ABSTRACTIn regression problems, we often test a null hypothesis which, according to prior knowledge, is likely to be wrong. In order to decrease the error of the second kind, we then raise the power function and thus, also increase the significance level. In this paper, we will represent our prior knowledge by certain prior probility functions and will apply Bayesian methods to test the null hypothesis. We will show that the results obtained by the Bayesian method are equivalent to the sampling methods with a raised power function.