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 to go, driving each route 15 days. He finds that Route A takes an average of 42 minutes, with standard deviation 5 minutes, and Route B takes an average of 43 minutes, with standard deviation 1 minute. Histograms of travel times for the routes are roughly symmetric and show no outliers. Complete parts a and b. a) Find a 95% confidence interval for the difference between the Route B and Route A commuting times, (HB - HA). The confidence interval is (, ). (Round to two decimal places as needed.) b) Should the man believe the old-timer's claim that he can save an average of 5 minutes a day by always driving Route A? Explain. because the confidence interval for the difference 5 minutes