑ xiB = 425

∑ xiB = 100

*UXSDGHVWXGHQ LHVWHPDLRPRJHQ GLQSXQFWXOGHYHGHUHDOFXQRúWLQ HORUDFXPXODWH

a) la disciplina A; b) la disciplina B; c) la ambele disciplLQHH[LVW

DFHODúLJUDGGHRPRJHQLWDWH

d) QXVXQWVXILFLHQWHGDWHSHQWUXDILVWXGLDW RPRJHQLWDWHD e) QX VH SRW FRPSDUD RPRJHQLW LOH FXQRúWLQ HORU OD FHOH

GRX  GLVFLSOLQH GHRDUHFH

punctajele testelor au fost diferite. 29) (YROX LDQXP

UXOXLGHERYLQHúLYROXPXOSURGXF LHLGHFDUQHDXHYROXDWDVWIHO

Anii Nr. bovine (mii) Prod. carne (mii tone)

1990 5381 2232

1991 4355 2023

1992 3683 1895

1993 3597 1935

1994 3481 1852

1995 3496 1846

1996 3435 1868

1997 3431 1871

'HSHQGHQ D GLQWUH FHOH GRX  YDULDELOH VH P VRDU  FX DMXWRUXO FRHILFLHQWXOXL 6SHDUPDQ DOH F UXLYDORULVXQW

a) 0,738; b) 0,901; c) -0,675; d) 0,991; e) 0,307. 30) Media ( x  XQXL HúDQWLRQ GH PDUH YROXP Q  SRDWH IL FRQVLGHUDW QRUPDO GHPHGLH

x 0 úLDEDWHUHPHGLHS

WUDWLF HURDUHPHGLH 

 F  XUPHD]  R GLVWULEX LH

σ în cazul unui sondaj simplu n

cu revenire. Pentru o probabilitate 1− α intervalul de estimare (de încredere) a parametrului

σ 3HQWUXFDSUHFL]LDHVWLPD LHLV n x 0 YROXPXOHúDQWLRQXOXL k ∈ (0;1) ) este: x 0 este x − x 0 ≤ zα

ILHPDLPLF FX

zα2 σ 2 a) n ≤ ⋅ ; k 2 x 20 b) n ≥

zα2 k

c) n =

2

(CV )2

σ2 k2 x0

XQGH&9HVWHFRHILFLHQWXOGHYDULD LH

;

z 2 k 2σ 2 d) n = α ; x0 e) Q!XQLW LvQRULFHVLWXD LH

k% din valoarea lui

TESTUL 13

 5HFHQV PkQWXOSRSXOD LHLHVWH D RREVHUYDUHWRWDO XQLF  E RREVHUYDUHWRWDO LQWHJUDO SHULRGLF  F RREVHUYDUHFXUHQW SHULRGLF 

d) o observare curHQW

GHRVLQJXU GDW 

H RREVHUYDUHSHULRGLF SDU LDO 

2) (URULOHGHUHSUH]HQWDWLYLWDWHVXQWVSHFLILFHFHUFHW

ULORU

a) prin sistemul rapoartelor statistice; b) prin sondaj; F SULQUHFHQV PkQW G SULQREVHUYDUHDS U LLSULQFLSDOH

e) prin monografii.

3) 3URSULHWDWHDGHWHUPLQDQW

DYDULDELOHL[vQED]DF UHLDVHGHWHUPLQ PHGLDDULWPHWLF HVWH

a) f ( x 2 , x 2 , ... , x 2 ) = f ( x12 , x 22 , ... , x 2n ) ; b) f ( x1 , x2 , ... , xn ) = f ( x , x , ... , x ) ;

c) f ( x1 , x22 , ... , xnn ) = f ( x , x , ... , x ) ; d) f ( x1m , xm2 , ... , xmn ) = f ( x1 , x2 , ... , xn ) ; e) f ( x1 , x2 , ... , xn ) = f ( x1 , x2 , ... , xn ) .

4) 6HFXQRVFGDWHFRQYHQ LRQale referitoare la valorile unei caracteristici: Grupe

)UHFYHQ H

9,0 - 9,5

3

9,5 - 10,0

1

10,0 - 10,5

42

10,5 - 11,0

23

11,0 - 11,5

9

11,5 - 12,0

1

12,0 - 12,5

1

Total

n = 80

&XQRVFkQG F  PHGLD DULWPHWLF  D FDUDFWHULVWLFLL [ HVWH  RPRJHQLWDWHYDULD LH HVWHGH

a) 4,62 %;

  XQLW

L FRHILFLHQWXO GH

b) 13,32 %; c) 22,19 %; d) 23,32 %; e) 14,62 %.

5) 6WDELOLUHDLQGLFHOXLSUH XULORUEXQXULORU GHFRQVXPVHIDFHGXS

UHOD LD

∑ q1 p1 a) ∑ q1 p0 ; ∑ p1 ( q1 + q0 ) b) ∑ p0 ( q1 + q0 ) ;

∑ p1 q0 ∑ p1 q1 ⋅ ∑ p0 q0 ∑ p0 q1

c)

∑ i p q0 p0 d) ∑ q0 p0 ; ∑ q1 p1 1 ∑ p q1 p1 e) i .

;

6) )DFWRUXO GH FRUHF LH LQWURGXV vQ FDOFXOXO HURULL DEDWHULL  PHGLHL GH VRQGDM vQ YDULDQWD SUHOHY QHUHSHWDWHDXQLW

LORUHVWHHJDOFX

σ2 a) n ; b) 1 - (n / N) ; 1 c) N - 1 ; 1 d) N ; e)

 1  1   /   n  N  .

7) &XQRVFkQGUHSDUWL LDYDULDELOHL[ )UHFYHQ H

Grupe 1,1 - 1,3 1,3 - 1,5 1,5 - 1,7 1,7 - 1,9

6 9 4 1

∑ ni

Total valoarea quantilei doi (Q2 HVWHHJDO a) 1,375; b) 1,51; c) 1,40;

FX

= 20

ULL

d) 1,45; e) 1,55.

8) 6HFXQRVFXUP

WRDUHOHGDWHFRQYHQ LRQDOH DVXSUDUHSDUWL LHLXQHLFDUDFWHULVWLFL

)UHFYHQ H

Grupe 11,0 - 13,0 13,0 - 15,0 15,0 - 17,0 17,0 - 19,0 Total

12 18 8 2 n = 40

'DWH ILLQG YDORDUHD PRGDO  0R [mo

) = 13,75; valoarea medie = 14,0, coeficientul de asimetrie

(Pearson) are valoarea: a) 0,377; b) 0,677; c) 1,377; d) 0,963; e) 0,09.

9) ÌQ OHJ

WXU  FX H[HUFL LXO DQWHULRU VH FHUH V  VH GHWHUPLQH GLVSHUVLD FDUDFWHULVWLFLL DOWHUQDWLYH

ELQDUH QXP UXQLW

LFXYDORULPDLPDULFD

'LVSHUVLDDFHVWHLFDUDFWHULVWLFLHVWHHJDO FX

a) 0,1875; b) 0,2875; c) 0,0912; d) 1,1725; e) 0,5000.

10) Se cunosc GDWHFRQYHQ LRQDOH DVXSUDYROXPXOXLYkQ]

ULORUvQOXQD PDUWLH OD6&*,*,

,03(;VUOSHQWUXWUHLSURGXVHGLQQRPHQFODWRUFkWúLPRGLILFDUHDSUH XULORU

Produsul

Valoarea vânz rilor în

Modificarea procenWXDO

SHULRDGDFXUHQW PLLOHL

SUH XULORU

13.860 51.300 57.200 Σ= 122.360

+ 5,0 - 10,0 + 10,0 X

1 2 3 TOTAL

D

0RGLILFDUHD DEVROXW  D YROXPXOXL YkQ] ULORU FDX]DW  GH PRGLILFDUHD SUH XULORU OD FHOH WUHL SURGXVHDIRVWHJDO FX

a) 0 (zero) mii lei; b) - 80,0 mii lei; c) + 160,0 mii lei; d) + 180,0 mii lei; e) - 102,0 mii lei.

11) &XQRVFkQG UH]XOWDWHOH FHUFHW

ULL FDUDFWHULVWLFLL ; GLQWU-XQ VRQGDM Q   XQLW L SUHOHYDWH 2 XQLW LúLDQXPH = 17,45 u.m., respectiv S = 0,61 u.m., pentru o probabilitate P = 95 % (Za  LQWHUYDOXOGHvQFUHGHUHSHQWUXPHGLDSRSXOD LHL DOHDWRUúLQHUHSHWDWGLQWU RSRSXOD LH1

JHQHUDOHHVWHHJDOFXYDORULURWXQMLWHFXGRX ]HFLPDOH 

a) (17,01 ; 17,93); b) (16,25 ; 19,73); c) (10,63 ; 22,75); d) (14,29 ; 21,33); e) (17,29 ; 17,61).

12) 6H FXQRVF XUP

WRDUHOH GDWH  FRQYHQ LRQDOH  UHIHULWRDUH OD YDORDUHD YkQ] ULORU SHQWUX GRX 

SURGXVHvQ SHULRDGD GHED]  UHVSHFWLY LQGLFLL SUH XULORU úL PRGLILFDUHD SURFHQWXDO  D YROXPXOXL

fizic. ,QGLFHOHSUH XULORU

0RGLILFDUHDSURFHQWXDO D

SHULRDGDGHED] POGOHL

(%)

volumului fizic (%)

1

10

130

0

2

12

100

0

Total

S = 22

X

X

Produsul

Valoarea vânz

ULORUvQ

0RGLILFDUHD UHODWLY  D YROXPXOXL YDORULF DO YkQ] ULORU OD QLYHOXO DQVDPEOXOXL FHORU GRX 

produse este eJDO

FX

a) + 100 %; b) + 13,64 %; c) 0 %; d) - 25,0 %; e) + 117,5 %.

13) ÌQ FDGUXO DQDOL]HL GLVSHUVLRQDOH ELIDFWRULDOH XWLOL]DW  SHQWUX D WHVWD VHPQLILFD LD IDFWRULORU GH i = 1,r ), respectiv B ( j = 1,p  DWXQFL QXP UXO LQIOXHQ  GDF   YDORULOH  IDFWRUXOXL $  gradelor de libertate al dispersiei reziduale este: a) rp - 1; b) r(r - 1); c) (r - 1)(p - 1); d) r(p - 1)p; e) r2(p - 1).

