Suppose that X1, X2,....Xm and Y1,Y2,....,Yn are independent random samples, with the variables Xi normally distributed with mean

and variance

and the variables Yi normally distributed with mean

and variance

. The difference between the sample means,

is then a linear combination of m + n normally distributed random variables and is itself normally distributed.

Suppose that

= 2,

= 2.5, and m=n. Find the sample sizes so that (

) will be within 1 unit of (

) with probability .95.

I don't know how to solve this one. I've tried to set up P((

= .95

but I don't if that's right. And, if so, how do I go on?