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 ?2 be based? (b) How does your answer in Part (a) change if there are 7 campuses rather than 5? (c) How does your answer in Part (a) change if there are 4 rather than 3 categories for political philosophy?

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2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.