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, (sigma(adsbygoogle = window.adsbygoogle || []).push({}); _{1})^{2}and (sigma_{2})^{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:

(X_{1}bar X_{2}bar) +- z_{a/2}s.e.(X_{1}bar-X_{2}bar) given that the samples are sufficiently small enough.

For unknown, I think it's:

(X1bar X2bar) +- t_{((n1+n2-2),a/2)}s.e(X_{1}bar-X_{2}bar) <<s.e has a tilda over it, also this formula assumes the sigmas are the same.

Is this correct?

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# Confidence intervals, which formula to use

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