On a conjecture concerning the least favorable configuration of a two-stage selection procedure

Given k normal populations with unknown means and a common known variance a two-stage procedure p1 with screening in the first stage to find the population with the largest mean using the indifference-zone approach is under concern. It was proposed and studied previously by Cohen (1959), Alam (1970) and Tamhane and Bechhofer (1977, 1979). But up to now a conjecture concerning the least favorable parameter configuration of p1remained unproved for k ≥ 3. In this paper we give a non-standard proof of the conjecture in case of k = 3 for p1. which (under minor changes) works also for a simplified version of p1,. Besides, a counterexample is provided to show that another (more intuitive) method of proof fails to work.