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 382.5
3) Random: Data is representative of typical classes at BMHS
Name: Chi Square GOF Test
Test Stats:
(400 382.5) 2
(365 382.5) 2
 ... 
 7.1243
382.5
382.5
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.
Example: The distribution of AP Statistics scores between BMHS and NHS is shown
below. Is there evidence that one of the schools performs better than the other school?
AP Score
BMHS
NHS
5
2
1
4
10
5
3
8
5
2
3
11
1
2
3
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
ECF: We must combine 1’s and 2’s
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
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:
(12  9) 2
(14  9.5) 2
 ... 
 6.955
9
9.5
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 between
the 2 schools. It appears students at BMHS tend to score higher.
Example: The distribution of Precalculus grades between males and females at a local
high school are shown below. Is there evidence of an association?
Grade
Males
Females
A
25
20
B
30
30
C
35
40
D
15
25
F
5
10
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
ECF:
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
Name: Chi Square Independence Test
Test Stats:
(25  21.2) 2
(10  8) 2
 ... 
 4.11
21.2
8
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 gender
In the Precalculus classes at this school
Parameter: B = linear association
between farms and acreage