Question: Suppose you were to compare two routes to school or work by timing yourself on each route for five days. Suppose the times on one route were (in minutes) 10, 12, 13, 15, 20, and on the other route they were 10, 15, 16, 18, 21.

a. The average times for the two routes are 14 minutes and 16 minutes. Would you be willing to conclude that the first route is faster, on average, based on these sample measurements?

b. Give an example of two sets of times, where the first has an average of 14 minutes and the second an average of 16 minutes, for which you would be willing to conclude that the first route is faster.

c. Explain how the concept of natural variability entered into your conclusions in parts a and b.