In this paper, a single-sample procedure is proposed for obtaining an optimal confidence interval for the largest or smallest mean of several independent normal populations, where the common variance is unknown. It has been found that the optimal confidence interval in the sense of a reducing 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.
Optimal Confidence Interval for the Largest Normal Mean with Unknown Variance