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CHAPTER ONE Introductionand Data Collection

1.'I

WHY LEARNSTATISTICS

The reality TV seriesTheApprenticestarsthe real estatedeveloperDonald Trump. When it premieredseveralyearsago,Trump assignedtwo teamsof contestants the task of setting up and running a lemonadestand.At the time, a number of businesspeople criticizedthat task as not beinga realisticbusinesstask.They sawthe task of sellinglemonadeas a simple act of salesmanship that was moredependent on the persuasive skills of the sellerthan anythingelse. If you haveeversold lemonadeor held otherchildhoodjobs suchas sellingcookiesor you know your task was fairly simple.For example,to delive deliveringdaily newspapers, you needonly to keeptrackof a list of addresses newspapers, andperhapsrecordthe weeklyor monthlypayments.In contrast,salesand marketingmanagersof the newspaperneedto keep track of muchmoredata-including the incomes,educationlevels,lifestyles,andbuyingpreferencesof their subscribers-in orderto makeappropriatedecisionsaboutincreasingcircula tion andattractingadvertisers. But unlessthat newspaper hasa tiny circulation,thosemanager are probablynot looking at datadirectly.Insteadthey are looking at summaries,suchas the percentage who attendedat leastsomecollege,or trying to uncoverusefulpatof subscribers terns,suchaswhethermoresubscriptions aredeliveredto single-familyhomesin areasassoc atedwith heavysalesof luxury automobiles. That is to say,the managersat the newspaper are usingstatistics,the subjectofthis text. Statistics is the branchof mathematicsthat transformsdatainto useful informationfor decisionmakers.Thesetransformations often requirecomplexcalculationsthat arepracti if cal only doneby computer,so usingstatisticsusuallymeansalsousingcomputers. This is especiallytrue whendealingwith the largevolumesof datathat a typicalbusinesscollects Attempting to do statisticsusing manualcalculationsfor such data would be too timeconsumingto benefita business. Whenyou learnstatistics,you learna setof methodsand the conditionsunderwhich it is appropriatefor you to usethosemethods.And becauseso manystatisticalmethodsarepracti cal only when you use computers,learningstatisticsalso meanslearningmore aboutusing computerprogramsthatperformstatisticalanalyses.

1.2

FOR MANAGERS STATISTICS

Today,statisticsplaysan everincreasingimportantrole for businessmanagers. Thesedecisio makersusestatisticsto: T I I I

lThe statisticalterms population and sample are formally defined in Section 1.3,on page 5.

Presentanddescribebusinessdataand informationproperly Draw conclusionsaboutlargepopulations,usinginformationcollectedfrom samplesl Make reliableforecastsabouta businessactivitv Improvebusinessprocesses

"Statistics for managers" means knowing more than just how to perform these tasks Managers need a conceptual understanding of the principles behind each statistical analysis they undertake in order to have confidence that the information produced is correct and appropriate for a decision-making situation. To help you master these necessaryskills, every chapter of Statisticsfor Managers Using Microsoft Excel has a Using Statistics scenario. While the scenarios are fictional, they represen realistic situations in which you will be asked to make decisions while using Microsoft Excel to transform data into statistical information. For example, in one chapteq you will be askedto decide the location in a supermarket that best enhancessales of a cola drink, and in another chapter,you will be asked to forecast sales for a clothing store. (You will not be asked,as the television apprenticeswere asked,to decide how best to sell lemonadeon a New York City stree corner.)

1.2: Statistics for Managers

How This Text ls Organized en

Table 1.1 shows the chapters of Srali.sric'.s Jbr Managers [Jsing Microxlft Exc'el organized accordinsto the four activitiesfor which decisionmakersuse statistics.

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Presentingand DescribingInformation DataCollection(ChapterI ) PresentingDatain TablesandCharts(Chapter2) NumericalDescriptiveMeasures(Chapter3) DrawingConclusions About PopulationsUsing SampleInformation BasicProbability(Chapter4), a prerequisitefor the restof the chaptersof this group SomeImportantDiscreteProbabilityDistributions(Chapter5) The Normal Distributionand OtherContinuousDistributions(Chapter6) and Sampling and SamplingDistributions(Chapter7), which leadto ConfidenceIntervalEstimation (Chapter8) andHypothesis Testing(Chapters 9 12) DecisionMaking(Chapterl7) Making ReliableForecasts (Chapterl3) SimpleLinearRegression (Chapter14) lntroduction to MultipleRegression MultipleRegression Model Building(Chapter15) Time-SeriesForecasting and IndexNumbers(Chapter16) ImprovingBusinessProcesses Statistical Applications in QualityandProductivity (Chapterl8) Management Methodspresented in the ChaptersI 3 areall examplesof descriptivestatistics,thebranch of statisticsthat collects,summarizes, and presentsdata.Methodsdiscussed in Chapters7 through12 areexamplesof inferential statistics,the branchof statisticsthat usessampledata to drawconclusionsaboutan entirepopulation.(Chapters4 6 providethe foundationin probability and probabilitydistributionsneededfor Chapters1-12.) The definitionof inferential statisticsusesthe termssampleandpopulation,the secondtime you haveencountered these wordsin this section.You can probablyfigure out that you cannotlearnmuch aboutstatistics until you learnthe basicvocabularyof statistics.Continuenow with the first Using Statistics scenario, which will help introduceyou to severalimportanttermsusedin statistics.

USINGSTATISTICS @ Good Tunes Good Tunes,a growing four-storehome entertainmentsystemsretailer,seeksto double their number of stores within the next three years.The managershave decided to approach local area banks for the cash neededto underwrite this expansion.They need to prepare an electronic slide show and a formal prospectusthat will argue that Good Tunesis a thriving businessthat is a good candidatefor expansion. You have been asked to assist in the process of preparing the slide show and prospectus.What data would you include that will convincebankersto extendthe credit it needsto Good Tunes?How would you presentthat data?

