On Selecting a Subset Which Contains All Populations Better Than a Standard

A procedure is given for selecting a subset such that the probability that all the populations better than the standard are included in the subset is equal to or greater than a predetermined number $P^{ast}$. Section 3 deals with the problem of the location parameter for the normal distribution with known and unknown variance. Section 4 deals with the scale parameter problem for the normal distribution with known and unknown mean as well as the chi-square distribution. Section 5 deals with binomial distributions where the parameter of interest is the probability of failure on a single trial. In each of the above cases the case of known standard and unknown standard are treated separately. Tables are available for some problems; in other problems transformations are used such that the given tables are again appropriate.