The purpose of this work is to discover an optimum sample size to be used for deciding between two methods (populations) to choose for future production. The procedure involves the formulation of a loss function, expressing the expected loss due to choosing the population with the small mean, as a function of the difference between the population means, the amount to be produced and the cost of sampling. A minimax procedure is applied to obtain the optimum sample size. Since the function does not lend itself conveniently to mathematical considerations, special cases involving the difference between the means are considered and an optimum sample size is found for these cases. In all cases, the optimum sample size is an explicit function of the amount to be produced, the cost of sampling and the standard deviation. / Master of Science