(Solved): Suppose you want to estimate the difference between two population means correct to within 1.3 with ...

Suppose you want to estimate the difference between two population means correct to within 1.3 with a $95\%$ confidence interval. If prior information suggests that the population variances are approximately equal to ${\sigma }_1^2={\sigma }_2^2=11$ and you want to select independent random samples of equal size from the populations, how large should the sample sizes, ${\mathrm{n}}_1$ and ${\mathrm{n}}_2$, be? The sample sizes should be ${\mathrm{n}}_1={\mathrm{n}}_2=$ (Round up to the nearest integer.)