# Confidence intervals

#### willmoore21

##### Junior Member
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:

(X
[SUB]1[/SUB]bar X[SUB]2[/SUB]bar) +- z[SUB]a/2[/SUB]s.e.(X[SUB]1[/SUB]bar-X[SUB]2[/SUB]bar) given that the samples are sufficiently small enough.

For unknown, I think it's:

(X[SUB]1[/SUB]bar X[SUB]2[/SUB]bar) +- t[SUB]((n1[/SUB][SUB]+n2-2),a/2) s.e([/SUB]X[SUB]1[/SUB]bar-X[SUB]2[/SUB]bar) <<s.e has a tilda over it, also this formula assumes the sigmas are the same.

Is this correct?

[Edit: in context, this is just a tutorial question where I am demonstrating these techniques for revision for finals, it is not a proper investigation or report]

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