My Favorite One-Liners: Part 71

In this series, I’m compiling some of the quips and one-liners that I’ll use with my students to hopefully make my lessons more memorable for them.

Some of the algorithms that I teach are pretty lengthy. For example, consider the calculation of a 100(1-\alpha)\% confidence interval for a proportion:

\displaystyle \frac{\hat{p} + \displaystyle \frac{z_{\alpha/2}^2}{2n}}{\displaystyle 1 + \frac{z_{\alpha/2}^2}{n} } - z_{\alpha/2} \frac{\sqrt{\displaystyle \frac{ \hat{p} \hat{q}}{n} + \displaystyle \frac{z_{\alpha/2}^2}{4n^2}}}{\displaystyle 1 + \frac{z_{\alpha/2}^2}{n} } < p < \displaystyle \frac{\hat{p} + \displaystyle \frac{z_{\alpha/2}^2}{2n}}{\displaystyle 1 + \frac{z_{\alpha/2}^2}{n} } + z_{\alpha/2} \frac{\sqrt{\displaystyle \frac{ \hat{p} \hat{q}}{n} + \displaystyle \frac{z_{\alpha/2}^2}{4n^2}}}{\displaystyle 1 + \frac{z_{\alpha/2}^2}{n} }.


Proficiency with this formula definitely requires practice, and so I’ll typically give a couple of practice problems so that my students can practice using this formula while in class. After the last example, when I think that my students have the hang of this very long calculation, I’ll give my one-liner to hopefully boost their confidence (no pun intended):

By now, you probably think that this calculation is dull, uninteresting, repetitive, and boring. If so, then I’ve done my job right.

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