AP Statistics Inference Review

Chapters 26-27

Example: The expected distribution at BMHS is uniform across the 9th, 10th, 11th and 12th

grade. If there are 400 9th graders, 350 10th graders, 415 11th graders and 365 12th graders,is there evidence that the distribution has changed?

Parameter: Distribution of 9th – 12th graders at BMHS

Hypothesis: Ho: The distribution is uniform Ha: The distribution is not uniform

Asumptions:1) Data is in counts 2) ECF: Each expected count is 382.53) Random: Data is representative of typical classes at BMHS

Name: Chi Square GOF Test

Test Stats: 3 df

Obtain P: P = .068 (Draw distribution)

Make Decision: We fail to reject Ho.

Conclusion: Since P = .068 there is not enough evidence that the distribution has changed.

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Example: The distribution of AP Statistics scores between BMHS and NHS is shownbelow. Is there evidence that one of the schools performs better than the other school?

Parameter: Distribution of AP statistics scores between NHS and BMHS

Hypothesis: Ho: The distribution is the same for both high schools Ha: The distribution is not the same between the 2 high schools

Assumptions:1) Data is in counts 2) Random: Data is representative of typical classes at BMHS

AP Score BMHS NHS

5 2 1

4 10 5

3 8 5

2 3 11

1 2 3

AP Score BMHS NHS

5 2/1.5 1/1.5

4 10/7.5 5/7.5

3 8/6.5 5/6.5

2 3/7 11/7

1 2/2.5 3/2.5

ECF: We must combine 1’s and 2’s

AP Score BMHS NHS

5/4 12/9 6/9

3 8/6.5 5/6.5

1/2 5/9.5 14/9.5

Name: Chi Square Homogeneity Test

Test Stats: 2 df

Obtain P: P = .03 (Draw distribution)

Make Decision: We reject Ho.

Conclusion: Since P = .03 there is evidence that the distributions are not the same betweenthe 2 schools. It appears students at BMHS tend to score higher.

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Example: The distribution of Precalculus grades between males and females at a localhigh school are shown below. Is there evidence of an association?

Parameter: The association between Precalculus grade and gender at the local high school

Hypothesis: Ho: There is no association between grades and gender Ha: There is an association between grade and gender

Assumptions:1) Data is in counts 2) Random: Data is representative of typical Precalc classes

Grade Males Females

A 25 20

B 30 30

C 35 40

D 15 25

F 5 10

Grade Males Females

A 25/21.1 20/23.9

B 30/28.1 30/31.9

C 35/35.1 40/39.9

D 15/18.7 25/21.3

F 5/7.0 10/8.0

ECF:

Name: Chi Square Independence Test

Test Stats: 4 df

Obtain P: P = .39 (Draw distribution)

Make Decision: We fail to reject Ho.

Conclusion: Since P = .39 there is no evidence of an association between grade and genderIn the Precalculus classes at this school

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2.21)2.2125( 22

Parameter: B = linear associationbetween farms and acreage