Consider the Accompanying 2 $\times$ 3 Table Displaying the Sample Proportions That Fell in the Proportions

Consider the accompanying 2 $\times$ 3 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). $$\begin{array} { l c c c } \hline & \mathbf { 1 } & \mathbf { 2 } & \mathbf { 3 } \\\hline \mathbf { 1 } & .13 & .19 & .28 \\\hline \mathbf { 2 } & .07 & .11 & .22 \\\hline\end{array}$$
a. Suppose the sample consisted of n = 100 people. Use the chi-squared test for independence with significance level .10.
b. Repeat part (a) assuming that the sample size was n = 1000.
c. What is the smallest sample size n for which these observed proportions would result in rejection of the independence hypothesis?