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TITLE: Confidence Intervals for a Proportion - the Good, the Bad, and the Ugly
ABSTRACT:
Introductory statistics books teach how to calculate confidence intervals for a proportion as an easy application of formulas for the standard error in sampling from binomial or hypergeometric distributions. Assurances that “the approximation is good if the sample size n is at least 30” are typical. But even for much larger n the performance of the usual confidence intervals can best be described as “ugly”. Using better approximate methods only improves the results to “bad”. Analyzing how to get “good” performance turns out to be interesting and forces us to address questions about what we want confidence intervals to do.
