A particular state university system has 7 campuses. On each campus, a random sa

Question

A particular state university system has 7 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 7 campuses.

(a) On how many degrees of freedom will the resulting test X2 be based?

(b) How does your answer in Part (a) change if there are 8 campuses rather than 7?

(c) How does your answer in Part (a) change if there are 4 rather than 3 categories for political philosophy?

Explanation / Answer

Part-a

Degree of freedom=(row-1)*(colun-1)=(7-1)*(3-1)=12

Part-b

If there are 8 campuses, the degree of freedom=(8-1)*(3-1)=14

Part-c

If there are 4 categories, the degree of freedom=(7-1)*(4-1)=18

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