$ CI = \bar{x} \pm z s_{\bar x} = \bar{x} \pm z \frac{s}{\sqrt{n}} $ - $\bar{x}$ is the [[Sample Mean]] - $z$ is the [Z score](https://www.statisticshowto.com/probability-and-statistics/z-score/) (aka. Z statistic): how many [Standard Deviations](Standard%20Deviation.md) below or above the population mean a raw score/data point is. - $s_{\bar x}$ is the [[Standard Error of the Mean (SEM)]] - $s$ is the [Sample Standard Deviation](Sample%20Standard%20Deviation.md) If you are estimating the CI for a set of **Bernoulli trials**, both $n \times p \ge 5$ and $n \times (p-1) \ge 5$ should hold to use the above *normal approximation*. If not, you can use the [Clopper-Pearson intervals](Clopper-Pearson%20intervals.md) method for estimating the CI. The CI is useful to compare if two samples are most likely ***not*** from the same distribution: For two normally distributed variables of similar size, if their CIs do not overlap at $z = 1.96$, the probability that they are from the same distribution is $p < 0.05$.