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

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Abstract
A two-stage procedure 𝓅with screening in the first stage to find the population with the largest mean out of k ≧ 2 normal populations with unknown means and a common variance is under concern. It was proposed and previousiy studied by Cohen (1959), Alam (1970) and Tamhane and Bechhofer (1977, 1979) using the indifference-zone approach. The conjecture that the least favourable parameter configuration for the probability of a correct selection is of the slippage type remained unproved for k ≧ 3. Miescke and Sehr (1980) proved the conjecture for k=3. The problem was further discussed by Gupta and Miescke (1982). A general proof for rhe conjecture will be given in this paper.