Subset selection of superior populations when the number of populations is large

The situation where k populations are partitioned into one inferior group and one superior group is considered. The statistical problem is to select a random size subset of superior populations while trying to avoid including any inferior populations. A selection procedure is assumed to satisfy the condition that the probability of selecting at least one superior population is bounded below by P¹<1. The performance of a procedure is measured by the probability of including an inferior population.The asymptotic performance, as k→∞ of Gupta's traditional maximum type procedure ψ^G is considered in the location-model. For normally distributed populations, ψ^G turns out to be asymptotically optimal, provided the size of the inferior group does not become infinitely larger than the size of the superior group.