14) În cadrul analizei dispersionale unifactoriale, i = 1,r  QXP XQLW

j = 1,ni - QXP

UXO

LORU vQ JUXS  VXPD S WUDWHORU DEDWHULORU SHQWUX FDOFXOXO GLVSHUVLHL UH]LGXDOH vQ LQWHULRUXO

JUXSHL VHVWDELOHúWHFXUHOD LD

a) 2

   ∑ yij    2  j y ∑ij ij ∑i ni  ;

b)

c)

UXO JUXSHORU

  ∑ yij  j ∑i  ni

2

2

     ∑ ∑ yij      - i j  n ;

2

d)

   ∑ ∑ yij    2  i j  ∑ij yij ∑ ni ;

e)

   ∑ ∑ yij    j 2  i  y ∑ij ij n

2

;

2

2

     ∑ ∑ yij   ∑ yij      j j 2  i    ∑ij yij ∑ n ni i

15) ÌQWUHGRX

.

YDULDELOHOHJDWHXQDUH]XOWDWLY \úLDOWDIDFWRULDO [SHQWUXQ

REVHUYD LH

VH

FXQRVF

100

∑

DJUHJDWHOH

GH

FDOFXO

∑

SHUHFKLYDORULGH

100

100

∑

xi = 2105

1

;

xi2 = 49.665

1

;

100

∑

yi = 4160

1

xi yi = 96.640

; 1

.

ÌQLSRWH]DXQHLOHJ WXULOLQLDUH\x

DE[HFXD LDHVWH

a) yx = 0,963 + 12,735 x; b) yx = 1,259 + 0,799 x; c) yx = 22,933 + 12,811 x; d) yx = 5,937 + 1,694 x; e) yx = 7,339 + 2,437 x.

16) %XQXULOH GH IRORVLQ

 vQGHOXQJDW  úL FX GXUDW  PHGLH GH IRORVLQ

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DFXPXODW FXSULQG

a) Bunurile destinate s

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VSLULWXDOHDOHSRSXOD LHLFDGHH[HPSOXDXWRWXULVPHWHOHYL]RDUHDSDUDWHGHUDGLRIUL

gidere,

PRELO HWF

b) Bunurile destinate s

 VDWLVIDF  SH R GXUDW  GH SHVWH XQ DQ GLIHULWH FHULQ H PDWHULDOH úL

VSLULWXDOH DOH SRSXOD LHL FD GH H[HPSOX IRQGXO IXQFLDU FO GLULOH GH ORFXLW DXWRWXULVPHOH

televizoarele, aparatele de radio, frigiderele, mobila etc.; c) Bunurile destinate s VDWLVIDF SHRGXUDW PDLPDUHGHXQDQGLIHULWHFHULQ HPDWHULDOHúL VSLULWXDOH DOH SRSXOD LHL FD GH H[HPSOX FO GLULOH GH ORFXLW DXWRWXULVPHOH WHOHYL]RDUHOH

aparatele de radio, frigiderele, mobila etc.; d) Bunurile destinate s  VDWLVIDF  SH R GXUDW  GH PD[LP XQ DQ GLIHULWH FHULQ H PDWHULDOH úL spirituale, ca de exemplu: autoturisme, mijloace financiar-valutare, televizoare, aparate de UDGLRIULJLGHUHPRELO HWF

e) Bunurile materiale destinate s satisfac

 SH R GXUDW  GH SHVWH XQ DQ GLIHULWH FHULQ H

PDWHULDOH úL VSLULWXDOH DOH SRSXOD LHL FD GH H[HPSOX FO GLULOH GH ORFXLW DXWRWXULVPHOH PLMORDFHOHILQDQFLDUYDOXWDUHWHOHYL]RDUHDSDUDWHGHUDGLRIULJLGHUHPRELO HWF

17) (ILFLHQ DIRQGXULORUIL[HQRLVHGHWHUPLQ

e FN = a)

e FN = b)

e FN = c)

e FN = d)

e FN = e)

FXUHOD LD

∆ PIB i /i −1 FN i - 1 ; ∆ PIB i /0 FN i - 1 ; PIB

FN i ;

PIB Ff i

;

∆ PIB i /i −1 Ff i

.

unde: eFN -HILFLHQ DIRQGXULORUIL[HQRL PIB - produsul intern brut;

i = 0,n - LQGH[XOSHULRDGHORUGHUHIHULQ



Ffi - fondurile fixe în anul i; FNi - fondurile fixe noi; D -PRGLILFDUHDDEVROXW DLQGLFDWRULORU

18) 5HVXUVHOHGHPXQF

ODXQPRPHQWGDWVHGHWHUPLQ 

D  5HVXUVH GLVSRQLELOH

 7RWDO SRSXOD LH 

-

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 7RWDO SRSXOD LH DSW  GH PXQF   3RSXOD LD vQ YkUVW  GH PXQF 

dar în incapacitate) -3RSXOD LDvQDIDUDYkUVWHLGHPXQF F 5HVXUVHGLVSRQLELOH

GDUFDUHOXFUHD]

);

7RWDOSRSXOD LHDSW GHPXQF  3RSXOD LDvQYkUVW GHPXQF GDU

-

DIODW vQLQFDSDFLWDWHGHPXQF 3RSXOD LDvQDIDUDYkUVWHLGHPXQF GDUFDUHOXFUHD]  G  5HVXUVH GLVSRQLELOH

 7RWDO SRSXOD LH   3RSXOD LD vQ DIDUD YkUVWHL GH PXQF  GDU FDUH

OXFUHD] 3RSXOD LDDIODW vQLQFDSDFLWDWHGHPXQF  H  5HVXUVH GLVSRQLELOH

 7RWDO SRSXOD LH DSW  GH PXQF 

- (OHYL VWXGHQ L PLOLWDUL vQ

WHUPHQúRPHULFDVQLFH 3RSXOD LDDIODW vQLQFDSDFLWDWHGHPXQF 

19) Durata mediHD]LOHLGHOXFUXVHFDOFXOHD]



DZ ):

durata lunii de lucru durata zilei de lucru ; totalul orelor - om lucrate b) DZ = totalul om - zilelor lucrate ; totalul om - zilelor lucrate DZ = durata lunii de lucru ; c) totalul om - zilelor lucrate DZ = totalul om - orelor lucrate ; d) a) DZ =

totalul om - zilelor lucrate numarul mediu al salariatilor .

DZ = e)

20) 6HFXQRVFXUP

WRDUHOHGDWH

Indicatori

- mld. lei Modificarea (‘94/’93) %

1993

1994

12.670

31.442

+ 2,6

 &RQVXPXODGPLQLVWUD LHL

2.566

7.011

+ 3,1

 )RUPDUHDEUXW DFDSLWDOXOXLIL[

3.584

10.096

+ 20,7

4) Modificarea stocurilor

2.212

2.253

- 57,0

5) Exportul net

- 996

- 1.028

- 72,0

 &RQVXPXOILQDODOJRVSRG ULLORU

5DWDLQIOD LHLvQLQWHUYDOXO DIRVWHJDO FXFDOFXOHFXYDORULURWXQMLWH 

-

a) 73 %; b) 173 %; c) 313 %; d) 141 %; e) 256 %.

21) 'DF

VHQRWHD] 

L - durata medie a lunii de lucru; S -GXUDWDPHGLHDV SW PkQLLGHOXFUX Z - durata medie a zilei de lucru; TH - volumul om-orelor lucrate; TZ - volumul om-zilelor lucrate; WH, WZ -SURGXFWLYLWDWHDRUDU úL]LOQLF



$WXQFLSLHUGHUHDGHSURGXF LHFDXUPDUHDQHIRORVLULLLQWHJUDOHD]LOHLGHOXFUXVHGHWHUPLQ 

a) ∆Q = ( D L - durata normata) WH ;

b) ∆Q = ( DZ - durata normata) TH • WH ; c) ∆Q = ( D L - DS ) TH • WZ ; d) ∆Q = ( DZ - DS ) TH • WH ; e) ∆Q = ( DZ - 8) DS • WZ .

22) Dac

VHQRWHD] 

wi - productivitatea muncii pe subdiviziuni organizatorice ( i = 1,n ) iw -LQGLFLLLQGLYLGXDOLDLSURGXFWLYLW LLPXQFLL T -QXP UXOPHGLXDOVDODULD LORU g(T) -VWUXFWXUDVDODULD LORUSHVXEGLYL]LXQLRUJDQL]DWRULFH 0,1 -SHULRDGHOHFRPSDUDWHED] HIHFWLY $WXQFLHVWHYDODELO UHOD LD

a)

∑ w1 g(T) ∑ w0 T 1 1 = ∑ T1 ∑ w0 g (T) 0 ;

∑ w0 g (T) ∑ w0 T 1 ∑ w0 T 0 1 b) : = (T) ∑ T1 ∑ T0 ∑ w1 g 1 ;

∑ w1 T 1 ∑ w0 T 1 ∑ w1 T 1 ∑ w1 T 1 : = = 1 ∑ T1 ∑ T1 ∑ w0 T 1 ∑ w w1 T 1 i ; ∑ w0 T 0 ∑ w1 T 1 ∑ w1 T 1 d) : = ∑ T0 ∑ T1 ∑ w0 T 0 ; c)

e)

∑ w1 g (T) 0 ∑ w0 g (T) 0

=

∑ w1 T 1 ∑ w0 T 1 : ∑ T1 ∑ T1 .

23) &RQWXOVLQWHWLFGHEXQXULFRQWXO DUHvQFRPSRQHQ

XUP WRULLLQGLFDWRUL

a) R î9DORDUHDSURGXF LHLLQWHUQHSURGXF LHEUXW

- firme - stat -JRVSRG ULLPHQDMH × Import de bunuri -79$QHGHGXFWLELO

U × Consum intermediar - firme - stat -JRVSRG ULLPHQDMH × Consum final - privat - guvernamental î,QYHVWL LLEUXWH

× Impozite pe import

- firme - guvern × Export de bunuri 7RWDOXWLOL] UL

Total resurse

b) R × Valoarea ad ugat

QHW

× Import de bunuri -79$QHGHGXFWLELO × Impozite pe import

U × Consum intermediar - firme - stat -JRVSRG ULL × Consum final - privat - guvernamental î,QYHVWL LLEUXWH

- firme - guvern × Export de bunuri Total resurse

7RWDOXWLOL] UL

c) R î9DORDUHDSURGXF LHLLQWHUQHSURGXF LHEUXW

- firme - guvern (stat) -PHQDMHJRVSRG ULL × Import de bunuri -79$QHGHGXFWLELO

U × Amortizarea capitalului fix - firme - guvern (stat) -JRVSRG ULL × Consum final - privat - guvernamental î,QYHVWL LLEUXWH

× Impozite pe import

- firme - guvern 7RWDOXWLOL] UL

Total resurse d) R î9DORDUHDSURGXF LHLLQWHUQHSURGXF LHEUXW

- firme - guvern (stat) -PHQDMHJRVSRG

U )

ULL

× Consum intermediar - firme - guvern (stat) -JRVSRG ULL

× Export de bunuri -79$QHGHGXFWLELO

× Consum final - privat - guvernamental

× Impozite pe export

î,QYHVWL LLEUXWH

- firme - stat (guvern) × Import de bunuri 7RWDOXWLOL] UL

Total resurse e) R

U

î9DORDUHDSURGXF LHLLQWHUQHSURGXF LHEUXW

- firme - guvern (stat) -PHQDMHJRVSRG

ULL

× Export de bunuri - TVA nedeductLELO

× Consum intermediar - firme - guvern (stat) -JRVSRG ULLPHQDMH × Consum final - privat - guvernamental × Amortismente - firme - guvern

Total resurse

7RWDOXWLOL] UL

24) 'DF



X =  reprezinta vectorul productiei ramurilor  X1     X2     .  .    .    .    X n Y =   - vectorul productiei finale  Y1     Y2     .  .    .    .    Y n  a11 a12 ... a1n  a a ... a2n  A =  21 22 matricea coeficientilor cheltuielilor directe  ... ... ... ...    an1 ann ... ann  I - matricea unitate; T - transpus Corect HVWHUHOD LD a) Y = (I - A)-1 X; b) Y = (I - A) X; c) X = (1 - A) Y; d) X = [AT]-1 X + Y; e) Y = (1 - A) XT.

