Question

An AP Statistics teacher claims that the AP Statistics grade distribution is as follows:

Grade	A	B	C	D	F
%	20	40	20	15	5

Suppose that a sample of 100 students taking AP Statistics class yields the observed counts shown below:

Grade	A	B	C	D	F
# of Students	25	35	15	17	8

Use a 0.10 significance level to test the claimed AP Statistics grade distribution is correct. (a) Identify the appropriate hypothesis test and explain the reasons why it is appropriate for analyzing this data. (b) Identify the null hypothesis and the alternative hypothesis. (c) Determine the test statistic. (Round your answer to two decimal places) (d) Determine the p-value. (Round your answer to two decimal places) (e) Compare p-value and significance level α. What decision should be made regarding the null hypothesis (e.g., reject or fail to reject) and why? (f) Is there sufficient evidence to support that the claimed AP Statistics grade distribution is correct? Justify your answer.

Answer 1

a) Chi square test for goodness of fit is the best test statistics which fits the data. This test is used to determine whether sample data are consistent with a hypothesized distribution as is our case also.

b) We will set up our hypothesis.

or AP Statistics grade of sample of 100 student is equal to AP Statistics teacher claims.

or AP Statistics grade of sample of 100 student is not equal to AP Statistics teacher claims.

c) Under the null hypothesis the test statistics is

Grade
A	25	20	25	1.25
B	35	40	25	0.625
C	15	20	25	1.25
D	17	15	4	0.26
F	8	5	9	1.8
				5.185

d) The corresponding P.value = 0.26

e) Since calculated P.value = 0.26 is greater then 0.05. Hence we will accept our null hypothesis.

f) Since we have accepted our null hypothesis hence we will conclude that AP Statistics grade of sample of 100 student is equal to AP Statistics teacher claims.