I have created 1000 random samples of size 10, where X~N(8,2). For each sample I have calculated the sample mean, sample variance, (sigma1)2 and (sigma2)2. I want to find a 95% confidence interval for the mean assuming the population variance is known, and a 95% confidence interval for the mean assuming the population variance is unknown. What formula do I use for these? I think, given that I am sampling from a normal distribution, for the known confidence interval, would be: (X1bar X2bar) +- za/2s.e.(X1bar-X2bar) given that the samples are sufficiently small enough. For unknown, I think it's: (X1bar X2bar) +- t((n1+n2-2),a/2) s.e(X1bar-X2bar) <<s.e has a tilda over it, also this formula assumes the sigmas are the same. Is this correct?