25) 5DWDDQXDO

DLQIOD LHLUHSUH]LQW 

D  &UHúWHUHD SUH XULORU GH FRQVXP P VXUDW  SULQ LQGLFHOH SUH XULORU GH FRQVXP vQ OXQD

decembrie a anului curent ID GHOXQDGHFHPEULHDDQXOXLSUHFHGHQW b) &UHúWHUHDSUH XULORUGHFRQVXPP VXUDW SULQLQGLFHOHSUH XULORUGHFRQVXPvQOXQDGHFHPEULH DDQXOXLFXUHQWID

GHOXQDRFWRPEULHOXQDSUHPHUJ WRDUHOLEHUDOL] ULLSUH XULORU

F  &UHúWHUHD SURFHQWXDO  D SUH XULORU GH FRQVXP P VXUDW  SULQ LQGLFHOH SUH XULORU GH FRQVXPvQDQXOFXUHQWID

GHDQXOGHED] 

G  0HGLD FUHúWHULORU OXQDUH DOH SUH XULORU P VXUDW  SULQ LQGLFHOH SUH XULORU GH FRQVXP FDOFXODW  FD PHGLH JHRPHWULF  D LQGLFLORU OXQDUL DL SUH XULORU GH FRQVXP FX ED]  PRELO  ODQ GLQDQXOGHFDOFXO H 6F GHUHDSURFHQWXDO DSUH XULORUGHFRQVXPP VXUDW SULQLQGLFHOHSUH XULORUGHFRQVXP vQDQXOFXUHQWID

GHDQXOGHED] 

26) 6HFXQRVFXUP

WRDUHOHGDWHUHIHULWRDUHODUHVXUVHOH3,%SHQWUXDQXl 1997 (miliarde lei): - industrie: 88.944,7 -DJULFXOWXU VLOYLFXOWXU H[IRUHVWLHU  -FRQVWUXF LL - servicii: 84.689,3 -DMXVWDUHSHQWUXSURGXF LDVHUYLFLLORUEDQFDUH- 4.415,0 -LPSR]LWHúLVXEYHQ LLSHSURGXV,6 -YDORDUHDG XJDW EUXW 

Produsul intern brut pentru anul 1997 este egal cu: a) 479.484,8; b) 249.750,2; c) 254,165,2; d) 229.734,6; e) 459.469,2.

27) 'DF

vQDQXOFkúWLJXOVDODULDOPHGLXQRPLQDOQHWDIRVWFRPSDUDWLY

cu anul 1996,

LDUSUH XULOHGHFRQVXPDXHYROXDWDVWIHO 

-P UIXULDOLPHQWDUH -P UIXULQHDOLPHQWDUH - servicii: 276,5 în structura pe cele trei categorii: -P UIXULDOLPHQWDUH -P UIXULQHDOLPHQWDUH - servicii: 11,8 % 'LQDPLFDVDODULXOXLPHGLXUHDODIRVWvQDQXOFRPSDUDWLYFXHJDO FX

a) 112,5; b) 88,9; c) 53,9; d) 250,1; e) 77,6.

28) 8WLOL]DUHDEXQXULORUúLVHUYLFLLORUvQHFRQRPLDQD LRQDO a) Consumul priYDW  FRQVXPXO JXYHUQDPHQWDO FDSLWDOXOXLIL[PRGLILFDUHDVWRFXULORU

PRGLILFDUHD VWRFXULORU

EXQXUL úL VHUYLFLL

 FRQVXPXO WRWDO  IRUPDUHD EUXW  D

XWLOL]DUHDILQDO DEXQXULORUúLVHUYLFLLORU

E  &RQVXPXO SULYDW  FRQVXPXO JXYHUQDPHQWDO

capitalul fix +

VHVWDELOHúWHFRQIRUPUHOD LHL

 FRQVXPXO ILQDO  LQYHVWL LLOH EUXWH vQ

 XWLOL]DUHD ILQDO  vQ LQWHULRUXO

ULL  H[SRUWXO GH

 XWLOL]DUHD ILQDO  D EXQXULORU  LPSRUWXO GH EXQXUL úL VHUYLFLL

-

 XWLOL]DUHD

bunurilor ce compun PIB; F &RQVXPXOSULYDWFRQVXPXOJXYHUQDPHQWDOLQYHVWL LL

le nete + modificarea stocurilor +

importul - exportul = utilizarea bunurilor; G  &RQVXPXO VWDWXOXL JXYHUQDPHQWDO   LQYHVWL LLOH EUXWH GH FDSLWDO  H[SRUWXO GH EXQXUL úL

-

servicii -LPSRUWXOGHEXQXULúLVHUYLFLL-XWLOL]DUHDILQDO serviciilor ce compun PIB;

DEXQXULORU

XWLOL]DUHDEXQXULORUúL

H  &RQVXPXO SULYDW  FRQVXPXO VWDWXOXL JXYHUQDPHQWDO   LQYHVWL LLOH QHWH GH FDSLWDO IL[  PRGLILFDUHDVWRFXULORUH[SRUWXOQHW

XWLOL]DUHDEXQXULORUúLVHUYLFLLORUFHFRPSXQ3,%

29) 6HFXQRVFXUP -

WRDUHOHGDWH

Produsul Intern Brut (PIB) în anul 1996: 108396 mld. lei pr. curente PIB 1997: 249750 mld. lei pr. curente PIB 1998 (previziune): 411.135 mld. lei pr. curente Modificarea PIB: 1997/1996 : - 6,6 % 1998/1997 : 0 %

5DWDLQIOD LHLvQLQW

ervalul 1996 - 1998 va fi de:

a) 64,50 %; b) 125,75 %; c) 115,12 %; d) 305,99 %; e) 225,75 %.

30) &DUH GLQ HOHPHQWHOH GH PDL MRV FH LQWU

 vQ FRQVXPXO GLUHFW DO SRSXOD LHL VH LQFOXGH vQ FDOFXOXO

LQGLFHOXLSUH XULORUGHFRQVXP

a) cheltuieli aferenWH SO LL PXQFLL SHQWUX SURGXF LD JRVSRG ULHL DUDW VHP îngrijirea culturilor, cositul fânului, tratamentul medical al animalelor etc.); E FKHOWXLHOLFDUHVH UHIHU ODSO

QDW SU úLW

LOHHIHFWXDWHODFUHGLWH UDWHGHDVLJXUDUHDPHQ]LMRFXULGH

noroc, impozite etc.; F FKHOWXLHOLSHQWUXSURFXUDUHDSURGXVHORUYkQGXWHSHSLD D

U QHDVF 

G  FKHOWXLHOL FX FDUDFWHU GH LQYHVWL LL úL DFXPXODUH FXPS UDUHD GH ORFXLQ H PDWHULDOH GH FRQVWUXF LLIRORVLWHSHQWUXFRQVWUXLUHDGHORFXLQ HQRLVDXHIHFWXDUHDGHUHSDUD LLODORFXLQ HOH

vechi etc.); H  FRQVXPXO GLQ UHVXUVH SURSULL UHSUH]HQWkQG FRQWUDYDORDUHD FDQWLW

LORU GH SURGXVH

FRQVXPDWHGHSRSXOD LHDOWHOHGHFkWGLQFXPS U WXULVWRFSURGXF LHSURSULHFDGRXULHWF 

TESTUL 14   3HQWUX GLVWULEX LD DQJDMD LORU XQHL FRPSDQLL GXS  QLYHOXO GH SUHJ WLUH SURIHVLRQDO  QX VH SRDWH

calcula: a) structura; E WRWDOXODQJDMD LORU

c) valoarea medie; G YDORDUHDPRGDO  H IUHFYHQ HOHQXOHGDF H[LVW   5DWDúRPDMXOXLQXVHSRDWHFDOFXODUDSRUWkQG

a) popula LDQHRFXSDW

ODSRSXOD LDFXUHQWDFWLY 

E QXP UXOGHúRPHULODSRSXOD LDDFWLY  F SRSXOD LDQHRFXSDW ODSRSXOD LDDFWLY  G QXP UXOGHúRPHULODSRSXOD LDWRWDO  H QXP UXOGHúRPHULODIRU DGHPXQF 

3) Pe termen lung poate fi doar atenuat, dar QXHYLWDWúRPDMXO a) ciclic; b) structural; c) tehnologic; d) nici una din formele de mai sus; H SRWILHYLWDWHWRDWHIRUPHOHGHúRPDM  7LWOXULOHUHSUH]HQWDWLYHDOHS U LORUVRFLDOHGHILQHVFvQ&RQWDELOLWDWHD1D LRQDO  D REOLJD LXQLOH

b) bonurile de tezaur; c) orice hârtie de valoare; G DF LXQLOH H DFHDVW GHILQL LHQXDSDUHLQ&RQWDELOLWDWHD1D LRQDO    ,QWHUYDOXO GH vQFUHGHUH SHQWUX HVWLPDUHD PHGLHL SRSXOD LHL JHQHUDOH SRUQLQG GH OD YDORDUHD FDOFXODW SHQWUXHúDQWLRQVHPDLQXPHúWHúL

a) evantaiul valorilor estimate; b) parametru de încredere; c) interval previzionat; G FODV HYDOXDW  H QXH[LVW VLQRQLPSHQWUXQR LXQHDGHLQWHUYDOGHvQFUHGHUH  ,QGLFDWRUXOWHQGLQ HLFHQWUDOHFHVLQWHWL]HD] YDORULOHvQUHJLVWUDWHDOHXQHLFDUDF

este: a) cuartila a 3-a; b) coeficientul de asimetrie; c) media; d) mediana; H QXH[LVW XQDVWIHOGHLQGLFDWRU

teristici cantitative

  &RQWXO VWDWLVWLF vQ FDUH VH vQUHJLVWUHD]   WUDQ]DF LLOH GH EXQXUL úL VHUYLFLL vPSUHXQ  FX

transferurile publice sau private dintr-RSHULRDG

vQWUHR DU úLH[WHULRUUHS H]LQW 

r

D EDODQ DFRPHUFLDO  E EDODQ DGHSO

L

F EDODQ DRSHUD LXQLORUFXUHQWH G EDODQ DOHJ WXULORUGLQWUHUDPXUL

e) tabelul input-output. 8) Sinonimul pentru ecart statistic este: a) difHUHQ VHPQLILFDWLY b) abatere; c) echilibru; d) clopotul lui Gauss;



