The numerical values in Examples 8.5.1 and 8.5.4 emphasize the importance of deciding whether the appropriate alternative hypothesis in a given problem is one – sided or two – sided. When the hypotheses (8.5.3) were tested at the level of significance 0.05. The hypothesis that was rejected. When the hypotheses (8.5.7) were tested at the same level of significance, and the same data were used, the hypothesis that was accepted.