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.

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

Answer 1

The degrees of freedom for the chi-square test of independence involving 7 campuses and 3 political affiliations will be 12.

Step-by-step explanation:

The question involves a chi-square test for independence which is used to determine if there is a significant association between two categorical variables.

Here we are comparing the political affiliations (liberal, moderate, conservative) across 7 campuses.

The degrees of freedom for this test are calculated by the formula (r - 1) * (c - 1), where 'r' is the number of rows and 'c' is the number of columns in the contingency table.

Since there are 7 campuses and 3 political affiliations, the degrees of freedom will be (7 - 1) * (3 - 1), which equals 12.