H HFXD LHVWDWLVWLF 

 &DUWRJUDPDVHIRORVHúWHSHQWUXDUHSUH]HQWDJUDILF

D XQLW

b) c)

LVWDWLVWLFHFXGRX GLPHQVLXQLvQWRWGHDXQDGXS RFDUDFWHULVWLF 

XQLW XQLW

G XQLW

LVWDWLVWLFHFXGRX GLPHQVLXQLvQWRWGHDXQDGXS PDLPXOWHFDUDFWHULVWLFL LVWDWLVWLFHFXGRX GLPHQVLXQLQLFLRGDW GXS PDLPXOWHFDUDFWHULVWLFL LVWDWLVWLFHFXGRX GLPHQVLXQLGXS XQDVDXPDLPXOWHFDUDFWHULVWLFL

e) cartograma nu este un grafic utilizatGHVWDWLVWLF  0XO LPHDXQLW



LORUVWDWLVWLFHH[WUDVHDOHDWRULXGLQWU RFROHFWLYLWDWHVWDWLVWLF HVWHGHQXPLW úL

-

D SURE  E HúDQWLRQDUH F VFKHP SUREDELOLVWLF  G SDVGHQXP UDUH H ED] GHVRQGDM

 3HQWUXDRE LQHFHUHUHDLQWHUQ EUXW VHDGXQ ODFHUHUHDLQWHUQ QHW 

D LPSR]LWHOHLQGLUHFWHI U VXEYHQ LL E YHQLWXOQD LRQDO F LPSR]LWHOHLQGLUHFWHFXVXEYHQ LL

d) amortizarea; e) cei doi indicatori sunt egali.  'DF GLQ311H[SULPDWvQSUH XULOHSLH HLVHVFDGLPSR]LWHOHLQGLUHFWHI U VXEYHQ LLVHRE LQH

D YHQLWXOQD LRQDO

b) PNN; c) PIB; G 311H[SULPDWvQSUH XULOHIDFWRULORU

e) PNB.

  ,QGLFDWRUXO FH FDUDFWHUL]HD]  DFWLYLWDWHD XQHL HFRQRPLL QD LRQDOH SULQ vQVXPDUHD RSHUD LXQLORU HIHFWXDWHGHDJHQ LLHFRQRPLFLVHPDLQXPHúWH

a) aglomerat macroeconomic; E VXP PDFURHFRQRPLF 

c) agregat macroeconomic; d) agent macroeconomic; e) acord macroeconomic.  $F LXQHDGHFRUHFWDUHDYDORULORUvQUHJLVWUDWHDOHXQXLIHQRPHQHFRQRPLFR WHQGLQ

-social la curba sa de

GHILQHúWHRSHUD LXQHDGH

a) eliminare a valorilor aberante; b) ajustare; c) grupare; G HúDQWLRQDUH H FRUHF LHDHURULORUVLVWHPDWLFH

m

15) Prin formula

n

∑∑ f i =1 j =1

ij

(

)

⋅ y j − y ⋅ (xi − x )

VHGHILQHúWH

D QXP U WRUXOUDSRUWXOXLGHFRUHOD LH

b) numitorul coeficientului GHFRUHOD LHOLQLDU



F QXP U WRUXOFRHILFLHQWXOXLGHFRUHOD LHOLQLDU  G QXPLWRUXOUDSRUWXOXLGHFRUHOD LH H FRHILFLHQWXOGHFRUHOD LHOLQLDU 

 &RPSOHWD LVSD LXOOLEHUGLQDILUPD LD

³&RYDULDQ D UHSUH]LQW  JHQHUDOL]DUHD QR LXQLL GH ««« DSOLFDELO  XQXL VHW GH SHUHFKL GH GDWH

(atribute statistice)”, alegând dintre variantele: a) variabilitate; E YDULDQ



F YDULD LH G YDULDQW  H YDULDELO 

 &RHILFLHQWXOGHHODVWLFLWDWHVHFDOFXOHD] DVWIHO

a) ritmul de modificare a variabilei factoriale raportat la ritmul de modificare a variabilei rezultative; E  ULWPXO GH PRGLILFDUH D YDULDELOHL IDFWRULDOH vQPXO LW FX ULWPXO GH PRGLILFDUH D YDULDELOHL

rezultative; c) ritmul de modificare a variabilei rezultative raportat la ritmul de modificare a variabilei factoriale; G  ULWPXO GH PRGLILFDUH D YDULDELOHL UH]XOWDWLYH vQPXO LW FX ULWPXO GH PRGLILFDUH D YDULDELOHL

factoriale; H  PRGLILFDUHD DEVROXW  D YDULDELOHL UH]XOWDWLYH UDSRUWDW OD PRGLILFDUHD DEVROXW  D YDULDELOHL

factoriale.

18) Extrapolarea UHSUH]LQW

RSHUD LXQHDVWDWLVWLF GH

a) prelungire a valorilor unei serii cronologice dincolo de perioada pe care s-au efectuat REVHUYD LLOHFRQIRUPXQHLOHJLGHWHQGLQ



b) interpolare; c) estimare a unei valori dintr-o serie de date continue, cunoscâQGYDORULOHGLQGUHDSWDúLGLQ stânga sa; d) determinare a unui interval de încredere; H GHWHUPLQDUHDWHQGLQ HLGHHYROX LHDXQXLIHQRPHQ

  &XQRVFkQG GHILQL LLOH QR LXQLORU GH PHGLH DULWPHWLF  úL DUPRQLF  GDF  DFHVWHD VXQW FDOFXODWH SHQWUXDFHODúLVHWGHGDWHSUHFL]D LFHDILUPD LHHVWHDGHY UDW 

D RFUHúWHUHDYDORULLPHGLHLDULWPHWLFHYDGHWHUPLQDRFUHúWHUHDYDORULLPHGLHLDUPRQLFH E YDULD LDPHGLHLDULWPHWLFHGHWHUPLQ YDULD LDvQVHQVFRQWUDUDPHGLHLDUPRQLFH F  FUHúWHUHD PHGLHL DUPRQLFH YD DWUDJH GXS  VLQH vQ PRG DXWRPDW FUHúWHUHD PHGLHL

aritmetice; G VF GHUHDYDORULORUFDUDFWHULVWLFLLVWDWLVWLFHvQUHJLVWUDWHYDDWUDJHGXS VLQHVF GHUHDPHGLHL DUPRQLFHúLDULWPHWLFH H  PHGLD DULWPHWLF  HVWH LQGHSHQGHQW  GH FHD DUPRQLF  úL DPkQGRX  VXQW LQGHSHQGHQWH GH HYROX LDYDORULORUvQUHJLVWUDWHDOHFDUDFWHULVWLFLL

 9DORULOHDMXVWDWHDOHXQHLVHULLGHWLPSSRWILID

GHFHOHvQUHJLVWUDWH

a) <; b) >; c) =; d) <, =, >; e) nu se pot compara.   'DF  SHQWUX R VHULH FURQRORJLF  VXPD YDORULORU DMXVWDWH HVWH DSUR[LPDWLY HJDO  FX VXPD

valorilor înregistrate, atunci: D PHWRGDGHDMXVWDUHDOHDV QXHVWHSRWULYLW  E PHWRGDGHDMXVWDUHDOHDV HVWHRSWLP 

c) metoda de aMXVWDUHDOHDV

HVWHXQLF 

G PHWRGDGHDMXVWDUHDOHDV HVWHFRUHFW  H PHWRGDGHDMXVWDUHDOHDV HVWHH[DFW 

 5DSRUWXOGLQWUHRYDORDUHvQUHJLVWUDW úLFHDWHRUHWLF DIODW SHFXUEDGHUHJUHVLHSRDWHIL

a) supraunitar; b) subunitar; c) unitar; d) negativ; e) pozitiv. $OHJH L FRPELQD LD SRWULYLW  GLQWUH FHOH QRWD

te cu majuscule: A = a,b,d; B = b,d,e; C = a,b,c; D =

a,b; E = a

  'DF  vQ XUPD JUXS ULL XQXL VHW GH GDWH SH LQWHUYDOH GH YDULD LH HJDOH VH RE LQ IUHFYHQ H QXOH DWXQFLVHUHFRPDQG  D V VHUHJUXSH]HGDWHOHGXS RDOW FDUDFWHULVWLF 

b) se utilizea]

vQFRQWLQXDUHDFHHDúLGLVWULEX LHQH LQkQGFRQWGHIUHFYHQ HOHQXOH

F VHXWLOL]HD] vQFRQWLQXDUHGLVWULEX LDGDF HVWHGRDURVLQJXU IUHFYHQ

QXO 

G VHUHJUXSHD] GDWHOHP ULQGQXP UXOGHLQWHUYDOHGHYDULD LH H VHUHJUXSHD] GDWHOHP ULQGGL

mensiunea intervalului.

