Refer to the previous exercise. After the semester, students were asked whether the quizzes were beneficial, with

Question:

Refer to the previous exercise. After the semester, students were asked whether the quizzes were beneficial, with possible answers

(i) Yes, I realized that I knew more than I thought,

(ii)Yes, I realized that I knew less than I thought,

(iii) No. Results of the survey are shown in the following table.

Is there evidence that the distribution of the student responses differ between the two courses?

Beneficial Group Yes, Less Yes, More No 3 18 STAT 5 CS 12 20

a. Formulate the null and alternative hypotheses of interest.
b. Suggest a test statistic to use for this test.
c. If all expected cell counts were at least 5, what distribution would the test statistic from part b follow?
d. Of 10,000 random permutations, 2,660 resulted in an X² statistic as large or larger than the observed one of 3.2. Approximate the permutation P-value and write a conclusion for the test.

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...