On December 1, 1969, during the Vietnam War, a lottery was used to determine who would be drafted into the U.S. Army, but the lottery generated considerable controversy. The different dates in a year were placed in 366 individual capsules. First, the 31 January capsules were placed in a box; then the 29 February capsules were added and the two months were mixed. Next, the 31±March capsules were added and the three months were mixed. This process continued until all months were included. The first capsule selected was September 14, so men born on that date were drafted first. The accompanying list shows the 366 priority dates in the order of selection. This list is available for download at www.TriolaStats.com.

Analyzing the Results

a. Use the runs test to test the sequence for randomness above and below the median of 183.5.

b. Use the Kruskal-Wallis test to test the claim that the 12 months had priority numbers drawn from the same population.

c. Calculate the 12 monthly means. Then plot those 12 means on a graph. (The horizontal scale lists the 12 months, and the vertical scale ranges from 100 to 260.) Note any pattern suggesting that the original priority numbers were not randomly selected.

d. Based on the results from parts (a), (b), and (c), decide whether this particular draft lottery was fair. Write a statement explaining why you believe that it was or was not fair. If you decided that this lottery was unfair, describe a process for selecting lottery numbers that would have been fair.