Aman 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 20 days. he finds that route a takes an average of 40 minutes, with standard deviation 3 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. a) find a 95% confidence interval for the difference in average commuting time for the two routes. (from technology, df = 33.1) 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.