 8QULWPGHPRGLILFDUHDXQXLIHQRPHQULWPFHDUHYDORDUHDSR]LWLY LPSOLF vQPRGQHFHVDU D YDORDUHDVXSUDXQLWDU DLQGLFHOXLGHGLQDPLF  E YDORDUHDQHJDWLY DPRGLILF ULLDEVROXWH F YDORDUHDQHJDWLY DVSRUXOXLFXED] IL[  G GHVFUHúWHUHDIHQRPHQXOXL

e) stagnarea fenomenului .  3HQWUXVHULDGHGDWHUHSUH]HQWkQGGLVWULEX LDIDPLOLLORUGXS QLYHOXOGHYHQLW

Venit

Foarte VF

Nr. familii

6F ]XW

Mediu

Ridicat

20

40

20

]XW

10

Foarte ridicat 10

coeficientul de asimetrie propus de Pearson este: a) zero; b) unitar; c) egal cu -1; d) nu se poate calcula; H HJDOFXFRHILFLHQWXOGHYDULD LH

  'DF  GRX  VHULL GH GLVWULEX LH SDUDOHOH SUH]LQW  R WHQGLQ P VXUDUHDLQWHQVLW

 FXUELOLQLH SURQXQ DW  DWXQFL

LLOHJ WXULLGLQWUHFHOHGRX YDULDELOHVHDSUHFLD] vQIXQF LHGHYDORDUHD

D FRHILFLHQWXOXLGHFRUHOD LHOLQLDU  E FRYDULDQ HL F UDSRUWXOXLGHFRUHOD LH

d) valorilor ajustate; H  QX VH SRDWH FDOFXOD XQ LQGLFDWRU FH LQGLF  LQWHQVLWDWHD OHJ WXULL GDF  DFHDVWD

este

curbilinie.  9DULD LDXQHLFDUDFWHULVWLFLVWDWLVWLFHWLQGHOD]HURGDF FROHFWLYLWDWHDDQDOL]DW HVWH

a) de volum normal; E QRUPDOGLVWULEXLW GXS RFDUDFWHULVWLF  F HWHURJHQ  G RPRJHQ  H DVLPHWULF 

28) 'DF

 SHQWUX  VHULH GH GLVWULEX LH GH IUHFYHQ H FRHILFLHQWXO GH YDULD LH LQGLF  XQ QLYHO ULGLFDW GH

HWHURJHQLWDWH DWXQFL VH UHFRPDQG  vPS U LUHD FROHFWLYLW

semnificativ, ceea ce va duce la:

LL vQ JUXSH GXS  XQ IDFWRU GH JUXSDUH

D FUHúWHUHDJUDGXOXLGHRPRJHQLWDWHvQLQWHULRUXOJUXSHORU

b FUHúWHUHDJUDGXOXLGHHWHURJHQLWDWHvQLQWHULRUXOJUXSHORU F VF GHUHDJUDGXOXLGHRPRJHQLWDWHvQLQWHULRUXOJUXSHORU G FUHúWHUHDQLYHOXOXLFRHILFLHQWXOXLGHYDULD LHvQLQWHULRUXOJUXSHORU

e) nivelul de omogenitate în interiorul grupei va fi întotdeauna egal cu cel calculat pentru GLVWULEX LDPDUJLQDO   3HQWUXRSLD

FXQRDúWHPGDWHOH

Bunuri

3UH XUL

A B C D E

(u.m.) 45 90 260 115 118

&DQWLW

L

(u.c.) 300 500 900 300 800

3UH XUL

&DQWLW

(u.m.) 65 105 320 150 128

L

(u.c.) 400 500 1100 600 700

Atunci: D ÌQFRVW FXPDLPXOWGHFkWvQSHQWUXDDFKL]L LRQDDFHHDúLFDQWLWDWHGH PDUI  E ÌQFRVWDFXPDLSX LQGHFkWvQSHQWUXDDFKL]L LRQDDFHHDúLFDQWLWDWHGH PDUI FDvQ F $FHHDúLFDQWLWDWHGHEXQXULFXPS UDWHvQODSUH XULOHGLQFRVW FXPDL VFXPSGHFkWHYDOXDWHODSUH XULOHGLQ G 'DF FDQWLW

LOHFXPS UDWHvQV-DUILDFKL]L LRQDWODSUH XULOHGLQDUILFRVWDWFX 20,41% mai scump; e) sunt date insuficiente pentru a alege a,b,c, sau d.

 'DF vQWU R DU VDODULXOPHGLXDIRVWvQDQXOW0GHPLOLRQOHLúL,3&

în anul t1VDODULXOPHGLXDDMXQVODQLYHOXOGHPLOLRDQHOHLúL,3& FRQGL LLsalariul real: a) a crescut; E DVF ]XW F DU PDVQHVFKLPEDW G QXVHSRDWHSUHFL]DHYROX LDVD

e) este egal cu cel nominal din anul t1.  3 WUDWXODEDWHULLWLSP VRDU 

a) amplitudinea dispersiei unui set de date în jurul mediei lor; b) omogenitatea unui set de date; F DVLPHWULDXQHLGLVWULEX LL G WHQGLQ DFHQWUDO DXQXLVHWGHGDWH H JUDGXOGHFRQFHQWUDUHDIUHFYHQ HORU  2UDW GHVFUHVF WRDUHDLQIOD LHLSRDWHV GXF OD D FUHúWHUHDúRPDMXOXL E GHVFUHúWHUHDú

omajului; c) stagnarHDúRPDMXOXL

G úRPDMXOHVWHXQIHQRPHQLQGHSHQGHQWGHLQIOD LH

,33

,33

LDU

ÌQDFHVWH

d)

VXQW LQVXILFLHQWH LQIRUPD LL SHQWUX D SXWHD SUHFL]D LQIOXHQ D  IHQRPHQHORU GH FUHúWHUH JHQHUDOL]DW DSUH XULORUDVXSUDúRPDMXOXL

 3XWHUHDGHFXPS UDUHDPRQHGHLQD LRQDOHHVWHLQYHUVSURSRU LRQDO FX D QLYHOXOSUH XULORU

b) nivelul veniturilor; c) nivelul PIB/locuitor; G YROXPXOEXQXULORUúLVHUYLFLLORURIHULWHSHSLD



H HVWHRP ULPHLQGHSHQGHQW    /D R EDQF  VH DQDOL]HD]  GLVWULEX LD GHELWRULORU GXS  VLWXD LD ]LOHORU GH vQWkU]LHUH D UDPEXUV ULL

creditelor, astfel: ,QWHUYDOHGHYDULD LHDQXP UXOXL GH]LOHGHvQWkU]LHUHDSO

LL

Nr. debitori “mai mult decât OLPLWDLQIHULRDU ´

10-20 20-30 30-40 40-50 50-60 60-70

120 85 37 16 7 2

9DORDUHDPHGLDQ FDOFXODW XWLOL]kQGIUHFYHQ HUHODWLYHHVWH

a) 25 zile; b) 35 zile; c) 27 zile; d) 23 zile; H QXVHSRDWHFDOFXODPHGLDQDXWLOL]kQGIUHFYHQ HUHODWLYH

35) Dintr-XQVRQGDMDXUH]XOWDWGDWHOHUHIHULWRDUHODJUDGXOGHvQDYX LUHDVWIHO 1LYHOGHvQDYX LUH Procente ale populD LHL $1LYHOIRDUWHVF ]XW 50 %1LYHOVF ]XW 25 C. Nivel minim acceptabil de avere 10 '1LYHOPHGLXGHvQDYX LUH 10 (1LYHOULGLFDWGHvQDYX LUH 3 F. Nivel extrem de ridicat ...

6WUXFWXUDDYX LHL

10 20 10 15 25 ...

'HFLGH LGDF  D DYX LDHVWHHJDOGLVWULEXLW 

b) curba lui Lorentz coincide cu linia de egalitate; c) DYX LD HVWH GLVWULEXLW  LQHFKLWDELO DYDQWDMD L ILLQG FHL FX QLYHO vQDOW úL IRDUWH vQDOW GH vQDYX LUH G  DYX LD HVWH GLVWULEXLW  LQHFKLWDELO DYDQWDMD L ILLQG FHL FX QLYHO VF ]XW úL IRDUWH VF ]XW GH vQDYX LUH

e) nu se poate discuta echitatea distribuirii veniturilor.  ÌQIRUPXODHURULLPD[LPHYROXPXOHúDQWLRQXOXLVHQRWHD] FX

nGDF

a) de serii; E UHDOL]DWSHXQHúDQWLRQIRUPDWGLQXQLW

LFRPSOH[H

F UHDOL]DWSHXQHúDQWLRQIRUPDWGLQXQLW

LVLPSOH

;

VRQGDMXOUHDOL]DWHVWH

G UHDOL]DWSHXQHúDQWLRQIRUPDWGLQXQLW

e) cu nVHQRWHD]

LVLPSOHVDXFRPSOH[HLQGLIHUHQW

GHRELFHLYROXPXOSRSXOD LHLJHQHUDOH

 ÌQWUHGHFLODDWUHLDúLDúDSWHDVHDIO 

a) 40% din termenii seriei; b) 60% din termenii seriei; c) 50% din termeni seriei; d) 30% din termenii seriei; e) 70% din termenii seriei. 38) Formula lui Sturges se poate aplica pentru determinarea: D DPSOLWXGLQLLYDULD LHLXQHLFDUDFWHULVWLFL

b) valorii maxime dintr-un set de date; c) valorii minime dintr-un set de date; G QXP UXOXLGHJUXSH H QXP UXOXLGHFDUDFWHULVWLFL  'LVSHUVLDHVWHLQYHUVSURSRU LRQDO FX D YROXPXOHúDQWLRQXOXL

b) volumul caracteristicilor studiate; c) abaterea standard; d) coeficientul de asimetrie; H HVWHRP ULPHLQGHSHQGHQW    5DSRUWXO GLQWUH LQGLFHOH DJUHJDW DO SUH XULORU FDOFXODW GXS  SURFHGHXO /DVSH\UHV vQWU

-o

HFRQRPLH LQIOD LRQLVW  úL LQGLFHOH DJUHJDW DO SUH XULORU FDOFXODW GXS  SURFHGHXO 3DDVFKH HVWH GH

obicei: a) supraunitar; b) subunitar; c) unitar; d) negativ; e) QXVHúWLHH[DFW

TESTUL 15

 &RHILFLHQWXOGHYDULD LHDUDW  D GHFkWHRULHVWHPDLPDUHDEDWHUHDVWDQGDUGWLS ID

GHPHGLDDULWPHWLF 

E FXFkWHSURFHQWHHVWHGHS úLW OLPLWDGHRPRJHQLWDWHDGPLV  F FXFkWHVWHPDLPDUHDEDWHUHDVWDQGDUGID

GHPHGLDDULWPHWLF 

d) de câte ori se cuprinde abaterea standard în medie; H FkWHSURFHQWHGLQDEDWHUHDVWDQGDUGUHSUH]LQW PHGLDDULWPHWLF   'DF XQIHQRPHQHYROXHD] GXS IXQF LDWVXPDS WUDWHORUDEDWHULORUGLQWUHRSDUWHGLQ YDORULOHvQUHJLVWUDWH úLFHOHDMXVWDWHFRQVLGHUkQGYDORULOHFRUHVSXQ] WRDUHGLQ

vectorul timpului : 2,4,5,6,7: a) 0,5; b) 130; c) 133; d) 100; H DOW YDULDQW «

3) Cunoscând dRDUKLVWRJUDPDXQHLGLVWULEX LLGHIUHFYHQ HQXSXWHPUHSUH]HQWDJUDILF a) structura; E RJLYDIUHFYHQ HORUFXPXODWH

c) corelograma; G SROLJRQXOIUHFYHQ HORU H GLVWULEX LDIUHFYHQ HORUUHODWLYH  'XS ULWPLQIOD LDQXSRDWHIL

a) târâtoare; b) GHVFKLV  F JDORSDQW 

d) deflatoare; H IRUPHOHLQIOD LHLQXVHFODVLILF GXS ULWPXOGHPRGLILFDUH

5) Pentru o serie de momente nu se pot calcula: D VSRUXULFXED] vQODQ  E VSRUXULFXED] IL[ 

c) indici; d) ritmuri; H PHGLDDULWPHWLF DWHUPH

nilor seriei.

