# Confidence Interval

## Main Question or Discussion Point

Hello

May I know what is the difference between

Confidence Interval for Population Mean (μ) when σ Known vs Confidence Interval for Population Mean (μ) when σ unknown..

any example to show me??

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MarneMath
What you'll typically see in a beginners course varies. If for some reason you form a CI with the s.d known you'll use a z-test. If it isn't known, you'll typically have to use a t-test. There are some caveats to this, and it really depends on how loose you want to be with it. An important thing to note is that if you are using SAS, it will assume that the s.d is unknown (because that's common) and give you values based on a t-test.

phion
Gold Member
$$\overline{X} \pm (z_{conf})(\sigma_\overline{x})$$

Try using a sample standard deviation by using the bessel correction in the computation formula for s within $$\frac{\sigma}{\sqrt{n}}$$

DrDu
One important difference is that if the std is known, then the CI's will be all of the same width, while if sigma has to be estimated, the width will also vary between repetitions.