Two conservative sample size approximations are given for the Bechhofer formulation of the problem of selecting the population with the largest mean, when the populations have a common known variance. A table of numerical comparisons of these approximations with the exact sample size is included. In addition, both of these results are applied to the problem of selecting the factor with the largest mean from a single multivariate normal population with known covariance matrix.
"Selection Sample Size Approximations." Ann. Math. Statist. 43 (6) 1977 - 1980, December, 1972. https://doi.org/10.1214/aoms/1177690869