A company is investigating how long it takes its drivers to deliver goods from its factory to a nearby port for export. Records reveal that with a standard specified driving route, the last =48 delivery times have a sample mean of =432.7 minutes and a sample standard deviation of =19.39 minutes. A new driving route is proposed, and this has been tried =10 times with a sample mean of =403.5 minutes and a sample standard deviation of =16.78 minutes.
a. Test the hypothesis that the variance of the delivery time for the standard route equals that of the new route.
b. Assuming equal variances, is there evidence that the new route is quicker than the standard route? Calculate the P-value for this test.