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?