Abstract
Two rules for identifying the population of origin of each observation sampled from two normal mixed (or not mixed) population are proposed. They have a preliminary test under the null hypothesis H_0 : "The population is not mixed." And one of them is MER (Minimum Error Rate) rule and the other is MSE (Minimum Mean Squared Error) rule. Let p be a mixture rate and put δ=(μ_2-μ_1)/δ≧0. Theoretically, the preliminary test doesn't give performance under MER rule, but good one under MSE rule when p and δ fail in the region p≦Φ(-δ/2). In conclusion, by the Monte Carlo method containing step of estimation of unknown p and δ, it will be seen that the both rules with preliminary test have good performance, where its significant level α is nearly equal to 0.5.
