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 n = 48 delivery times have a sample mean of ¯x= 432.7 minutes and a sample standard deviation of sx = 19.39 minutes. A new driving route is proposed, and this has been tried m = 10 times with a sample mean of ¯y = 403.5 minutes and a sample standard deviation of sy = 16.78 minutes.
b. Assuming equal variances, is there evidence that the new route is quicker than the standard route? Calculate the P-value for this test.