 &RPSOHWD LVSD LXOOLEHUFXXQDGLQYDULDQWHOHD

- e:

Ž9DULDELOD GLVFUHW  ; XUPHD]  OHJHD GH UHSDUWL LH ««« D SDUDPHWULORU IUHFYHQ DVDHVWHFRQIRUP

f = Cnx ⋅ p x ⋅ (1 − p)

n− x

D QRUPDO  E ELQRPLDO 

, n > 1, n ∈ Ν ,0 < p < 1 ¨

n úL p , atunci când

c) Student; d) Gauss Laplace; H QXH[LVW DFHDVW IXQF LHGHUHSDUWL LH  6WDELOL LFHUHOD LHHVHDGHY UDW 

a) PIB = VA + TVA + taxe vamale - servicii bancare imputate nerepartizate; b) PIB = VA + TVA + taxe vamale; c) PIB = VA + TVA; d) PIB = e) PIB = VA + TVA + taxe vamale + servicii bancare imputate nerepartizate.

VA;

 7HUPHQXOVWDWLVWLFGHŽUDW ŽHVWHVLQRQLPFXFHOGHŽLQGLFHŽ

a) întotdeauna; E QLFLRGDW  F GRDUGDF UDWDH[SULP RHYROX LH G GRDUGDF H[SULP SRQGHUHDXQHLS U LvQvQWUHJ

e) doar

vQFD]XOH[FHS LLORU

 /DUHFHQV PkQWVHFXOHJLQIRUPD LLGHQDWXU  D GHPRJUDILF HFRQRPLF VRFLDO  E FXOWXUDO  F GRDUHFRQRPLF  G GRDUVRFLDO  H GRDUGHPRJUDILF   6LQRQLPXOSHQWUXDEDWHUHDWLSQXVHPDLQXPHúWH

a) abatere standard; E DEDWHUHPHGLHS WUDWLF 

c) ecart tip; G YDULDQ



H YDULDQW   &RPSRQHQWDVH]RQLHU DXQHLVHULLGHWLPSDSDUHFDUH]XOWDWDODF LXQLL D  IOXFWXD LLORU OHJDWH GH DQRWLPS VDX FH VH UHSURGXF VLPLODU vQ WLPS vQ FXUVXO XQHL ]LOH V SW PkQLOXQL

trimestre;

E IOXFWXD LLORUFLFOLFH

c) factorilor aleatori; G WHQGLQ HL

e) componenta sezonieU

QXH[LVW 

 &RPSRQHQWDFLFOLF DSDUHFDXUPDUHDDF LXQLL

a) factorilor sezonieri; E IDFWRULORUFHGHWHUPLQ ID]HOHGHFRQWUDF LHúLUHOD[DUHDIHQRPH

nelor;

c) factorilor aleatori; G WHQGLQ HL H QXH[LVW DFHDVW FRPSRQHQW   &XQRVFkQGRJLYDIUHFYHQ HORUFXPXODWHQXVHSRDWHUHSUH]HQWDJUDILFvQFRQWLQXDUH

a) structura; b) histograma;

c) poligonul frecYHQ HORUDEVROXWH G SROLJRQXOIUHFYHQ HOor relative; H JUDILFXOGHHYROX LH   'DF   UDSRUWXO GLQWUH LQGLFHOH DJUHJDW DO SUH XULORU úL LQGLFHOH DJUHJDW DO YROXPXOXL IL]LF HVWH

supraunitar, atunci, indicele valorii poate fi: a) supraunitar; b) subunitar; c) unitar; d) a,b,c; e) negativ. 15) 3HQWUX P VXUDUHD HYROX LHL SUH XULORU OD QLYHOXO DJHQWXOXL HFRQRPLF VH UHFRPDQG sistemului de ponderare:

 XWLOL]DUHD

a) Laspeyres; b) Paasche; c) Fisher; d) Edgeworth; e) nici unul din cele precizate mai sus.   3HQWUX P VXUDUHD HYROX LHL SUH XULORU OD QLYHO PDFURHFRQRPLF vQ 5RPkQLD VH XWLOL]HD] 

sistemul de ponderare: a) Laspeyres; b) Paasche; c) Fisher; d) Edgeworth; e) nici unul din cele precizate mai sus. 17) În anul t1ULWPXOFLIUHLGHDIDFHULDXQHLILUPHDIRVWGHID

GHW0

. În anul XUP

WRUW2

, cifra GHDIDFHULDFUHVFXWFXùWLLQGF VSRUXODEVROXWDOFLIUHLGHDIDFHULvQSHULRDGDW2 - t0 a fost de 100 u.m., cifra de afaceri din anul t1 a fost de: a) 60 u.m.; b) 120 u.m.; c) 20 u.m.; d) 27,27 u.m.; e) nu se poate calcula datorLW 18)

LQIRUPD LHLLQVXILFLHQWH

'DF  SH R SHULRDG  GH FLQFL DQL LQGLFHOH PHGLX GH FUHúWHUH D SURGXF LHL XQXL DJHQW HFRQRPLF D

IRVW GH  vQ FRQGL LLOH vQ FDUH SURGXF LD HVWH R YDULDELO  vQVXPDELO  úWLLQG F  vQ XOWLPXO DQ QLYHOXO SURGXF LHLDIRVWFXGHXQLW

LPDLPDUHGHFkWvQSULPXODQYDORDUHDLQL LDO DSURGXF LHLDIRVWGH

a) 44,21; b) 4,21; c) 2,24; d) 3; e) nu se poate calcula.   'DF  FKHOWXLHOLOH SHQWUX FRQVXP VXQW  XP úL LQYHVWL LLOH UHSUH]LQW   GLQ YHQLWXO QD LRQDO LPSRUWXO  UHSUH]LQW 

comerciale este:

 GLQ YHQLW úL H[SRUWXO

 GLQ LQYHVWL LL DWXQFL VROGXO EDODQ HL

a) 875 u.m.; b) -875 u.m.; c) 1250 u.m.; d) 375 u.m.; e) 500 u.m..  $JUHJDWHOHPDFURHFRQRPLFHVHFDOFXOHD] 

D vQXQLW

LIL]LFH

E vQXQLW

LYDORULFH

;

F H[FOXVLYvQSUH XULOHIDFWRULORU G H[FOXVLYvQSUH XULOHSLH HL H vQSUH XULOHIDFWRULORUúLvQSUH XULOHSLH HL

 $FWLYLWDWHDGHUHGLVWULEXLUHDYHQLWXULORUDUHORFGDF 

D VHSO WHVFDMXWRDUHOHVRFLDOH E VHSO WHVFVDODULLOHDQJDMD LORU

statului;

F VHSO WHVFSHQVLLOH G VHDFKLW LPSR]LWHOH

e) a, c.  6ROGXOEDODQ HLFRPHUFLDOHVHFDOFXOHD] 

D FDUDSRUWLQWUHYDORDUHDH[SRUWXOXLúLYDORDUHDLPSRUWXOXL E FDGLIHUHQ

vQWUHFDQWLWDWHDH[SRUWDW úLFHDLPSRUWDW 

F FDGLIHUHQ

vQWUHYDORDUHDLPSRUWXOXLúLDH[SRUWXOXL

G FDGLIHUHQ

vQWUHYDORDUHDH[SRUWXOXLúLDLPSRUWXOXL

H FDGLIHUHQ

vQWUHFDQWLWDWHDLPSRUWDW úLFHDH[SRUWDW 

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LL RIHULWH SH R SLD

 HVWH GH  úL D SUH XOXL HVWH GH  FRH

ficientul

GHHODVWLFLWDWHDFHUHULLODHYROX LDSUH XOXLHVWH

a) unitar; b) supraunitar; c) subunitar; d) 3; e) 0,33.  8QDJUHJDWPDFURHFRQRPLFFHFDUDFWHUL]HD] QLYHOXOGHGH]YROWDUHDHFRQRPLHLQD LRQDOHHVWH

a) IPC; b) IPP; c) PNN/locuitor; d) PIB real; H YROXPXOSURGXF LHLWRWDOH

25) Sunt egale cu zero: D HURDUHDPD[LP GDF GLVSHUVLDHVWHHJDO FX E UDSRUWXOGHQHGHWHUPLQD LHGDF YDULD LDUH]LGXDO HVWHHJDO FX]HUR F PHGLDGDF VXPDYDORULORUFDUDFWHULVWLFLLHVWHHJDO FX]HU

o;

G FRHILFLHQWXOGHDVLPHWULHGDF PHGLDQDHVWHHJDO FXYDORDUHDPRGDO 

e) coeficientul de reprezentativitate, dac media este un indicator reprezentativ.   6WDELOL L QXP UXO FRHILFLHQ LORU vQWRWGHDXQD  VXSUDXQLWDUL VWXGLD L GH 6WDWLVWLFD 6RFLDO

-

(FRQRPLF  D WR LFRHILFLHQ LLVXQWVXSUDXQLWDUL

b) nici unul nu este întotdeauna supraunitar; F WR LFRHILFLHQ LLVXQWVXEXQLWDUL G PDMRULWDWHDFHORUVWXGLD L

e) indicii.  &RHILFLHQWXOGHDVLPHWULHSURSXVGH3HDUVRQVHDIO vQUHOD LHGHLQYHUV SURSRU LRQDOLWDWHFX

a) abaterea standard; E DEDWHUHDVWDQGDUGúLYDORDUHDPRGDO  F GLVSHUVLDúLYDORDUHDPRGDO  G PHGLDDULWPHWLF  H YDORDUHDPRGDO 

 &RHILFLHQWXOGHFRUHOD LHOLQLDU VHDIO vQUHOD LHGHGLUHFW SURSRU LRQDOLWDWHFX

a FRYDULDQ D E DEDWHUHDVWDQGDUGFDOFXODW SHQWUXYDULDELODIDFWRULDO  F DEDWHUHDVWDQGDUGFDOFXODW SHQWUXYDULDELODUH]XOWDWLY 

d) volumul datelor studiate; e) este un indicator independent.   'DF  XQ IHQRPHQ HFRQRPLF vQUHJLVWUHD]  VF GHUL FX R UDW  FUHVF WRDUH DWXQFL XOWLPXO QLYHO

observat va fi, comparativ cu primul: a) mai mare; b) mai mic; c) egal; d) nu se poate compara; H LQIRUPD LDSUH]HQWDW HVWHLQVXILFLHQW 

