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 𝜒2 be based?
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 𝜒2 be based?
Solution
The degrees of freedom for the resulting test 𝜒2 will be based on (number of categories - 1) multiplied by (number of campuses - 1). In this case, there are 3 categories (liberal, moderate, conservative) and 7 campuses. Therefore, the degrees of freedom will be (3-1) * (7-1) = 2 * 6 = 12.
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