Right now I'm teaching an introductory course on statistical inference for Economics students. We've been dealing with confidence intervals, starting off (as usual) with one for the mean of a Normal population. For a given confidence level, the shorter the interval is, the more "informative" it is. The question that then arises is how to make the interval as short as possible, everything else being equal? Good question! First, let's review some basic results. Say I want to construct a...