In this scenario,you needto identifythe mostrelevantdatafor the bankers.BecauseGood Tunesis an ongoingbusiness,you can startby reviewingthe company'srecords,which show both its currentand recentpaststatus.BecauseGoodTirnesis a retailer,presentingdataabout thing to do.Youcould includethe detailsof everysales the company'ssalesseemsa reasonable that GoodTunes transactionthat hasoccurredfor the pastfew yearsasa way of demonstrating is a thrivingbusiness. would overwhelm However,presentingthe bankerswith the thousandsof transactions them and not be very useful.As mentionedin Section1.1,you needto transformthe transactions datainto informationby summarizingthe detailsof eachtransactionin someusefulway that would allow the bankersto (perhaps)uncovera favorablepatternaboutthe salesover time. Onepieceof informationthat the bankerswouldpresumablywantto seeis the dollarsales totalsby year.Tallyingandtotalingsalesis a commonprocessof transformingdatainto information and a very commonstatisticalanalysis.When you tally sales or any otherrelevant dataaboutGoodTunesyou chooseto use-you follow normalbusinesspracticeandtally by a businessperiodsuchas by month,quarter,or year.Whenyou do so, you end up with multiple values:salesfor this year,salesfor lastyear,salesfor the yearbeforethat,andso on. How best to referto thesemultiplevaluesrequireslearningthe basicvocabularyof statistics.

1 . 3 BASICVOCABULARY OF STATISTICS Variablesare characteristics of itemsor individualsand arewhat you analyzewhenyou usea by year,andnet profit by year statisticalmethod.For the GoodTunesscenario,sales,expenses arevariablesthat the bankerswould wantto analyze. VARIABLE A variable is a characteristic of an item or individual.

When usedas an adjectivein everydayspeech,variablesuggeststhat somethingchangesor andnet profit to havedifferentvaluesfrom year varies,andyou would expectthe sales,expenses, with a variable,andmoresimply,the "data" to year.Thesedifferentvaluesarethe data associated to be analyzed.In latersections,you will be sometimesaskedto enterthecell rangeof a variablein Excel.Whenyou seesuchan instruction,you shouldenterthecell rangeof thedifferentvaluesthat collectivelyarethe datato be analzyed.(Section1.6on page I 1 explainswhat a cell rangeis and how to enterdatain Excel.) furtherdiscusses Variablescan differ for reasonsotherthantime. For example,if you conductedan analysis of the compositionof a largelectureclass,you would probablywant to includethe variables classstanding,gender,and major field of study.Thosevariableswould vary,too, becauseeach studentin the classis different.Onestudentmight be a freshmanmaleEconomicsmajor,while anothermay be a sophomorefemaleFinancemajor. unlesstheir variableshaveoperaYou alsoneedto rememberthat valuesaremeaningless tional definitions. Thesedefinitionsare universallyacceptedmeaningsthat are clearto all with an analysis.While the operationaldefinitionfor salesper yearmight seem associated couldoccurif onepersonwasreferringto salesper yearfor theentire clear,miscommunication chain of storesand anotherto salesper year per store.Even individual valuesfor variables sometimesneeddefinition-for the classstandingvariable,for example,whatexactlyis meant by the words sophomorearrdjunior? (Perhapsthe most famous exampleof vaguedefinitions elecwasthe definitionof a valid vote in the stateof Floridaduringthe 2000U.S.presidential Supreme a U.S. required ultimately aboutthe operationaldefinitionsthere tion. Vagueness Courtruling.) Understandingthe distinctionbetweenvariablesand their valueshelps in learningfour in previoussections. otherbasicvocabularyterms,two of which you havealreadyencountered

POPULATION A population consistsof all the items or individualsaboutwhich you want to draw a conclusion. SAMPLE A sampleis the portion of a populationselectedfor analysis. PARAMETER A parameter is a numericalmeasurethat describesa characteristicof a population. STATISTIC A statistic is a numericalmeasurethat describesa characteristicof a sample. All the GoodTunessalestransactionsfor a specific year,all the customerswho shoppedat GoodTunesthis weekend" all the full-time studentsenrolledin a college,and all the registered votersin Ohio are examplesof populations.Examplesof samplesfrom thesefour populations would be 200 GoodTunessalestransactionsrandomlyselectedby an auditorfor study,30 Good Tunescustomers askedto completea customersatisfaction survey,50 full-timestudentsselected for a marketingstudy,and 500 registeredvotersin Ohio contactedvia telephonefor a political poll. In eachsample,the transactions or peoplein the samplerepresent a portionof the itemsor individualsthat makeup the population. "The averageamountspentby all customerswho shoppedat GoodTunesthis weekend"is an exampleof a parameterbecausethe amountspentin the entirepopulationis needed.In contrast, "the averageamountspentby the 30 customerscompletingthe customersatisfactionsurvey"is an exampleof a statisticbecausethe amountspentfrom only the sampleof 30 peopleis required.

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TheExcel Companion to Chapter 2 and suitshowyouliketo learn. Doyouliketo learn thosefor laterchapters will helpyouunder- bybuilding thingsfromscratch, onestepat a standhowyoucanapplythestatistical meth- time?lf sq using Excel waywouldbe theBasic odsdiscussed in thisbookbyusingMicrosoft thebestwayforyou.Doyouworryaboutthe youwill timeit takesto buildthingsandthetypingenors program Foreachmethod Usinganycomputer is a two-step Excel. discussed, process learntwo waysthatyoucanuse youmightmake? 0r do youliketo learnby thatbegins withlearning to operate typically theprogram Oneway,labeled BasicExcel,uses closely examining a solution to discover its andthenadvances to mastering Excel. process howto applythe program withoutanyoutside enhancements to details, a discovery somecallreverse to a decision- Excel Theotherway,labeled making task-andExcel theprogram. PHStat2, engineering? In eitherof thesecases, using isnoexception. uses thefreePHStat2 statistics add-in* thatis PHStaO wouldbeyourbestchoice. TheExcel Companion to thischapter will youwill not helpyou become familiarwith operating included onthisbook's CD. Fora fewstatistical methods, These two waysaretrulyinterchange- findeithera BasicExcelwayor a PHStat2 way, Excel. In writingthatCompanion, we have youcreateusing dueto thelimitations of Excel. Forsuchmethassumed thatyouhaveoperated a personal able.TheExcelsolutions (ornearly either waywillbeidentical so)to ods,youwillfindExcel workbook filesonthe computer inthepastto dosomething suchas play eachotherandtheexample worksheets and book's CDthatyoucanopenanduseasa temsurftheWeb,sendan instantmessage, (Actually, youseein thisbook.Youcanswitch plateforcreating yourownsolutions. music or games, or writehomework assign- charts thetwowaysat anytimeasyouuse youwillfindfilesthatcontain template examments. lfyouhavenever useda personal com- between plesforevery puter foranyoftheseorsimilar anycomprehension of statistical method discussed inthe activitielyou thistextwithoutlosing youto per theExcel material. Thatthisbookincludes trruo Excel Companions workshould aska friendto introduce andfor everyExcel youreadtheCom- complementary waysof learning Microsoft sheetor chartillustrated in thisbook. A good sonal computers before pointfortheseexamples panion isa distinctive feature of thebook. starting aretheExcel forthischapter. WhilethisCompanion Excel wasprimarily workbook filesnamed forthechaoters of this writtenfornovices, experienced Itr?cii'lr n'rr.l,rv ht.sf.fitr Excel text, such as Chapter 2.xls.) users will benefitfromlearning the "1'tttt';' yourinstructor youto useone wordsusedto describe requires Regardless oI thewayyouuseandlearn the Excel ooerations Unless youareinvitedto goonlineand way,youmaywantto choose Excel, inthisbook. a waythatbest Microsoft Ithoughwe havetalkeda lot aboutstatistics to this point, we haven'tmentioned much aboutusingMicrosoftExcel.

