Tech Tips: Confidence Intervals for Proportions

Suppose $x$ elements of a sample of size $n$ have a certain characteristic. To find a confidence interval for the proportion of the population that has that characteristic, one first checks to see if the requisite assumptions are satisfied. Here, we determine if both $x$ and $n-x$ greater than or equal to 5. Then, presuming these assumptions are met, one can compute a confidence interval (with confidence level of $1-\alpha$) using $$\widehat{p} \pm z_{\alpha/2} \sqrt{\frac{\widehat{p}\widehat{q}}{n}}$$ We can, of course, leverage technology to make these same calculations,