14 - One Proportion

Summary

Estimating a proportion is one of the most basic problems in statistics. Although basic, it arises in a number of important real-life situations. Examples include election polls, conducted to estimate the proportion of people that will vote for a particular candidate; quality control, where the proportion of defective items manufactured at a particular plant or assembly line needs to be monitored, and one may resort to statistical inference to avoid having to check every single item; and clinical trials, which are conducted in part to estimate the proportion of people that would benefit (or suffer serious side effects) from receiving a particular treatment. The fundamental model is that of Bernoulli trials. The binomial family of distributions plays a central role. Also discussed are sequential designs, which lead to negative binomial distributions.