youwill explore theWebsiteforthisbook.Ihere, findsupplementary material aboutusingExcel, including discussions of Excel techniques that theauthors werenotableto include inthebook because ofspace limitations.

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Postscript:lsn't Usingan Add-in a BadThing? lfyouareanexperienced Microsoft Excel user, youmayhaveconcerns aboutusinganadd-in Youmaybeconcerned suchas PHStat2. that youwillbecome you dependent onsomething wouldnotbeableto usein business or think thatusingPHStat2 somehow means thatyou

1.4

arenotreallyusingandlearning Microsoft It istruethatotheradd-intincluding addExcel. insfor otherintroductory business statistics Bothof theseconcerns areunfounded. textbooks, canobscure Microsoft Excel bynot PHStat2 isa learning toolwhose solepurpose building an Excel-based solution andonly information isto helpyouunderstand howExcel canbe reporting outcomes andstatistical (andinvisibly) usedto support specific statistical methods. thattheadd-inhasinternally PHStat2 is designed to makeusingMicrosoft computed. Usingsuchadd-ins wouldnotbe Excel moreconvenient, by doingthe"busy truly"learning" Microsoft Excel, andusing such work"activities of creating an Excel solution, add-ins wouldleaveyoudependent ontheir PHStat2 modelExcel suchascellformatting, for you,Whenyou use.Incontrast, creates youwillunder- solutions readtheExcel Companions, thatyoucanexamine andincorporate isdoingforyouin a gen- intovourownExcel solutions. standwhatPHStat2 eralized wayaswellaswhatit isdoingspecificallyfor a problem(followingthe BasicExcel i instructions).

*SectionEl.6 that beginson page 28 exolains whatan add-inis.

DATACOLLECTION The managersat Good Tunesbelievethat they will havea strongerargumentfor expansionif they can showthe bankersthat the customersof GoodTlnes are highly satisfiedwith the service theyreceived.How couldthe managersdemonstrate thatgoodservicewasthetypicalcustomerexperienceat GoodTunes? Unlike the earlierGoodTirnesscenario,in which salesper yearwasautomatically collected as part of normal businessactivities,the managersnow facethe twin challengesto first identiff relevant variablesfor a customersatisfactionstudy and then devise a method for data collection-that is, collectingthevaluesfor thosevariables. Many differenttypesof circumstances, suchasthe following,requiredatacollection: : r r r

A marketingresearchanalystneedsto assessthe effectivenessof a new television advertisement. A pharmaceuticalmanufacturerneedsto determinewhethera new drug is more effective thanthosecurrentlyin use. An operationsmanagerwantsto monitor a manufacturingprocessto find out whetherthe quality of productbeing manufacturedis conformingto companystandards. An auditor wantsto review the financial transactionsof a companyin order to determine whetherthe companyis in compliancewith generallyacceptedaccountingprinciples.

In eachof theseexamples,andfor theGoodTunesmanagers aswell, collectingdatafrom every item or individualin the populationwould be too difficult or too time-consuming. Becausethis is the typical case,datacollectionalmostalwaysinvolvescollectingdatafrom a sample.(Chapter7 methodsof sampleselection.) discusses Unlike the GoodTunesexamplethat beginsthis section,the sourceof the datato be collectedis not alwaysobvious.Data sourcesare classifiedas being eitherprimary sourcesor secondarysources.Whenthe datacollectoris the oneusingthe datafor analysis,the sourceis primary.Whenthepersonperformingthe statisticalanalysisis not the datacollector,the source is secondary. Sourcesofdata fall into oneoffour categories: I ' I r

Data distributedby an organizationor an individual A designedexperiment A survey An observational study

Organizations and individualsthat collectandpublishdatatypicallyusethat dataasa primary sourceand then let othersuse it as a secondarysource.For example,the United States federal governmentcollects and distributesdata in this way for both public and private purposes.The Bureauof Labor Statisticscollectsdata on employmentand also distributesthe monthly consumerprice index. The CensusBureauoverseesa variety of ongoing surveys

r e g a r d i n gp o p u l a t i o n ,h o u s i n g ,a n d r n a r r u f - a c t u r i nagn d u n d e r t a k e ss p e c i a ls t u d i e so n t o p r c s such as crime. travel,and healthcare. alsodistributedatapertainirrgto specificindusMarket researchfirms and tradeassociations tries or markcts.Investmcntservicessuch as Mergent'sprovidefinancial dataon a cornpany-bycorrpanybasis.SyndicatedservicessuchasAC Nielsenprovideclientswith datathat enablesthe of client productswith thoseof thcir competitors.Daily newspapersare filled with cor.nparison numericalinfbmrationregardingstockprices.weatherconditions,and sportsstatistics. O u t c o m e so f a d e s i g n e de x p e r i m e n ta r e a n o t h e r d a t a s o u r c e .T h e s e o u t c o m e sa r e t h e resultsof an experirnent,such as a test of severallaundry detergentsto comparehow well each detergentreulovesa ccrtain type of stain.Developingproper experimentaldesignsis a subject rnostlybeyondthe scopeofthis text becausesuchdesignsoften involve sophisticatedstatistical procedures.However.some of the fundamentalexperimentaldesignconceptsare discussedin C h a p t e r s1 l a n c l1 2 . are askedquesConductinga survey is a third type of data source.Peoplebeing sr-rrveyed tions about their beliefs, attitudes,behaviors,and other characteristics.For example,people could be askcdtheir opinion about which laundry detergentbestremovesa certaintype of stain. (This could lead to a resultdifferentfrorn a designedexperimentseekingthe sameanswer.) Conducting an observationalstudy is the fourth important data source.A researcherco[lectsdataby directly observinga behavior,usuallyin a naturalor neutralsetting.Observational grottps use./bclt.s studiesare a colnlron tool fbr data collection in business.Market researchers to a target audiposed a moderator questions by to responses open-ended to elicit unstructured building. group and consensus involve dynamics ence.Other, more strllcturedtypes of str.rdies Observationalstudy techniquesare also used in situationsin which cnhancingteamwork or goal. improving the quality of prctductsar.rdserviceis a rnanagetnent l d e n t i f y i n g t h e r n o s t a p p r o p r i a t es o u r c ei s a c r i t i c a l t a s k b e c a u s ei f b i a s e s .a r n b i g u i t i e s , o r o t h e r t y p e s o f e r r o r s f l a u , t h e d a t a b e i n g c o l l e c t e d ,e v e n t h e m o s t s o p h i s t i c a t e ds t a t i s tical rnethodswill not produce useful infbruration. For the Good Tunes exarnple,variables r e l c v a n t t o t h e c u s t o m e r e x p e r i c n c ec o u l d t a k e t h e f o r m o f s u r v e y q u e s t i o n sr e l a t c d t o v a r i o u s a s p e c t so f t h e c u s t o n r e re r p e r i e n c e ,e x a l l r p l e so f w h i c h a r e s h o w u i n F i g u r e l . l .

