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 he 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 10 days. He finds that Route A takes an average of 49 minutes, with standard deviation 2 minutes, and Route B takes an average of 50 minutes, with standard deviation 4 minutes. Histograms of travel times for the routes are roughly symmetric and show no outliers. (alpha =0.05)
Find a 95% confidence interval for the difference between the Route B and Route A commuting times.