# Confidence intervals for mean, when variance is unknown

When calculating the confidence interval for the population mean and the variance is unknown, I take it that you have to use the t-distribution.

However, do you use the one-tailed or two-tailed test values for $\alpha/2$?

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This question doesn't make complete sense to me. You calculate confidence intervals for sample means. Yes, if the variance is unknown, you should use the t-distribution, rather than the normal. As for 1 vs 2 tailed CI's, you could use either, depending on what is more relevant for your substantive question. –  gung Nov 29 '12 at 5:00

## 1 Answer

It depends on your alternative hypothesis about the mean. If your alternative hypothesis is: true mean is not equal to 0, that means true mean can be both greater than 0 or less than 0. Thus it becomes a two tail test. If you are using R, you may find this link useful: http://www.r-tutor.com/elementary-statistics/interval-estimation/interval-estimate-population-mean-unknown-variance

A (1 - a) confidence lower bound for the distribution mean is:

$\bar{x}-t_{n-1,1-a}\frac{S}{\sqrt{n}}$

A (1 - a) confidence upper bound for the distribution mean is:

$\bar{x}+t_{n-1,1-a}\frac{S}{\sqrt{n}}$

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