Suppose you have data $X_i | \mu, \sigma^2 \sim N(\mu, \sigma^2)$, for $i = 1, …, n$, i.e, $n$ normally distributed data points with mean $\mu$ and variance $\sigma^2$ (or standard deviation $\sigma$). Assume you don’t know $\sigma^2$, which is usually the case anyway. You could estimate $\mu \approx \bar{X}$ and call it a day, but you probably want some measure of uncertainty, i.e, an interval estimate. Note: Throughout this article, I use the convention that uppercase variables are rand...
