Exam scores from two semesters for a given class (not this one!) are given on th

ID: 3182877 • Letter: E

Question

Exam scores from two semesters for a given class (not this one!) are given on the following page. The professor hypothesizes that if the exams were equivalent in terms of the material covered, number of questions, types of questions asked, etc. average score and variability of the scores should be the same from one semester to the next. To help the professor determine whether his hypotheses are correct, complete the following:

a. State the null hypotheses in terms of the mean and variation.

b. Manually carry out a formal test of these hypotheses (for both the mean and variance) assuming an alpha value of 0.05.

c. Which tests did you choose for b? Why did you choose them?

d. State your conclusion both formally, and in plain English

e. What assumption(s) have you made in order to carry out the test?

ExamFall

ExamSpring

ExamFall

ExamSpring

Explanation / Answer

a) H0: 1 - 2 = 0 i.e. (1 = 2)

H1: 1 - 2 0 i.e. (1 2)

Assuming population variances are equal, we would have to calculate pooled-variance t-Test

Sp^2= (n1-1)S1^2+(n2-1)S2^2/(n1-1)+(n2-1)

= (31-1)*10.40^2+(28-1)*11.17^2/30+27

= 3244.8+3368.76/57

=116.03

tSTAT=(X1-X2)-(µ1-µ2)/Sp^2(1/n1+1/n2)

=(77.52-75.39)-0/116.03(1/31+1/28)

=2.13/0.3656

=5.83

tCRIT is 2.0025 and hence reject the null hypothesis

For Variance:-

H0: 21 = 22

H1: 21 22

FSTAT=S1^2/S2^2=10.40^2/11.17^2=108.16/124.77=0.87

FCRIT=2.13

Hence, we cannot reject null hypothesis

ExamFall ExamSpring 84 54 68 88 57 54 69 76 76 88 87 86 74 69 61 85 82 74 62 55 91 75 89 88 72 63 88 80 87 89 77 79 88 78 74 68 86 84 90 71 82 69 80 91 73 74 54 68 65 88 82 69 70 85 84 63 91 77 83 77.51613 75.3928571 Mean 10.40151 11.1731798 SD