##### Description

This simulation shows the confidence interval, $$\bar{x} \pm m$$, for $$μ$$ based on random samples of size $$n$$ from a normal population with mean $$μ$$ and standard deviation $$\sigma$$, where $$\bar{x}$$ is the sample mean and $$m$$ is the margin of error for a level $$C$$ interval. There are two cases, corresponding to when $$\sigma$$ is assumed known, or is not known and is estimated by the standard deviation in the sample. For the known $$\sigma$$ case, $$m = \sigma z^{*} / \sqrt{n}$$, where the critical value $$z^{*}$$ is determined so that the area to the right of $$z^{*}$$ is $$(1 – C) / 2$$. Similarly in the unknown $$\sigma$$ case, $$m = t^{*} s / \sqrt{n}$$, where $$s$$ is the sample standard deviation and $$t^{*}$$ is the critical value determined from a t-distribution with $$( n – 1)$$ degrees of freedom.

This simulation runs on desktop using the free Wolfram Player. Download the Wolfram Player here.