Hypotheses testing is an effective technique for making a decision about the process capability. The adversity to test (Formula presented.) based on determining the distribution of its natural estimator is very complex, even under the Normal distribution. Thus, the Monte Carlo simulation approach is an executable procedure for the hypotheses testing of (Formula presented.) based on the natural estimator. The proposed approach is a testing technique to evaluate whether products quality meets the preset specification limits. This procedure implies a Monte Carlo statistical test, which is applicable to Normal processes. A case study in an automobile factory is presented to check out the products, and numerical computations are presented to show the effect of the Monte Carlo critical values for making a reliable decision on the hypotheses testing of (Formula presented.).