Sequential Tests for Hypergeometric Distributions and Finite Populations

Abstract

While usual sequential analysis deals with i.i.d. observations, this paper studies sequential tests for the dependent case of sampling without replacement from a finite population. A general weak convergence theorem is obtained and it is applied to the asymptotic analysis of the tests. Motivated by such applications as election predictions and acceptance sampling, the case of hypergeometric populations is studied in detail and a simple test with a triangular continuation region is proposed and is shown to have many nice properties. The paper concludes with a general heuristic principle of "finite-population correction" which is applicable to both sequential testing and fixed-width interval estimation problems.