A human resources director wishes to assess the benefits of sending a company's managers to an innovative management course. Twelve of the company's managers are randomly selected to attend the course, and a psychologist interviews each participating manager before and after taking the course. Based on these interviews, the psychologist rates the manager's leadership ability on a l-to-100 scale. The pretest and posttest leadership scores for each of the 12 managers are given in Table 18.5.
a. Let D1 be the distribution of leadership scores before taking the course, and let D2 be the distribution of leadership scores after taking the course. Carry out the Wilcoxon signed ranks test to test whether A), and D2 are identical (that is, the course has no effect on leadership scores) versus the alternative that D2 is shifted to the right or left of D, (that is, the course affects leadership scores). Use α = .05.
b. Carry out the Wilcoxon signed ranks test to determine whether D2 is shifted to the right of D1. Use α = .05. What do you conclude?