Why the Null Hypothesis is Not Accepted (2 of 5)
Thus, if the data do not provide a basis for rejecting the null hypothesis that µ1- µ2 = 0 then they almost certainly will not provide a basis for rejecting the hypothesis that µ1- µ2 = 0.001. The data are consistent with both hypotheses. When the null hypothesis is not rejected then it is legitimate to conclude that the data are consistent with the null hypothesis. It is not legitimate to conclude that the data support the acceptance of the null hypothesis since the data are consistent with other hypotheses as well. In some respects, rejecting the null hypothesis is comparable to a jury finding a defendant guilty. In both cases, the evidence is convincing beyond a reasonable doubt. Failing to reject the null hypothesis is comparable to a finding of not guilty. The defendant is not declared innocent. There is just not enough evidence to be convincing beyond a reasonable doubt. In the judicial system, a decision has to be made and the defendant is set free. In science, no decision has to be made immediately. More experiments are conducted.