F I G U R E1 . 1 O u e s t i o n sa b o u t t h e G o o d T u n e sc u s t o m e r expenence

1. H o w m a n v d a v s d i d i t t a k e f r o m t h e t i m e y o u o r d e r e d y o u r m e r c h a n d i s e t o t h e t i m e you received it?_ 2. Did you buy any merchandise that was featured in the Good Tunes Sunday newspaper sales flyer for the week of your purchase? Yes -

3 . W a s t h i s y o u r f i r s t p u r c h a s ea t G o o dT u n e s ?Y e s-

No

No

4, Are you likely to buy additional merchandise from Good Tunes in the next 12 months? Yes

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5 . H o w m u c h m o n e y { i n U . S . d o l l a r s )d o y o u e x p e c t t o s p e n d o n s t e r e o a n d c o n s u m e r electronics equipment in the next 12 months?'6 . H o w d o y o u r a t e t h e o v e r a l l s e r v i c e p r o v i d e d b y G o o d T u n e s w i t h r e s p e c tt o y o u r recent purchase? Excellent E

Very good n

Fair !

Poor !

7. How do you rate the selection of products offered by Good Tunes with respect to other retailersof home entertainment systems? Excellent I

Very good n

Fair E

Poor n

8. How do you rate the quality of the items you recently purchased f rom Good Tunes? Excellent !

Very good n

Fair I

Poor !

The survey might also ask questionsthat seekto classify customersinto groups for later analysis. One good way for Good Tunesto avoid data-collectionflaws would be to distributethe questionnaire to a randomsampleof customers(asdiscussed in Chapter7). A poor way would be to rely on a businessrating Web site that allows online visitors to ratea merchant.SuchWeb sitescannotprovide assurancethat thosewho do the rating are customers.

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eb-based surveys andratingsseemto beofgrowing importance for manymarketers. Iheiruseandmisuseraisemanyconcerns. Bycoincidence, while writing Section 1.4,oneof usreceived anemail requesting thatheratetheManiottRewards travelloyaltyprogram a perfect" 10" inthevoting for the InsideFlyer Freddie Awards. The authorhadneverheardof thoseawards, but soonhe received otheremailsfromvarious programl othertravelloyalty alsoasking that thesame highrating besubmitted. Heevengot anemailfora program forwhichhehadjust signed up in thepriormonth(andfora travel company ofwhichhewasnotyeta customer). Atthesame time,another oneof usfound anarticlein IheNer,v YorkTimes thatreoorted

thatInternet travelsiteshadto closely monitor submitted reviews to avoidfraudulent claims "HotelReviews (C.Elliott, Online: In Bedwith Hope,Half-Truths andHype,"TheNewYork pp.C1, C8).lhe Ilmes, February 7,2006, article alsoreported thata hotelin KeyWest,Florida, offered itsguests a 10%discount if theypublisheda ravereviewof thathotelona particulartravelWebsite!Ourco-author withallthe "Freddie" emails feltcheated. Haveyoueverreceived an emailasking you to ratean onlinemerchant? Manyof us have,especially whenwe havejustpurchased something froman onlinemerchant. Often, suchemails comewithanincentive, not unlikethe KeyWesthotel'sdiscount. Would an incentive causeyou to rate the merchant? Wouldtheincentive affectyouropinion?

Whatwouldyousayabouta ratings Web sitethataccepts advertising frommerchants thatareratedon thesite?Whatwouldyou Websitethatgetspaida sayabouta ratings if a visitor firstviewsa rating commission and thenclickson a linkforthemerchant? These practices areamongthe several thatmay raiseethical concerns forsome. lf youdousea ratings Website,besure to checkoutthe "fineprint"on yournext youwill finda privacy visit.Although statementthatexplains howtheWebsiteuses you,most datathatcanpersonally identify likelyyouwill not find a "datacollection statement" thatexolains the methods the Websiteusesto collectits data.Perhaps findsucha statement. voushould

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1.5

TYPESOF VARIABLES Statisticiansclassifyvariables as eitherbeing categoricalor numericaland further classify numericalvariablesas havingeitherdiscreteor continuousvalues.Fisure 1.2 showsthe relationshipsandprovidesexamplesof eachtype of variable.

F I G U R E1 . 2 Typesof variables

AuestionTypes

Data Type Categorical

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How tall are you?

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Categoricalvariables(alsoknownas qualitative variables)havevaluesthat canonly be placedinto categories,suchas "yes" and "no". Questions24 in Figure l.l are examplesof categoricalvariables,all ofwhich have"yes" or "no" astheir values.Categoricalvariablescan alsoresultin more thantwo possibleresponses. An exampleof this type of variableis asking customersto indicatethe day of the week on which they madetheir purchases.Questions6-8 resultin oneoffour possibleresponses. Numerical variables (alsoknown as quantitative variables)havevaluesthat represent quantities.For example,Questions1 and 5 in Figure l.l are numericalvariables.Numerical variablesare further subdividedas discreteor continuousvariables.

