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.  

Nearly all common statistical approaches assume complete information for all variables involved in the analysis, which making missing data problematic. Imputation is the process of substituting a missing value with a specific value, and it is most likely the most popular method for compensating for missing item values in a survey. This study suggests use of mathematical goal programming approach to impute missing data in statistical matching. The suggested approach adopts the regression method in imputation of the missing values. The regression coefficients are estimated using an estimated mathematical goal programming approach. The paper studies the cases when having variables with different skewed probability distributions (lognormal, Cauchy, chi square). The results of the simulation study indicate a good performance of the suggested approach in cases of skewed probability distribution. Using goal programming in regression is based on the minimizing the sum of absolute errors which is less affected by outliers compared to sum of squares of errors.