 ³([WHULRUXO´UHSUH]LQW vQ&RQWDELOLWDWHD1D LRQDO 

D DJHQ LLHFRQRPLFLQD LRQDOLLPSOLFD LvQWUDQ]DF LLFXVWU LQ WDWHD E DJHQ LHFRQRPLFLGLQFHOHODOWHHFRQRPLLQD LRQDOH F DJHQ LLHFRQRPLFLFHGHVI úRDU DFWLYLW

LGHFRPHU H[WHULRU

d) a,b,c; e) b,c.  ,QWHUYDOXOGHvQFUHGHUHSHQWUXPHGLDDULWPHWLF HVWHFXDW

ât mai mic cu cât:

D YROXPXOHúDQWLRQXOXLHVWHPDLPLF E SUREDELOLWDWHDFXFDUHVHJDUDQWHD] UH]XOWDWHOHHVWHPDLPLF  F UD LDGHVRQGDMHVWHPDLPDUH G YROXPXOHúDQWLRQXOXLVFDGH H SUREDELOLWDWHDGHJDUDQWDUHDUH]XOWDWHORUHVWHFRQVWDQW 

32),QIOD LDHVWHFDX]DW

GHGHILFLWXOEXJHWDUGDF 

D FUHúWHUHDFKHOWXLHOLORUVWDWXOXLGHS úHúWHFUHúWHUHDYHQLWXULORU E FKHOWXLHOLOHVWDWXOXLGHS úHVFYHQLWXULOH F FUHúWHGDWRULDLQWHUQ DVWDWXOXL G VHHPLWHPRQHG I U DFRSHULUHvQEXQXULúLVHUYL H VHHFKLOLEUHD] EDODQ DGHSO

cii;

L

 2SHUD LXQLOHHFRQRPLFHGHFRQVXPVXQWUHDOL]DWHGHF WUH D GRDUGHF WUHDJHQ LLHFRQRPLFLFHHIHFWXHD] RSHUD LXQLDVXSUDEXQXULORUúLVHUYLFLLORU E WR LDJHQ LLHFRQRPLFL F WR LDJHQ LLHFRQRPLFLH[FOXVLYPHQDMHOHúLDGPLQLVWUD LLOHSXEOLFH G DGPLQLVWUD LLOHSULYDWH H VRFLHW

LOHILQDQFLDUHQHILQDQFLDUH

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b) administrD LLOHSULYDWH F VRFLHW

LOHGHDVLJXUDUH

G VRFLHW

LOHEDQFDUH

H VRFLHW

LOHFRPHUFLDOHQHILQDQFLDUH

 /XQJLPHDRSWLP DXQHLYDORULHVWLPDWHSHED]DGDWHORUGLQHúDQWLRQHVWH D GLIHULW GHFHDFDOFXODW SHQWUXSROXOD LDWRWDO  E DSURSLDW GHFHDFDOFXODW SHQWUXSROXOD LDWRWDO  F HJDO FXFHDFDOFXODW SHQWUXSROXOD LDWRWDO  G QXVHSRDWHGHWHUPLQDRYDORDUHRSWLP 

e) variantele a - d sunt false, corect este......…  0HWRGDLQGLFLORUQXSRDWHILXWLOL]DW SHQWUXDQDOL]D

a) compaUD LLORUvQSURILOWHULWRULDO E GHVFRPSXQHULLXQXLIHQRPHQFRPSOH[SHIDFWRULGHLQIOXHQ F GHWHUPLQ ULLJUDGXOXLGHLQIOXHQ



DXQXLIDFWRUDVXSUDDOWXLIDFWRU

G HYROX LHLXQXLIHQRPHQ

e) analiza estimatorilor unui fenomen complex. 37) 9DULD LDWRWDO

DXQHLFDUDFWHULVWLFLVWXGLDWHSHQWUXXQHúDQWLRQHVWHLQYHUVLQIOXHQ DW GH

D YROXPXOHúDQWLRQXOXL E YDULD LDUH]LGXDO  F YDULD LDVLVWHPDWLF  G YDULD LDH[SOLFDW  H FRHILFLHQWXOGHYDULD LH

38) 'DF

 VH JUXSHD]  XQ VHW GH GDWH SH LQWHUYDOH HJDOH GH YDULD LH SHQWUX D RE LQH  R GLVWULEX LH D

IUHFYHQ HORU PDL DSURSLDW  GH IRUPD GLVWULEX LHL QRUPDOH QXP UXO GH JUXSH úL GLPHQVLXQHD ILHF UXLLQWHUYDO

D YRUFUHúWH

b) vor scade; F U PkQFRQVWDQWH G HYROXHD] vQVHQVFRQWUDU

e) nu se poate preFL]DHYROX LDORU 39) Cuartila întâi este: D PHGLDDULWPHWLF GLQWUHFXDUWLODDGRXDúLDWUHLD E GLIHUHQ DGLQWUHFXDUWLODDGRXDúLDWUHLD F UDSRUWXOGLQWUHFXDUWLODDGRXDúLDWUHLD G RYDORDUHVLWXDW ODGLQWHUPHQLLVHULHL H HJDO FXYDORDUHDPLQLP DFDUDFWHULVWLFLL  ÌQWUHGHFLODD]HFHDúL[minVHDIO 

a) 90% din termenii seriei analizate; b) 10% din termenii seriei; c) 100% din termenii seriei; G MXP WDWHGLQWHUPHQLLVHULHL H GHFLODD]HFHDQXH[LVW 

TESTUL 16 1) DesprHSURGXF LDPDUI Filiala

DILOLDOHORUXQHLVRFLHW

Structura valorii

0RGLILFDUHDDEVROXW DYDORULLSURGXF LHL

SURGXF LHLPDUI vQ

PDUI FDXUPDUHDPRGLILF ULLSUH XULORU

în T1ID

perioada T0 (%) 25 35 …

A B C

LFRPHUFLDOHVHFXQRVFXUP WRDUHOHGDWH

GH70

0RGLILFDUHDUHODWLY D SUH XULORUvQ71ID

(mld.lei)

GH

T0 (%) +20 +25 +8

10 18 6

6H FXQRDúWH GHDVHPHQHD F  YDORDUHD SURGXF LHL PDUI  OD ILOLDOD & vQ 70 FDUDFWHUL]D vQ GLQDPLF  SURGXF LD PDUI  D VRFLHW

a fost 80 mld. lei. Pentru a e s-a determinat indicele valorii,

LL FRPHUFLDO

YROXPXOXL IL]LF úL DO SUH XULORU SUHFXP úL FRHILFLHQWXO GH FRUHOD LH U  GLQWUH LQGLFLL LQGLYLGXDOL DL YROXPXOXLIL]LFúLDLSUH XULORU9DORULOHDFHVWRUDvQRUGLQHDSUHFL]DW PDLVXVVXQW

2)

a)

úLU



b)

úLU! 

c)

úLU! 

d)

úLU 

e)

úLU 

);

8Q VRQGDM $ GH YROXP Q vQ ED]D F UXLD VH HVWLPHD]  PHGLD P D SRSXOD LHL VWDWLVWLFH SHQWUX YDULDELOD ; SULQ HVWLPD LD

x a  HVWH PDL HILFLHQW GHFkW VRQGDMXO % GH DFHODúL YROXP Q vQ ED]D

F UXLDVHHVWLPHD] DFHHDúLPHGLHPSULQHVWLPD LD

xb GDF

H[LVW UHOD LD

a) M ( x a ) = M ( x b ) = m si D( x a ) < D( x b ) ; b) M ( x a ) = M ( x b ) sau D ( x a ) < D ( xb ) ; c) M ( x a ) = M ( x b ) m si D ( x a ) > D ( x b ) ; d) M ( x a ) < M ( x b ) si D( x a ) < D( x b ) ; e) M ( x a ) < M ( x b ) sau D ( x a ) < D ( x b ) . 1RW 0[ úL'[ UHSUH]LQW PHGLDúLGLVSHUVLDOXL;

3) Dintre conturile macroeconomice, din SCN, nu are sold: a) FRQWXOGHUHSDUWL LHDYHQLWXULORU b) contul de creare a veniturilor; c) FRQWXOSURGXF LH d) contul sintetic de bunuri; e) contul de modificare a patrimoniului; 4)

3HED]DYDORULORULQGLYLGXDOHDOHDFHOHLDúLYDULDELOHQXPHULFH;vQUHJLVWUDWHODFHOHQXQLW SRSXOD LHLVWDWLVWLFH3V DFDOFXODWPHGLDDULWPHWLF 

-

x YDORDUHDPHGLDQ

LDOH

0H úLXQLFDYDORDUH

PRGDO  0R  ÌQWUH FHOH WUHL YDORUL VLQWHWLFH V D VWDELOLW F  H[LVW  XUP WRDUHD LQHJDOLWDWH

-

x < Me < Mo $FHDVW

a)

LQHJDOLWDWH

VXJHUHD] F FHOHPDLPXOWHXQLW

LGLQ3vQUHJLVWUHD] YDORULLQGLYLGXDOHGHSODVDWHF WUH

valorile mari; b)

VXJHUHD]  F  FHOH PDL PXOWH YDORUL LQGLYLGXDOH GLQ FHOH vQUHJLVWUDWH VXQW GHSODVDWH F WUH

valorile mici; c)

HYLGHQ LHD] FRQFHQWUDUHDYDORULORULQGLYLGXDOHF WUH0R

d)

HYLGHQ LHD] VLPHWULDUHSDUWL LHLVWDWLVWLFH

e)

QXDUHQLFLRVHPQLILFD LHHFRQRPLF 

5) Soldul contului macroeconomic „Crearea veniturilor” este:

6)

a)

9DORDUHDDG XJDW EUXW 

b)

3URGXVXOLQWHUQEUXWODSUH XULOHIDFWRULORU

c)

3URGXVXOLQWHUQEUXWODSUH XULOHSLH HL

d)

3URGXVXOLQWHUQQHWODSUH XULOHIDFWRULORU

e)

3URGXVXOQD LRQDOQHWODSUH XULOHIDF

torilor.

