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The study is concerned with the transforming theoretical Mathematical models into applied Mathematical programming models that are easy to handle and use. These Mathematical programming models can be applied and used in statistical inference, which used in many applied fields, for example, quality control and its application. The aim of this paper is to suggest two mathematical programming models for hypotheses tests, which make a balance between the high power (1-β), and the probability of a type I error, significance (), of the test. The paper introduces a simulation study to evaluate the performance of the two suggested mathematical programming models for tests hypotheses. The two suggested mathematical programming models solved with different sample sizes and different level of significance. The suggested models calculate the critical values which determine the rejection region exactly and the results are easy to interpret clearly. Then the conclusion for the suggested mathematical programming models makes balance between the power and the significance.