Final answer:
When P is greater than α, the test statistic is inside the acceptance region, indicating that the null hypothesis is not rejected. A P-value higher than the significance level of α suggests insufficient evidence against the null hypothesis.
Step-by-step explanation:
When P > α, the standardized test statistic lies inside the acceptance region, meaning it does not fall into the rejection regions at the ends of the distribution. This occurs because α is the threshold for the significance level of the test—it represents the probability of rejecting the null hypothesis when it is actually true (Type I error). If a test produces a P-value that's greater than α, the result is not considered statistically significant, and therefore, we fail to reject the null hypothesis as there isn't enough evidence against it.
For example, if you conduct a hypothesis test at the 0.05 significance level (α = 0.05) and find a P-value of 0.08, you would not reject the null hypothesis because the result isn't in the rejection region (α > P-value). However, if the P-value were 0.02, it would fall in the rejection region, leading to the null hypothesis being rejected, indicating that there's a statistically significant difference.