On uncertainty of a proportion from a stratified random sample of a small population

This article considers the uncertainty of a proportion based on a stratified random sample of a small population. Using the hypergeometric distribution, a Clopper-Pearson type upper confidence bound is presented. Another frequentist approach that uses the estimated variance of the proportion estimator is also considered as well as a Bayesian alternative. These methods are demonstrated with an illustrative example. Some aspects of planning, that is, the impact of specified strata sample sizes, on uncertainty are studied through a simulation study.