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?