AP StatisticsInference Review

Chapters 18-25

Remember Your Formulas

1 Proportion:

CI =

Hypothesis Test: z =

n

qpzp

ˆˆˆ

npq

pp ˆ

2 Proportion:

CI =

Hypothesis Test: z =

2

22

1

1121

ˆˆˆˆ)ˆˆ(

n

qp

n

qpzpp

21

21 0)ˆˆ(

n

qp

n

qp

pp

poolpoolpoolpool

1 Sample or Matched Pairs t-test

CI =

Hypothesis Test: tdf = n

sx

n

stx df

2 Sample t-test:

CI:

Hypothesis Test: tdf =2

22

1

21

21 0)(

ns

ns

xx

2

22

1

21

21 )(n

s

n

stxx df

Remember PANIC for CI’s and PHANTOMS for Hypothesis Tests

ParameterAssumptionName Test and StatisticsInterval (Include Formula)Conclusion

ParameterHypothesis (p or mu)Assumptions/ConditionsName TestTest StatisticsObtain P (Include formula and distribution)Make Decision (Never accept Ho

State Conclusion (In Context)

Name Statistics: n = 50, p-hat = .7, q-hat = .3

Interval:

50

)3)(.7(.96.17. CI

Conclusion:

Parameter: p = proportion of city workers who are also in the union

Hypothesis:

Independent: Each person being in The union should be independent

Name: One proportion z-test

Test Statistics: p-hat = .12, p = .135, q = .865, n = 2000

Obtain P:2000

)865)(.135(.

135.12. z

Decision:

Conclusion:

Parameter:

Assumptions:

Name: 2 Proportion z-Interval

Interval: 1000

)983)(.017(.

1000

)935)(.065(.576.2)017.065(. CI

Conclusion:

Parameter: Ps = Proportion of suburban students that failed AP exam Pr = Proportion of rural students that failed AP exam

Hypothesis: Ho: Ps = Pr, Ha: Ps ≠ PrAssumptions:

10%: Both 107 and 143 are less than 10%of rural and suburban students that took AP exam.

Name: 2 Proportion z-test

Test Statistics:

Obtain P:

59.

143)7)(.3(.

107)7)(.3(.

0)315.280(.

z

P =.56

Make Decision: Fail to reject Ho

State Conclusion:

Parameter:

Assumptions:

Random: It is a random selection of daysduring the year.Nearly Normal: The histogram is roughly unimodal and symmetricIndependent: Each car’s speed shouldbe independent10%: 20 cars is less than 10% of all carsthat pass through when the sign is flashing

Name Test:

Interval:

20

24.76.24 19tCI

Conclusion:

Parameter: U = average # of hours students watch TV per week from Central High

Hypothesis: Ho: U = 13, Ha: U > 13

Assumptions:

Nearly Normal: Histogram is roughly unimodaland symmetric.

Random: Students were randomly selected

Independent: TV watching among students should be independent

10%: 25 students is less than 25% of all studentsat CHS.

Name Test:

Test Statistics:

Obtain P:

Conclusion:

Parameter:

Assumptions:

Name:

Interval:

16

53.2

16

12.3131.2)14625.15(

22

CI

Conclusion:

Parameter: Um = mean death age of men, Uw = mean death age of women

Hypothesis: Ho: Um = Uw, Ha: Um < Uw

Assumptions:

Name Test:

Test Statistics:

Obtain P:

4043.16

4849.12

0)7.7833.68(228.71

t

Conclusion:

Parameter: Ud = The mean difference in unemployment rate between Australia and UK

Assumptions:

Assumptions continued:

Nearly Normal: Histogram is roughlyunimodal and symmetric

10%: 1990 – 2000 represents less than 10% ofAll of the years

Name:

Interval:

Conclusion:

Parameter: Ud = The mean difference in employment rate between Males and Females

Hypothesis:

Assumptions:Name: Match paired t-test

Test Statistics:

Obtain P:

8

166.7130125.346

7

t

Make Decision: Fail to reject Ho

State Conclusion: