Question: The US Olympic Committee is trying to determine the most effective training methods to be used in training long distance runners. The two methods are Method A, long distance training on alternate days with sprint work on "off" days, or, Method B, long distance training on alternate days with swimming on "off" days. One hundred distance runners from across the nation are assigned at random to carefully controlled plans: Fifty using Method A, fifty using Method B. In August, all 100 runners were assembled in Atlanta for a 10,000-meter race. As a result of the race, each runner was assigned a rank from 1st to 100th.

1. What statistical procedure could be used to test the hypothesis of no significant
   statistical difference between the ranks of runners trained through Method A and those trained through Method B? [Hint: Consider the application of non-parametric tests].
2. Suppose that rather than rank the 100 runners on the basis of position of finishing the

race, the elapse times for each runner was determined and the mean elapsed time for Method A was compared with the mean elapsed time for Method B. What statistical procedure would be used to make this comparison? What are the advantages and disadvantages of using elapsed times as opposed to ranks?

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