A professor would like to test the hypothesis that the average number of minutes that a student needs to complete a statistics exam has a standard deviation that is less than 5.0 minutes. A random sample of 15 students was selected and the sample standard deviation for the time needed to complete the exam was found to be 4.0 minutes. Using α = 0.05, the conclusion for this hypothesis test would be that because the test statistic is
A)more than the critical value, we fail to reject the null hypothesis and conclude that the standard deviation for the time to complete an exam is less than 5.0 minutes.
B)less than the critical value, we fail to reject the null hypothesis and cannot conclude that the standard deviation for the time to complete an exam is less than 5.0 minutes.
C)less than the critical value, we reject the null hypothesis and cannot conclude that the standard deviation for the time to complete an exam is less than 5.0 minutes.
D)more than the critical value, we fail to reject the null hypothesis and cannot conclude that the standard deviation for the time to complete an exam is less than 5.0 minutes.

Question

Quizplus · Accepted Answer

The correct interpretation of the hypothesis test outcome when the test statistic is more than the critical value is that we fail to reject the null hypothesis. However, failing to reject the null hypothesis does not allow us to conclude that the standard deviation is less than 5.0 minutes; it simply means there is not enough evidence to support the alternative hypothesis that the standard deviation is less than 5.0 minutes.

A Professor Would Like to Test the Hypothesis That the Average