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 1 that 2 was rejected. When the hypotheses (8.5.7) were tested at the same level of significance, and the same data were used, the hypothesis 3 that 4 was accepted.