1.5: Typesof Variables

Discrete variables havenumericalvaluesthat arisefrom a countingprocess."The number of magazinessubscribedto" is an exampleof a discretenumericalvariablebecausethe response is one of a finite numberof integers.You subscribeto zero,one,two, and so on magazines.The numberof daysit takesfrom the time you orderedyour merchandiseto the time you receiveit is a discretenumericalvariablebecauseyou arecountingthe numberof days. Continuous variables producenumericalresponsesthat arise from a measuringprocess. The time you wait for teller serviceat a bank is an exampleof a continuousnumerical variablebecausetheresponsetakeson anyvaluewithin a continuum,or interval,dependingon theprecision of the measuringinstrument.For example,your waiting time could be I minute, 1.I minutes,I . I I minutes,or 1.I 13minutes,dependingon the precisionof the measuringdeviceyou use. Theoretically,with sufficient precision of measurement,no two continuousvalues will be identical.As a practicalmatter,however,most measuringdevicesarenot preciseenough to detectsmall differences,and tied valuesfor a continuousvariable(i.e., two or more items or individualswith the samevalue)are often found in experimentalor surveydata.

Levelsof Measurementand MeasurementScales Using levels of measurementis anotherway of classifyingdata.There are four widely recognizedlevelsof measurement: nominal,ordinal.interval,andratio scales. Nominal and Ordinal Scales Data from a categoricalvariableare measuredon a nominal scaleor on an ordinalscale.A nominal scale(seeFigure 1.3)classifiesdatainto distinct categoriesin which no ranking is implied. In the GoodTirnescustomersatisfactionsurvey,the answerto the question'Are you likely to buy additionalmerchandise from GoodTirnesin the next 12 months?" is an exampleof a nominal scaledvariable,as are your favorite soft drink, your political party affiliation, and your gender.Nominal scalingis the weakestform of measurementbecauseyou cannotspecify any ranking acrossthe variouscategories.

Categorical Variable PersonalComputer Ownership

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F I G U R E 1 . 3 E x a m o l eosf n o m i n asl c a l e s An ordinal scaleclassifiesdatainto distinct categoriesin which ranking is implied. In the GoodTlrnessurvey,the answersto the question"How do you rate the overall serviceprovided by Good Tuneswith respectto your recent purchase?"representan ordinal scaledvariable becausethe responses"excellent,very good"fair, and poor" are rankedin order ofsatisfaction level.Figure1.4lists otherexamplesof ordinalscaledvariables.

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Categorical Variable

Ordered Categories

Student classdesignation Product satisfaction

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Faculty rank

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Freshman Sophomore Junior Senior Very Unsatisfied Fairly Unsatisfied Neutral Fairly Satisfied Very Satisfied Professor Associate Professor Assistant Professor

lnstructor -> AAA AA A BBB BB B CCC CC C DDD DD Standard& Poor'sbond ratings+ Studentgrades +-*ABCDF

F I G U R E 1 . 4 E x a m o l eosf o r d i n asl c a l e s

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than nominalscalingbecausean observed Ordinal scalingis a strongerform of measurement value classified into one categorypossessesrnore of a property than does an observedvalue classified into another category.However, ordinal scaling is still a relatively weak form of measurementbecausethe scale does not accourrtfor the amount of the differencesbetvveenthe categories.The ordering implies oriy which categoryis "greater,""better,"or "more preferred" notby hrnr nruc'h. Intervgl snd Rutio Scales Data from a numerical variable are measuredon an interval or a ratio scale.An interval scale (seeFigure 1.5) is an orderedscalein which the diflerencebefween measurementsis a meaningful quantity but doesnot involve a true zero point. For example,a noontime ter.nperature readingof 67 degreesFahrenheitis 2 degreeswarmer than a noontirnereadingo1' 65 degrees.In addition, the 2 degreesFahrenheitdifferencein the noontime temperaturereadings is the same as if the two noontirnetemperaturereadingswere 74 andl6 degreesFahrenheit becausethe differencehas the samemeaninganywhereon the scale.

F I G U R E1 . 5 E x a m p l e so f i n t e r v a l and ratio scales

Numerical Variable

Level of Measurement

T e m p e r a t u r (ei n d e g r e e sC e l s i u so r F a h r e n h e i t ) Standardizedexam score (e.9.,ACT or SAT) H e i g h t( i n i n c h e so r c e n t i m e t e r s ) W e i g h t( i n p o u n d so r k i l o g r a m s ) A g e ( i n y e a r so r d a y s ) S a l a r y( i n A m e r i c a nd o l l a r so r J a p a n e s ey e n )

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Interval Interval Ratio Ratio Ratio Ratio

A ratio scale is an ordered scale irl which the dif'ferencebetween the rneasurements involvesa true zero point, as in height,weight, age,or salaryrreasurements. ln the Good Tunes customer satisfactionsurvey,the amount of money (in U.S. dollars) you expect to spendon stereoequipment in the next l2 months is an example of a ratio scaledvariable.As another e x a m p l e . a p e r s o n w h o w e i g h s 2 4 0 p o u n d s i s t w i c e a s h e a v y a s s o m e o n ew h o w e i g h s 1 2 0 p o u n d s .T e r n p e r a t u r ei s a t r i c k i e r c a s e : F a h r e n h e i a t n d C e l s i u s( c e n t i g r a d e )s c a l e sa r e "zero" intervalbut not ratio scales;the value is arbitrary.not real.You cannotsaythat a noontime temperaturereadingof 4 degreesFahrenheitis twice as hot as 2 degreesFahrenheit.But a Kelvrn temperaturereading,in which zero degrecsmeansno molecularmotion, is ratio scaled.In contrast,the Fahrenheitand Celsiusscalesuse arbitrarilyselectedzero-degreebegirrningpoints. D a t a r r e a s u r e do n a n i n t e r v a l s c a l e o r o n a r a t i o s c a l ec o n s t i t u t et h e h i g h e s tl e v e l s o f measllrement.They are strongerforms of rreasurementthan an ordinal scalebecauseyou can not only which observedvalue is the largestbut also by how much. deterr.nine

Learning the Basics 1.1 Three different beveragesare sold at a fastnsstsr food restaurant soft drinks, tea, and coffee. I I a. E,xplainwhy the type of beveragesold is an exampleof a categoricalvariable. b. Explain why the type of beveragesold is an erarnplc of a nominal scaledvariable. 1.2 Soft drinks are sold in three sizes at a fast-food restaurant-small, rncdium,and large. Explain why the size of the soft drink is an examolcof an ordinal scaled variable. 1.3 Supposethat you measurethe tirne it takes to download an MP3 file fiom the Internct.

a. E,xplainwhy the downloadtime is a continuousnumencal variable. b. Explain why the download time is a ratio scaled variable.

