Transportation planners know that the average commuter travels 7.3 to work (each way), and the commuting distances follow a normal distribution. A detailed study is to be made of 20 commuters, and the average commuting distance is 7.8 miles with a standard deviation 1.2 miles. How can planners test whether the commuting distances of sampled commuters are indeed longer than average commuter?

Transportation planners know that the average commuter travels 7.3 to work (each way), and the commuting distances follow a normal distribution. A detailed study is to be made of 20 commuters, and the average commuting distance is 7.8 miles with a standard deviation 1.2 miles. How can planners test whether the commuting distances of sampled commuters are indeed longer than average commuter?