A particular state university system has 5 campuses On each

A particular state university system has 5 campuses. On each campus, a random sample of students will be selected, and each student will be categorized with respect to political philosophy as liberal, moderate, or conservative. The null hypothesis of interest is that the proportion of students falling in these three categories is the same at all 5 campuses. (a) On how many degrees of freedom will the resulting test X^2 be based? (b) How does your answer in Part (a) change if there are 6 campuses rather than 5? (c) How does your answer in Part (a) change if there are 5 rather than 3 categories for political philosophy? You may need to use the appropriate table in Appendix A to answer this question.

Solution

a) degrees of freedom = (no of rows-1)(no of columns-1)

As there are 3 categories and 5 campuses

df = (3-1)(5-1) = 8

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b) If no of campuses = 6

df = (3-1)(6-1) = 10

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c) If 5 categories and 5 campuses

df = (5-1)(5-1) = 16