Applying the Concepts For eachof the following variables,determine |-l-Elil1.4 whether the variable is categoricalor numerical. ffiffi If the variable is numerical.detennine whether the variableis discreteor continuous.In addition.determinethe level of r.neasurement for eachof the following. a. Nunrber oftelephonesper household b . L e n g t h ( i n m i n u t e s ) o f t h e l o n g e s t l o n g - d i s t a n c ec a l l made per month

c. Whethersomeonein the householdowns a cell phone d. Whetherthereis a high-speedInternetconnectionin the household 1.5 The following informationis collectedfrom studentsupon exiting the campusbookstoredurins the first weekof classes: a. Amountof time spentshoppingin the bookstore b. Numberof textbookspurchased c. Academicmajor d. Gender Classifyeachof thesevariablesas categoricalor numerical.If the variable is numerical.determinewhether the variableis discreteor continuous.In addition.determine thelevelof measurementfor thesevariables. 1.6 For eachof the following variables,determine whetherthe variableis categoricalor numerical.If the variableis numerical,determinewhetherthe vuiableis discreteor continuous.In addition,determinethe for eachof the following. lwel of measurement t. Nameof Internetprovider b. Amountof time spentsurfing the Internetper week c. Numberof emailsreceivedin a week d. Numberof online purchasesmadein a month 1.7 Foreachof the following variables,determinewhether thevariableis categoricalor numerical.If the variableis numerical,determinewhether the variable is discrete or In addition,determinethe level of measurement @ntinuous. foreachof the following. l. Amountof moneyspenton clothing in the pastmonth h Favoritedepartmentstore g Most likely time period during which shopping for clothingtakesplace(weekday,weeknight,or weekend) d"Numberof pairsof winter glovesowned

1.8 Supposethe following informationis collectedfrom RobertKeeler on his applicationfor a homemortgageloan at the Metro County Savingsand Loan Association: a. Monthly payments:51,427 b. Numberofjobs in past l0 years:I c. Annual family income:$86,000 d. Marital status:Married Classifueachofthe responses by type ofdata and level of measurement. 1.9 Oneof the variablesmostoften includedin surveysis income.Sometimesthe questionis phrased"What is your income (in thousandsof dollars)?" In other surveys,the respondentis askedto "Place an X in the circle correspondingto your income level" and given a number of incomerangesto choosefrom. a. In the first format,explainwhy incomemightbe consideredeitherdiscreteor continuous. b. Which of thesetwo formats would you prefer to use if you were conductinga survey?Why? c. Which of thesetwo formats would likely bring you a greaterrate of response?Why? 1.10 If two studentsscorea 90 on the same examination,what argumentscould be usedto showthat the underlyingvariable-test score-is continuous? 1.1 1 The directorof marketresearchat a largedepartment storechain wantedto conducta surveythroughouta metropolitan area to determinethe amount of time working womenspendshoppingfor clothing in a typical month. a. Describeboth the populationandthe sampleof interest, and indicatethe type of datathe director might want to collect. neededin (a) b. Developa first draft ofthe questionnaire questions and by writing a seriesof three categorical threenumericalquestionsthat you feel would be appropriate for this survey.

1.6 MICROSOFT EXCELWORKSHEETS When you use Microsoft Excel, you place the data you have collected in worksheets. Worksheetsappearas pagescontaininggridlinesthat separateindividuallyletteredcolumns from numberedrows. While worksheetslook like the simple tablesyou can createin a word processingprogram,worksheetshavespecialfeaturesthat areparticularlysuitedto dataanalysis. Understandingthe special featuresof worksheetswill help you to better understandthe interplayof dataandresultsin MicrosoftExcel.

WorksheetCells The intersectionsof the columnsand rows of worksheetsform boxescalledcells.You refer to a cell by its column letter and row number.For example,you refer to the cell in the first column and secondrow as cellA2 andthe cell in the fifth columnand first row ascell E 1. You enterin a cell a singlevalue or an expressionthat can includea referenceto anothercell. This flexibiliry asexplainedfurtherin SectionEl.3 of theExcelCompanionto this chapter,is oneof the special featuresthat makesMicrosoft Excel more thanjust a fancy table-orientedword processor.

You can refer to more than one cell in a cell reference. If you want to refer to a group of cells that forms a contiguous rectangular area, you can use a cell range in which referencesto the upper leftmost cell and the lower rightmost cell are joined with a colon. For example, the cell range Al:C2 refers to the six cells found in the first two rows and three columns of a worksheet.Excel also allows rangessuch asA:A or 4'.4,as a shorthandway of referring to all the cells in a column or a row. Later in this text, you will seecell rangessuch as D I :D8,FI :F8 that refer to cells from two non-adjacentarea of a worksheet. Worksheetsexist inside a workbook, a collection of worksheetsand other types of sheets, including chart sheetsthat help visualize data. Usually, you will use only one sheetat any given time and open to a worksheetby clicking its sheettab (see Section El.l). If someonesaysthat they are opening an "Excel file," they are most likely opening a workbook file. All versions of Excel can open workbook files saved using the .xls file format (and all Excel files on the Student CD are in this format). Excel 2007 can also open workbooks saved in the newer .xlsx format discussedin Appendix F.

