---
title: "t-statistics"
source: https://www.jemoka.com/posts/kbht_statistics/
---

confidence intervals, a review:
\begin{equation} statistic \pm z^*\sigma_{statistic} \end{equation}
Frequently, we don&rsquo;t have access to \(\sigma\) and hence have to guestimate. When we have a sample means and a proportion, we have ways of guestimating it from the standard error (available on the single-sample section of the AP Statistics formula sheet.)
However, for means, the standard error involves! \(\sigma\). How do we figure \(\sigma\) when we don&rsquo;t know it? We could use \(s\), sample standard deviation, but then we have to adjust \(z^*\) otherwise we will have underestimation. Hence, we have to use a statistic called \(t^*\).
We can use t-values to perform t-test, a hypothesis test of means.
