Abstract: Rules about the mean of a Gaussian distribution are presented and compared. Considering the square error loss function, our approximate Bayesian decision rule for the mean of a normal population is derived. Using normal data and SAS software, our approximate Bayesian test results were compared to their classical counterparts obtained with the well-known classical decision rule. It is shown that the proposed approximate Bayesian decision rule relies only on observations that are under study. The classical decision rule, which uses the standard normal and the student-t statistics, does not always yield the best results; the proposed approach performs often