Solved: Suppose that in a particular state consisting of four distinctregions, a random

Chapter 14, Problem 35

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Suppose that in a particular state consisting of four distinctregions, a random sample of nk voters is obtained from thek th region for . Each voter is then classifiedaccording to which candidate (1, 2, or 3) he or she prefersand according to voter registration. Let denote the proportion of voters inregion k who belong in candidate category i and registrationcategory j. The null hypothesis of homogeneous regions isH for all i, j (i.e., the proportion within each candidate/registration combination is the samefor all four regions). Assuming that H0 is true, determineand as functions of the observed , and use thegeneral rule of thumb to obtain the number of degrees offreedom for the chi-squared test.

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