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Likelihood Confidence Intervals for Proportions in Finite Populations

Certain applications often require confidence intervals on the number or proportion of items in a finite population that possess a particular characteristic. We propose a method for determining such confidence intervals based on the likelihood of the observed sample. When compared to the best currently available method, this approach results in shorter confidence intervals when averaged across all possible sample outcomes for a given population and sample size. It also has coverage probabilities that are closer to the nominal level. Although computationally more complex than existing methods, it can easily be implemented on a personal computer.