Samuels (1996) collected data to examine how well students do in follow-up courses if the prerequisite course is taught by a part-time or full-time instructor. The following table gives results for students in Math I and Math II.

a. The null hypothesis here is that the proportion of students receiving an A, B, or C is the same for each of the four combinations of instructor type. Is this a test of independence, homogeneity, or goodness of fit?
b. Perform a hypothesis test for the null hypothesis in (a), assuming students are independent.
c. Do you think the assumption that students are independent is valid? Explain.