Selecting the normal population with the largest mean when the variances are bounded

A multiple decision approach to the problem of selecting the population with the largest mean was formulated by Bechhofer (1954), where a single-sample solution was presented for the case of normal populations with known variances. In this paper the problem of selecting the normal population with the largest mean is considered when the population variances are unequal and unknown but are constrained only to be less than a specified upper bound. It is demonstrated that a slight modification of Bechhofer' s procedure will suffice to ensure the probability requirements under this simple constraint for cases of practical interest.