OPTIMAL CONFIDENCE INTERVAL FOR THE LARGEST NORMAL MEAN WITH UNKNOWN VARIANCE

A single-sample procedure for obtaining an optimal confidence interval for the largest or smallest mean of several independent normal populations is proposed. It is assumed that the common variance is unknown. It has been found that the optimal confidence interval is uniformly better than any other existing one-sample confidence interval in the sense of a reduced interval width. This optimal confidence interval is obtained by maximizing the coverage probability with the expected confidence width being fixed at a least favorable configuration of means. Tables of the critical values are given for the optimal confidence interval.