Designing Effective Worksheets Becausethousands of cellsareavailableon individualworksheets, you will neverhaveto worry aboutrunningout of cells to use.This spaciousness of worksheets invitescarelessuseand causessometo ignore the importantprocessof effectivelyarrangingworksheetdata.Poor arrangements can increasethe chanceofuser errors,createconfusingresults,leadto unattractiveprintouts.or worse. To be consistent with standard business usage,you shouldassociate columncell rangeswith variables.[n this arrangement, you usethe first (row 1) cell of a columnfor a namelabelfor a variableandplacethe datafor the variablein the subsequent cellsof thecolumn.Youdo not skip any rows as you enterdata,so columncell rangeswill nevercontainany emptycells.(Empty cellscaninterferewith Excelability'sto processyour dataandcanleadto inaccurate results.) This standardpracticeis alwaysusedin this text andin all of the Excelfiles on the student you shouldneverdeviCD. Becauseall of the Excelinstructionsassumethis dataarrangement, atefrom this practicewhenyou usethis book. Anothergoodpracticeis to placeall the variableson a worksheetthat is separatefrom the worksheetcontainingthe results.Suchseparationwill increasethe reusabilityof your results worksheetand minimize the chanceof inadvertentchangesto the valuesof your variables as you constructyour results.In the workbooksfound on the book'sCD as well as the workbooksproducedby PHStat2,you will generallyfind a Resultsworksheetshowingthe results separate from the worksheetcontainingthe variables. Sometimes, worksheetsusedin this book requireonly the valuesof certainparameters or goodpracticeis to statisticsandnot the valuesassociated with a variable.For suchworksheets, placethe parameters and statisticsat the top of the worksheetso that a usercaneasilyperform what-if analyses,changingvaluesto seetheir effectson the results.In this book, thesevalues alwaysappearin bol4 in cellstinteda shadeExcel callslight turquoiseand underthe heading Data.Whenyou seesuchtintedcells,you know that you canchangethe valuesin thosecellsto performwhat-if analysesand solveotheqsimilarproblems. Anothergood designpracticeis to allow the userto be ableto explicitly seethe chainof calculationsfrom the startingdata,throughany intermediatecalculations, to the results.This practiceis particularlyadvantageous whenpreparingstatisticalworksheets most"interbecause mediatecalculations"are statisticsthemselves.Showingthe chain of calculationshelpsyou reviewyour worksheetfor errorsandhelpsothersbetterunderstand whatyour worksheetdoes. In the worksheetsof this book, intermediatecalculationsappearunder the heading Intermediate Calculationsand are in a cell rangethat immediatelyprecedesthe cell range containingthe results.The resultsappearin cells that are tinted a light yellow and contain boldfacedtext.Thereis alsoa headingoverthe resultscellsthat varieswith the type of statistical analysisperformed. Whetheryou usethe worksheetdesignof this book or your own design,do not overlook the importanceof skippingrowsor columnsto createwhite spaceto separate differentregions

of the worksheetthat presentresults.In this book, worksheetstend to skip only a singlerow or a singlecolumn.This choiceis due moreto makingall illustrationscompactthan any hardor fast rule. You shouldexperimentwith your own worksheetswith an eyeto making them easyto follow on both the displayscreenand the printedpage.Do not hesitateto createtwo copiesof your worksheets-one optimized for the screen,the other for the printer, if you haveanything but the simplestworksheetto produce.

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erhapsyou haveheardfromsome i . people that Microsoft Excel I shouldn'tbe usedfor statistics or r the Internet . vou havesearched

nothaving Using Excel means to incur the statistical extracostsof usingspecialized programs. Mostbusiness users alreadv havesome familiarity withExcel. have anddiscovered thatstatistics educators . Excel is easyto useandeasyto learn, at hada long-running discussion overtheuseof leastforcasual users. intheclassroom. Excel graphical andstatistical functions Asauthors of a textwhose titleincludes . Excel canusethesameworksheet-based data Excelwe believe thephraseUsingMicrosoft provides thatusers havecreated forotherbusiness thatMicrosoft Excel a goodwayto purp0ses. youto basic introduce statistical methods and r SomeExcel graphical produce functions howto applythesemethods in demonstrate morevividvisualoutputs thansomespedecision making. Manymanagers, business programs. cialized statistical notingtheprevalence Excelon of Microsoft in theirbusinesses, havesimithecomputers Whilethesetraitsareattractive, those larlyconsidered usingExcel, ratherthana program, Microsolt Excelhavenot specialized statistical for statistical who havechosen considered theaccuracy andcomanalysis. Microsoft Excel seems likeanattrac- necessarily pleteness of thestatistical results thatExcel tivechoice because:

you havebeenintroducedto the role ofstaInthischapter, tisticsin turning data into information and the importance of usingcomputerprogramssuch as Microsoft Excel. In addition,you have studieddata collection and the various typesof datausedin business.In conjunctionwith the UsingStatisticsscenario,you were askedto reviewthe cushmersurveyusedby the GoodTunescompany(seepage7). Thefirst and fifth questionsof the survey shownwill pro-

variable categorical cell I I cellrange 12 chartsheet 12 variable continuous data 4 statistics descriptive variable 9 discrete inferential statistics

produces. Unfortunately, someinvestigators havedetermined Microsoft Excel thatcertain statistical capabilities contain flawsthatcan leadto invalidresults, especially whendata setsareverylargeor haveunusual statistical (seereference properties 1,2,and4).Even usingMicrosoft Excel withsmalldatasetsto produce therelatively simple descriptive sta(Asan tistics canleadto nonstandard results. for creating hisexample, seethediscussion tograms in theExcel Companion to chapter 2 on page86.)Clearly, whenyouuseMicrosoft youmustbecareful Excel, aboutthedataand youareusing. themethod Whether thiscomplication outweighs the benefits of Excel's attractive featuresis still an unanswered question in business today.

ducenumericaldata.Questions2,3, and4 will produce nominalcategoricaldata.Questions6-8 will produceordinal categoricaldata.The responsesto the first question (numberof days)arediscrete,and the responses to the fifth question(amountof money spent)are continuous.In the next two chapters,tables and charts and a variety of descriptivenumerical measuresthat are useful for data analysisaredeveloped.

intervalscale 10 nominalscale 9 numericalvariable 8 operationaldefinition 4 ordinalscale 9 parameter 5 population 5 primary source 6 qualitativevariable 8

quantitativevariable 8 ratio scale l0 sample 5 secondarysource 6 statistic 5 statistics 2 variable 4 workbook 12 worksheet 11

l4

CHAPTER ONE Introductionand Data Collection

CheckingYour Understanding 1.12 What is the differencebetweena sample trI#q l A s s r sI randa population?

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1.13 What is the differencebetweena statistic

l A s s r sI Tand a parameter? 1.14 Whatis the difference betweendescriptive and inferential statistics? l A s s r sI r

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1.15 What is the difference betweena categorimffi I A S S | sIr cal variableand a numericalvariable? 1.16 What is the differencebetweena discretevariable anda continuousvariable? 1.17 What is an operationaldefinitionand why is it so important? 1.18 Whatarethe four levelsof measurement scales?

