Question: The director of a management training program wants to test whether there is a positive association between an applicant's score on a test prior to her or his being admitted to the program and the same person's success in the program. The director ranks 15 participants according to their performance on the pretest and separately ranks them according to their performance in the program:

Participant:                  1     2      3      4      5      6        7      8       9     10     11      12     13     14     15

Pretest rank:                8     9      4      2      3     10       1      5       6     15     13      14     12      7      11

Performance rank:         7     5      9      6      1      8        2     10      15    14      4       3      11     12     13

Using these data, carry out the test for a positive rank correlation between pretest scores and success in the program.