confidence intervals, a review:

\begin{equation} statistic \pm z^*\sigma_{statistic} \end{equation}

Frequently, we don’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’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.