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.

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Instructor Instructor Grade in Math II for MathI for MathA, B, or C D, F, or Withdraw Total 461 Full Time Full Time Part Time Part Time Full Time Part Time Full Time Part Time 797 311 570 181 449 1571 1258 492 1050 1358 Total 2587 4158