Organizational analyst Ann T. Gravity is examining the Peter Principle, which contends that people will rise in an organization until they reach their level of incompetence. She feels that this means that proportionately more competent people will be found at the lower level of the organization. To test this question, she decides to ask students to rate assistant professors, associate professors, and full professors. Based on these ratings, she classified the competence of professors as high, medium, or low. Interpret the accompanying table; calculate any necessary statistics. Refer to the book€™s website for the calculation of gamma in larger tables.

Academic Rank Assistant 27 60 106 193 Associate 38 91 38 167 Full Competence Low Medium High Total Total 89 159 152 400 24 40