10.10 INTERPRETATION

In the present example, it can be concluded that, since the null hypothesis was rejected, the mean SAT math score for the local freshman class probably differs from the national average of 500. Although not a strict consequence of the present test, a more specific conclusion is possible. Since the sample mean of 533 (or its equivalent z of 3) falls in the upper rejection region of the hypothesized sampling distribution, it can be concluded that the population mean SAT math score for all local freshmen probably exceeds the national average of 500. By the same token, if the observed sample mean or its equivalent z had fallen in the lower rejection region of the hypothesized sampling distribution, it could have been concluded that the population mean for all local freshmen probably is below the national average. If the observed sample mean or its equivalent z had fallen in the retention region of the hypothesized sampling distribution, it would have been concluded that there is no evidence that the population mean for all local freshmen differs from the national average of 500.