Sequential Design for a Fixed Width Interval Estimation of the Common Mean of Two Normal Distributions. I. The Case of One Variance Known

Abstract

The objective is to provide a fixed-width interval estimator of the unknown common mean of two normal distributions having a prescribed coverage probability and minimal possible sample size. The variance of one distribution is known. The design problem is to decide sequentially while sampling the distribution with the unknown variance when to switch and sample from the distribution with the known variance. New types of boundaries are derived for this sequential design problem. The operating characteristics of this procedure are compared with those of two other ad hoc procedures by Monte Carlo simulation.