Ap Statistics Test Review

Inference Formulas & Procedures Situation/Tes t 1 sample z test

2 sample z test 1 sample t test

2 sample t test

Matched pairs t test

Conditions

Null Hypothesis

1. SRS And either: 2. Pop is normal, or large sample size ( n ≥  ), or if n<30, the sample dist is not severely skewed and does not have extreme outliers. Same as above for BOTH samples

H 0 :µ = µ

1. SRS and either: 2. Pop is normal, or n>40 (even if skewed & outliers), or 15
H 0 : µ = µ or H 0 : µ − µ =  H 0 :µ = µ

H 0 :µ = µ

H 0 :µ =  where µ d is the difference of dependent

Test Statistic z=

z=

t=

t=

t=

Confidence Interval

 − µ σ 

 σ  x ±     

  −   −  µ − µ  

 σ  σ   (x1 −   ±    +    

σ  σ  +    − µ  ; df = n-1 

  x ±   ; df = n-1   

  −   −  µ − µ 

    (x1 −   ±     +   ; df = n-1    

  +    

 

 − µ  ; df = n-1 

  x ±   ; df = n-1   

1 proportion z test

2 proportion z test

Chi Square Goodness of Fit

Chi Square Homogeneit y

1. SRS 2. Population ≥ 10n 3. CI: npö ≥  , n(1 −   ≥  HT: np0 ≥  , n(1 −   ≥  (Verify use of normal approx) 1. Populations are independent 2. SRS (both samples) 3. Populations ≥ 10n 4. CI: n1 pö1 ≥  , n1 (1 −    ≥  n2 pö2 ≥  , n2 (1 −    ≥  HT: n1 pö ≥  , n1 (1 −   ≥  n2 pö ≥  , n2 (1 −   ≥  (Verify use of normal approx) 1. All expected counts ≥ 1 2. 80% of expected counts ≥ 5

Same as above.

Chi Square Same as above. Independenc e

Linear Regression; regression slope

1. Independent ordered pairs 2. Roughly linear scatterplot

sample means H 0 : p = 

H 0 : p1 =  or H 0 : p1 −  = 

H 0 : Actual proportions are equal to hypothesized proportions H 0 : Proportions are all equal or a fixed value H 0 : No associations between variables or the variables are independent of each other H 0 :β =  no linear relationship between the two variables

z=

z=

 −    −   

   −    −   −  

    −    +       +  where pö =  + 

pö ±  

  −   

( pö1 −    ±  

   −       −    +  

(O - E)2 E df = k-1 k = # of categories

One-way table Single SRS, one categorical variable

(O - E)2 E df = (r-1)(c-1) (O - E)2 χ2 = å E df = (r-1)(c-1)

Two-way table Two SRS, two categorical variables

χ2 = å

χ2 = å

t=

 , df = n-2 

Two way table Single SRS, two categorical variables b ±    ; df = n-2

3. Standard deviation of response is constant (scatter around LSRL is consistent) 4. Response variable varies normally (residuals are approx normal)