Applyingthe Concepts 1.19 The Data and Story Library, lib.stat.cmu.edu/ DASL, is an online library of datafiles and storiesthat illustratethe useof basicstatisticalmethods.The stories are classifiedby methodand by topic. Go to this site and click on List all topics. Pick a story and summarizehow statisticswereusedin the story. 1.20 Go to the official Microsoft Excel Web site, www.microsoft.com/office/excel.Explain how you think Microsoft Excel could be useful in the field of statistics. 1.21 The Gallup organizationreleasesthe results of recentpolls at its Web site,www.galluppoll.com.Go to this siteandreadtoday'stop analysis. a. Give an exampleof a categoricalvariablefound in the poll. b. Give an exampleof a numericalvariablefound in the poll. c. Is thevariableyou selectedin (b) discreteor continuous? 1.22 The U.S.CensusBureausite,www.census.gov, contains surveyinformationon people,business,geography, and othertopics.Go to the site and click on Housing in the "Peopleand Households"section.Then click on AmericanHousingSurvey. a. Briefly describetheAmericanHousingSurvey. b. Give an exampleof a categoricalvariablefound in this survey. c. Give an exampleof a numericalvariablefound in this survey. d. Is thevariableyou selectedin (c) discreteor continuous?

1.23 On the U.S.CensusBureausite,www.census.gov, click on Surveyof BusinessOwners in the "Business& Industry" sectionand read aboutThe Surveyof Business Owners.Click on SampleSBO-1Form to view a survey form. a. Give an exampleof a categoricalvariablefound in this survey. b. Give an exampleof a numericalvariablefound in this survey. c. Is the variableyou selectedin (b) discreteor continuous? 1.24 An online survey of almost 53,000 people (N. Hellmich, "AmericansGo for the Quick Fix for Dinner,"USA Today,February14,2005,p.Bl) indicated that3To/o decidewhatto makefor dinnerat homeat the last minuteand that the amountof time to preparedinneraveragesl2 minutes,while the amountof time to cook dinner averages 28 minutes. a. Which of the four categories of datasourceslistedin page 1.4 you Section on 6 do think were usedin this study? b. Namea categoricalvariablediscussed in this article. c. Namea numericalvariablediscussed in this article. 1.25 According to a Harris Interactivesurvey of 502 seniorhuman resourceexecutives,58% respondedthat referralswereone of the methodsfor finding the bestcandidates.("USA Snapshots," USAToday,February9,2006, p.Al). a. Describethepopulationfor theHarrisInteractivesurvey. b. Is a responseto the question"By which methodsdo you feel you find the bestcandidates?" categorical or numerical? c. Fourteenpercentof the seniorhumanresourcesexecutives polled indicatedthat professionalassociations wereoneof the methodsfor finding the bestcandidates. Is this a Darameter or a statistic? 1.26 A manufacturerof cat food was planningto survey households in the United Statesto determinepurchasing habitsof cat owners.Among the questionsto be included arethosethat relateto 1. wherecat food is primarilypurchased. 2. whetherdry or moist cat food is purchased. 3. thenumberof catsliving in thehousehold. 4. whetherthe cat is pedigreed. thepopulation. a. Describe b. For eachof the four items listed.indicatewhether variableis categoricalor numerical.If it is numerical, i it discreteor continuous? c. Developfive categoricalquestionsfor the survey. d. Developfive numericalquestionsfor the survey.

End-of-Chapter Cases

Student Survey Data Base answered the 1.27 A sample of 50undergraduate students following survey. Malel. What is your gender'/ Female2. What is your age (a.so/'la.stbirthday)'!3. What is your height (in inches)?_ 4. What is your current registeredclassdesignation? Freshman_ Sophomore_ Junior_ Senior5. What is your major areaof study'/ Accounting_ Economics/Finance_ InformationSystems_ InternationalBusinessManagement_ Marketing/Retailing_ Other_ Undecided_ 6. At the presenttirne, do you plan to attend graduate school? Not sureYes_ No_ 7. What is your current cumulative grade point average'J_ 8. What would you expect your starting annual salary (in $000) to be if you were to seek employment immediately after obtaining your bachelor's degree?_ 9. What do you anticipate your salary to be (in $000) after five years of full-time work experience?_ 10.What is your current employmentstatus'l Full-time_ Part-time_ Unemployed_ g r o u p s . 1 1 .H o w r n a n y c l u b s , organizationso , r teams are you currently affiliated with on campus'/ 12.How satisfied are you with the student advisement serviceson campus?_ Extremely | 2 3 4 5 6 7 Extremely Neutral satisfied unsatisfied 13.About how much money did you spendthis semester for textbooksand supplies'l_ Theresultsof the survey are in the file GEEEE@!$iIIE. a. Whichvariablesin the survey are categorical'/ b. Whichvariablesin the survey are numerical? c. Whichvariablesare discretenumericalvariables?

I5

Male_ What is your gender? Female_ (a.s your What is age o./last birthclq,)'lWhat is your height (in inche.s)?_ What is your current major areaof study? Accounting _ Economics/Finance_ Information Systems_ InternationalBusinessManagement_ Marketing/Retailing._ Other_ Undecided_ 5. What is your graduate cumulative grade point index?_ 6. What was your undergraduatearea of specialization'? Biological Sciences_ BusinessAdministration_ EducationComputers or Math_ Engineering_ Humanities_ PerformingArtsPhysicalSciences_ Social Sciences_ Other_ cumulativegradepoint 7. What was your undergraduate average'?_ 8. What was your GMAT score'?_ 9. What is your current employment status'/_ Part-time_ Unernployed_ Full-time_ 10. How many different full-time jobs have you held in the past l0 years'.'_ | 1. What do you expectyour annual salary (in 5000) to be immediately after completion of the MBA program'?_ 1 2 . W h a t d o y o u a n t i c i p a t ey o u r s a l a r yt o b e ( i n $ 0 0 0 ) after five years of full-time work experience following the completionof the MBA program'?_ 13. How satisfied are you with the student advisement serviceson campus? E,xtremelyl23456 7 Extremely Neutral satisfied unsatisfied 14. About how much money did you spendthis semester for textbooks and supplies?_ l. 2. 3. 4.

The results of the survey are in the file FfFfl?lS. a. Which variablesin the survey are categorical? b. Which variablesin the survey are nurnerical'.) c. Which variablesare discretenumericalvariables'J

1.28 A sampleof 50 MBA studentsansweredthe followlngsurveY:

End-of-Chapter Cases A t t h e e n d o f m o s t c h a p t e r s ,y o u w i l l f i n d a c o n t i n u i n g casestudy that allows you to apply statisticsto problerns facedby the managementof the Springville Herald, a daily

newspaper.Complementing this case are a seriesof Web C a s e st h a t e x t e n d r n a n y o f t h e U s i n g S t a t i s t i c ss c e n a r i o s t h a t b e g i ne a c hc h a p t e r .