Exact confidence bounds when sampling from small finite universes. An easy reference based on the hypergeometric distribution
Consider a finite population of N units of which an unknown number A has a particular attribute or characteristic. Let \(P=A/N\) denote the population proportion of such units. Suppose that a simple random sample (srs) of size n is selected without replacement from this population and let a be the number of units in the sample which have the particular attribute or characteristic. The author discusses the problem of estimation of A (or equivalently P). Exact one-sided and two-sided confidence bounds for A (or P) are provided. The question of finding conservative confidence bounds for values of N and n not in this region is also discussed. Using the given table, exact one- and two-tailed tests of hypotheses for \(H_ 0: A=A_ 0\); \(H_ 0: A\leq A_ 0\); \(H_ 0: A\geq A_ 0\) at 2.5\%, 5\% and 10\% levels of significance, as well as determination of sample size n needed to estimate A (or P) under srs can be accomplished. Extensions to stratified random sampling and to comparison of two different population parameters are given as further applications. The table is based on the computer program `PROBHYPR' which is a part of the SAS system and was produced on an IBM 3033 computer. This volume is, according to the author, useful to `anyone who has reason to select a sample from a finite universe and construct a confidence interval or test a hypothesis'. However, certain applications need some statistical maturity and understanding.
scientific article; zbMATH DE number 50054