Two-Stage Normal Sampling in Two-Action Problems with Linear Economics

Abstract

Results are presented for optimal two-stage sampling, where the size of the second-stage sample can be conditioned on the first-stage sample outcome, in the case where (1) sample observations are drawn from a Normal population or process with known variance but unknown mean, (2) there are two terminal acts whose terminal values are linear functions of the unknown population or process mean, and (3) the cost of a sample of positive size at either stage depends linearly on the sample size. Computer programs for obtaining optimal sampling plans are described, the effects on these optima of changes in cost and statistical parameters are traced, various characteristics of optimal plans are discussed, the sensitivity of two-stage sampling plans to deviations from optimal design is explored, and extensions to a number of closely related problems are given.