6H FRQVLGHU  R SRSXOD LH VWDWLVWLF  3 GH YROXP 1 QXP UQDWXUDOQHQXOGLIHULWGH/DXQLW

s-D XUP

ULW YDULDELOD QXPHULF  ; DOH F

Q

.

k: unde, n- YROXPXO HúDQWLRQXOXL úL N- un LOHGHREVHUYDUHDHúDQWLRQXOXLGHYROXPQ– normal – xi = i (cu I=1,2,…,N). UHL YDORUL LQGLYLduale au fost

'LVSHUVLD PHGLHL GH VHOHF LH vQ FD]XO vQ FDUH HúDQWLRQXO D IRVW IRUPDW DOHDWRU úL I U  UHYHQLUH

este:

N +1 N ( N + 1) N (k − 1)( N + 1) k −1 ; (k − 1) 12 2 ; d). 12 b). ; c). ; e). 12 ; a). 2 7)

3HQWUXYHULILFDUHDOHJ WXULLDXWRUHJUHVLYHGHRUGLQXOvQWkLGLQWUHWHUPHQLLXQHLVHULLFURQRORJLFH VHXWLOL]HD] FHOPDLIUHFYHQW

a)

WHVWXOGHYHULILFDUHDQRUPDOLW

LLUH]LGXXULORU

n

d=

∑ (e − e

t −1

t

t =2

)2

n

∑e

2 t

t =1

b) testul Durbin-Watson definit prin

ˆ , unde et = yt − yt este eroarea de

PRGHOUH]LGXDO DIHUHQW YDORULLWDYDULDELOHLWLPS

n

d= c) testul Durbin-Watson definit prin

∑ (e − e t =3

t −1

t

)2

n

∑e t =1

2 t

;

n

d=

∑ (e − e t =2

t −1

t

n

∑e t =1

d) testul Durbin-Watson definit prin

)2

t

;

e) testul Student. 8)

$QDOL]kQG OHJ WXUD GLQWUH 6&1 úL WDEHOXO LQSXW RXWSXW 7,2  FRQVWDW P F  SULQ vQVXPDUHD

-

FRPSRQHQWHORUFDGUDQXOXLDO7,2VHRE LQH

a)

3,%ODSUH XULOHSLH HLSULQPHWRGDXWLOL] ULLILQDOH

b)

3,%ODSUH XULOHSLH HLSULQPHWRGDGHSURGXF LH

c) P1%ODSUH XULOHSLH HLSULQPHWRGDXWLOL]

9)

ULLILQDOH

d)

3,%ODSUH XULOHSLH HLSULQPHWRGDYHQLWXULORU

e)

311ODSUH XULOHIDFWRULORU

3HQWUX DFHHDúL VHULH FURQRORJLF  WUHQGXO V PHWRG V

-a calculat eroarea mHGLHS

-a determinat prin mai multe metode. Pentru fiecare -

WUDWLF DDMXVW ULL6 DXRE LQXWXUP WRDUHOHUH]XOWDWH

0HWRGDGHDMXVWDUHXWLOL]DW

(URDUHDPHGLHS WUDWLF DDMXVW ULLXP

•

0HWRGDLQGLFHOXLPHGLXGHGLQDPLF 0,0

29.51

•

Metoda sporului mediu (MSM)

27.88

•

Metoda mediilor mobile (MMM) cu periodicitatea p=5 ani

17.14

•

MMM cu p=2 ani

5.97

3UHFL]D LFDUHGLQDILUPD LLOHXUP WRDUHHVWHIDOV 

a)

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b)

FHYDPDLSUHFLV GDUQXVHPQLILFDWLYPDLEXQ HVWHDMXVWDUHDSULQ06

c)

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GHRDUHFHQHWH]LUHDRVFLOD LLORUHVWHPDLDFFHQWXDW 

d)

DMXVWDUHDSULQ000FXS

HVWHPDLEXQ GHFkWFHDSULQ000FXS



e)

FHD PDL EXQ  DMXVWDUH FRPSDUDWLY FX FHOHODOWH PHWRGH XWLOL]DWH HVWH FHD RE LQXW  SULQ 000 FX

p=2. 10) (IHFWXDUHDFDOFXOHORUPDFURHFRQRPLFHvQ6&1QXSRDWHIDFHDEVWUDF LHGHIOX[XULOHJHQHUDWHGH DFWLYLWDWHD VHFWRUXOXL ÄVWDW´ 5HIHULWRU OD DFHVW VHFWRU SUHFL]D L FDUH GLQ XUP WRDUHOH DILUPD LL HVWHIDOV 

St St a) veniturile sale provin din impozite de la menaje private ( I M ) , de la firme ( I F ) úLSDU LDO GLQSDUWLFLSDUHDODDFWLYLWDWHDHFRQRPLF 

b)

YHQLWXULOH VDOH VXQW IRORVLWH SHQWUX UHPXQHUDUHD DQJDMD LORU GLQ VHFWRUXO SXEOLF SHQWUX FXPS UDUHD GH EXQXUL GH OD ILUPH VXEYHQ LL 6 úLF WUHPHQDMHSULYDWH

-

c)

( PI ST ) 

(VSTT )

,

SHQWUX WUDQVIHUXUL F WUH ILUPH

M ST

(T ) ;

DFWLYLWDWHD VWDWXOXL GH SURGXFHUH D EXQXULORU FROHFWLYH GH UHJXO  VH FRQFHQWUHD]  vQ

fluxuri bilaterale; ST ST M M d) I M + I F = VST + PI ST + TST + S + EST , unde EST

e)

GLIHUHQ DGLQWUHYHQLWXULúLFKHOWXLHOL

DFWLYLWDWHDVWDWXOXLJHQHUHD] SUHSRQGHUHQWIOX[XULvQWU

-un singur sens.

11) În cazul sondajului simplu, de volum n, analizându-VH DEDWHUHD PHGLH S

WUDWLF  D PHGLHL GH

VHOHF LHFDP VXU WRUDOHURULLPHGLLGHUHSUH]HQWDWLYLWDWHVHFRQVWDW 

n ori;

a)

FkQGQFUHúWHSUHFL]LDHVWLP ULLSDUDPHWULORUFUHúWHDSUR[LPDWLYGH

b)

FkQGQFUHúWHSUHFL]LDHVWLP ULLSDUDPHWULORUFUHúWHH[DFWGH

c)

FkQGQVFDGHSUHFL]LDHVWLP ULLSDUDPHWULORUFUHúWHDSUR[LPDWLYGH

d)

FkQGQFUHúWHSUHFL]LDHVWLP ULLSDUDPHWULORUFUHúWHWRWGHQRUL

e)

FUHúWHUHDVDXUHGXFHUHDOXLQQXDIHFWHD] SUHFL]LDHVWLP ULLSDUDPHWULO

n ori; n ori; or.

12) &RQFRUGDQ DvQWUHUDQJXULOHGHODODQDOHYDORULORUYDULDELOHLIDFWRULDOHúLUDQJXULOHGHODOD Q DOH YDORULORU YDULDELOHL HIHFW VH SRDWH H[SULPD QXPHULF FX FRHILFLHQWXO GH FRUHOD LH DO OXL

Spearman (rs  úLFX FHODO OXL .HQGDOO Uk). În cazul îQ FDUH Q HVWH PDUH vQWUH FHL GRL FRHILFLHQ L

H[LVW UHOD LD

a)

rs =

2 2 rk rk = rs 3 ; b) 3 ; c) 2rk − 3rs = 1 ; d) rk + rs = 0 ; e) rk = rs .

13) &DOFXOXODYX LHLSURGXFWLYHVHUHDOL]HD]

SHED]DXUP WRDUHORUHOHPHQWH

a)

UHVXUVHOHQDWXUDOHVWRFXULúLUH]HUYHúLEXQXULGHFDSLWDO

b)

VWRFXULúLUH]HUYHSUHFXPúLXWLODMHPDúLQLúLHFKLSDPHQWH

c)

VWRFXULUH]HUYHúLPLMORDFHIL[H

d)

DYX LDGHFRQVXPDPHQDMHORUSULYDWHúLDVWDWXOXLVWRFXULUH]HUYHúLEXQX

e)

VWRFXULúLUH]HUYHXWLODMHPDúLQLHFKLSDPHQWHFRQVWUXF LL

14) 8Q DQDOLVW GH PDUNHWLQJ XUP

ri de capital;

UHúWH HIHFWXO FKHOWXLHOLORU FX UHFODPD [  DVXSUD YHQLWXULORU GLQ

YkQ] UL \  SH R SHULRDG  GH  GH OXQL ÌQ XUPD SUHOXFU ULL GDWHORU SULPDUH V

-au oE LQXW y = 18.84 . În

σ = 353.44 ; σ = 22.09 ; cov(x,y)= 70.7; x = 75.2  úL urma analizei statistice s-DDMXQV ODFRQFOX]LD F GHSHQGHQ DGLQWUHFHOHGRX  YDULDELOH SRDWHIL modelat  SULQWU-R IXQF LH GH JUDGXO vQWkL (FXD LD PRGHOXOXL GH UHJUHVLH úL YDORDUHD FDOFXODW  D

XUP WRDUHOH UH]XOWDWH

2 x

2 y

OXLWXWLOL]DW SHQWUXWHVWDUHDVHPQLILFD LHLFRHILFLHQWXOXLGHFRUHOD LHvQDFHDVW RUGLQHHVWH

a) yˆ = 3.8 + 0.2 x b) yˆ = 3.8 − 0.2 x

c) yˆ = 0.2 + 3.8 x d) yˆ = 0.2 + 3.8 x e) yˆ = 3.8 + 0.2 x

úLW



úLW



úLW



úLW



úLW



15) Despre patru firme dintr-XQFRQFHUQVHFXQRVFXUP

WRDUHOHGDWH

Firma

6WUXFWXUDSURGXF LH

3URGXF LDUHDOL]DW GHILUPHvQ

A B C D

în perioada T0 (%) 15 25 20 40

T1 în raport cu cea a firmei A 1.0 1.8 1.4 2.5

'HS úLUHDQHUHDOL]DUHD  SURJUDPXOXLGHSURGXF LHvQ71

6H PDL FXQRDúWH GH DVHPHQHD F  SURGXF LD UHDOL]DW  GH ILUPD $ vQ 71 GHYDQVkQGSURGXF LDUHDOL]DW GL DDMXQVODXUP WRDUHDFRQFOX]LH

a)

n T0FXÌQXUPDSUHOXFU

a fost de 75 mld. lei, -

ULLGDWHORUSHQWUXvQWUHJXOFRQFHUQV

SURJUDPXOGHSURGXF LHDIRVWGHS úLWFXLDUSURGXF LDUHDOL]DW GLQ71DIRVWHJDO FXFHD

din T0; b)

(%)

+20 -10 0 +30

SURJUDPXO GH SURGXF LH QX V

-a realizat cu 8.83%,

LDU SURGXF LD UHDOL]DW  vQ 71

a fost mai mare

decât cea din T0; c)

LQGLFHOH UHDOL] ULL SURJUDPXOXL GH SURGXF LH vQ 71 D IRVW GH  LDU SURGXF LD SURJUDPDW 

pentru T1DFUHVFXWID d)

GH70

cu 120%;

LQGLFHOHUHDOL] ULLSURJUDPXOXLGHSURGXF LHDIRVWGHLDUSURGXF LDUHDOL]DW vQ71 PDLPDUHGHFkWFHDUHDOL]DW vQ70

e)

a fost

cu 117.9 mld. lei;

SURJUDPXOGHSURGXF LHSHQWUX71DIRVWGHS úLWFXPOGOHLLDUSURGXF LDUHDOL]DW vQ71

fost mai mare decât cea din T0 cu peste 5%.

a