Optimum Double Sampling Tests of Given Strength I. The Normal Distribution

Abstract

For a normally distributed random variable with unknown mean θ and known variance, optimum double sampling tests of strength (θ₁, α, θ₂, β) are found and compared with the single sampling test and the SPRT of the same strength. Two optimality criteria are used—minimax ASN and Bayes ASN. Tables of these optimum tests are given. Approximations to optimum double sampling tests for Poisson and binomially distributed variables are discussed.