A retail electronic distributor has determined that the amount of time required to make a delivery from its warehouse to a retail store using an inner-city route is a normally distributed random variable. The shipping manager is considering a new route that would use freeways that bypass the city with the hope that the population mean time to make the trip on this new route will be less than the population mean time to make the trip on the current route. Let X1=the amount of time to make the delivery on the current route, and X2=the amount of time to make the delivery on the new route. Both X1 and X2 are assumed to be normally distributed random variables with unknown standard deviations. A random sample of 25 delivery times for each route is collected. The shipping manager wants to see the results of a hypothesis test that will determine if there is significant evidence to conclude that the population mean time for the new route, µ2, is less than the population mean time for the current route, µ1.

The delivery times for each route, in minutes, are given below:

X1 (Current): 55 53 56 47 49 43 41 56 54 57 49 52 58 56 59 42 44 41 55 47 48 58 54 56 54

X2 (New):32 43 44 47 39 38 41 43 40 37 42 46 41 40 34 46 43 39 41 45 42 35 38 34 45

• Use the AB testing approach to determine whether or not the shipping manager should make the change to the new route (you can assume the new route involves no additional costs). Refer to the appropriate numerical values in the Excel output when doing the test.
• What is the corresponding test statistic value?
• Identify the p-value associated with the observed value of the test statistic.
• What is your conclusion at the significance level α=.05? Is the new route significantly better? The shipping manager has decided she will only make the switch to the new route if the sample results provide significant evidence that the population mean time for the new route is less than the population mean time for the current route by more than 8 minutes; that is, new route is at least 8 minutes faster than the old one on average. ---Perform A/B test to determine whether she should make the switch. What is the corresponding p-value?
• What would your conclusion be if the level of significance is α=.05? Is the new route at least 8 minutes faster?