Question

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 40 minutes, with standard deviation 5 minutes​, and Route B takes an average of 41 ​minutes, with standard deviation 3 minutes. Histograms of travel times for the routes are roughly symmetric and show no outliers. Complete parts a and b. Use a = 0.05.

​a) Find a​ 95% confidence interval for the difference between the Route B and Route A commuting​ times, (Yb-Ya).

The confidence interval is ( _ , _ ).

​(Round to two decimal places as​ needed.)

​b) Should the man believe the​ neighbor's claim that he can save an average of 5 minutes a day by always driving Route​ A? Explain.

(Yes/No)​, because the confidence interval for the difference (does not contain/contains) 5 minutes.

Answer 1