A trucking company would like to compare two different routes for efficiency. Truckers are randomly assigned to two different routes. Twenty truckers following Route A report an average of

49

minutes, with a standard deviation of

3

minutes. Twenty truckers following Route B report an average of

54

minutes, with a standard deviation of

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 the commuting time for the two routes.

b) Does the result in part (a) provide sufficient evidence to conclude that the company will save time by always driving one of the routes? Explain.