Abstract
SYNOPTIC ABSTRACTIn this paper we consider the well known problem of finding the optimal sample size for obtaining a confidence interval of a pre-assigned precision (or length) for the proportion parameter of a finite or infinite binary population. We illustrate some special problems that arise due to the discreteness of the population and precision being measured by the length of the interval rather than by the variance. Specifically, the confidence level of an interval of fixed length does not necessarily increase as you increase the sample size. The practitioners usually associate precision with variance, and variance monotonically decreases as sample size increases, regardless of whether the population is discrete or continuous. However, other notions of precision, such as length of the confidence interval as discussed here do not monotonically improve with increasing sample size. Although the results shown here are implicit in previous work [see Brown, Cai, and DasGupta(2001, 2002, 2003) and Cai(2005)], the implications of these results have not fully been integrated into some popular audit programs.
Published Version
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