Interval estimators for the population mean for skewed distributions with a small sample size

1 Interval estimators for the population mean for skewed distributions with a small sample size SUMMARY In nite population sampling it has long been known that for small sample sizes, when sampling from a skewed population, the usual frequentist intervals for the population mean cover the true value less often than their stated frequency of coverage. Recently a noninformative Bayesian approach to some problems in nite population sampling has been developed which is based on thèPolya posterior'. For large sample sizes these methods often closely mimic standard frequentist methods. In this note a modiication of thèPolya posterior' which employs the weighted Polya distribution is shown to give interval estimators with improved coverage properties for problems with skewed populations and small sample sizes. This approach also yields improved tests for hypotheses about the mean of a skewed distribution.