A man who moves to a new city sees that there are two routes he could take to work. A neighbor who has lived there a long time tells him Route A will average 5 minutes faster than Route B. The man decides to experiment. Each day he flips a coin to determine which way togo, driving each route 20 days. He finds that Route A takes an average of 40 minutes, with standard deviation 5 minutes, and Route B takes an average of 43 minutes, with standard deviation 2 minutes. Histograms of travel times for the routes are roughly symmetric and show no outliers. Complete parts a and b.

a) Find a95% confidence interval for the difference between the Route B and Route A commutingtimes, BA.

(Round to two decimal places asneeded.)

b) Should the man believe theold-timer's claim that he can save an average of 5 minutes a day by always driving RouteA? Explain.