Houjun Liu


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.