A teacher figures that final grades in the statistics department are distributed

Question

A teacher figures that final grades in the statistics department are distributed as: A, 25%; B, 25%; C, 40%; D, 5%; F, 5%. At the end of a randomly selected semester, the following number of grades were recorded. Determine if the grade distribution for the department is different than expected. Use = 0.01. Identify the claim, state the null and alternative hypotheses, find the critical value, find the standardized test statistic, make a decision on the null hypothesis (you may use a P-Value instead of the standardized test statistic), write an interpretation statement

on the decision.

Grade

A

B

C

D

F

Number

36

42

60

14

8

Grade

A

B

C

D

F

Number

36

42

60

14

8

Explanation / Answer

Hypotheses:   

Ho: The distribution is as per the expectation   

Ha: The distribution is not as per the expectation; that is, it is different   

Decision Rule:   

= 0.01

Count = 5

Degrees of freedom =   5 - 1 = 4

Critical Value of 2 = 13.27670414

Reject Ho if 2 > 13.27670414

2 = 5.25   

p- value = 0.262594119   

Decision (in terms of the hypotheses):    

Since 5.25 < 13.27670414 we do not reject Ho

Conclusion (in terms of the problem):    

There is no sufficient evidence that the distribution is different.

Test Statistic: Recorded Expected (Recorded - Expected)^2 / Expected 36 40 0.4 42 40 0.1 60 64 0.25 14 8 4.5 8 8 0 2 = 5.25

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