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Test power in two-sample problem testing as the utility function in the theory of decision making under risk and uncertainty

In this paper, we construct types of alternative hypotheses for the test power research. For every type, it was obtained some alternative hypotheses that competing hypotheses are represented by various families of distribution. The test power is simulated for all alternative hypotheses and all two-sample tests using the Monte-Carlo method. Using the Wald test, we conclude what two-sample test is preferable. Such the conclusions can be applied in the practice.