Suppose you wanted to estimate the difference between two population means correct to within $3.3$ with probability $0.91$. If prior information suggests that the popluation variances are approximately equal to $\sigma^2_1 = \sigma^2_2 = 12$ and you want to select independent random samples of equal size from the poulations, how large should the sample sizes, $n_1$ and $n_2$ be?
answer: $n_1 = n_2 =$