Consider the accompanying table displaying the sample proportions that fell in the various combinations of categories (e.g., 13% of those in the sample were in the first category of both factors).

123 1 .13 .19 .28 2 .07 .11 .22 2 3 3 nijk eˆ ’s ijk pˆijk

a. Suppose the sample consisted of people. Use the chi-squared test for independence with significance level .10.

b. Repeat part (a), assuming that the sample size was

.

c. What is the smallest sample size n for which these observed proportions would result in rejection of the independence hypothesis?