Rankings of MBA programs. Business Ethics (Fall 2005) published rankings of master in business administration (MBA) programs worldwide. Each of 30 business schools was rated according to student exposure to social and environmental issues in the classroom. Ratings ranged from 1 star (lowest-rated group) to 5 stars (highest-rated group). A summary of the star ratings assigned to the 30 MBA programs is reproduced in the table. Criteria 5 stars 4 stars 3 stars 2 stars 1 star Total Student Exposure 2 9 14 5 0 30 Source: Based on the source D. Biello, “MBA Programs for Social and Environmental Stewardship,” Business Ethics, Fall 2005, p. 25.

a. Identify the categorical variable (and its levels) measured in this study.

b. How many of the sampled MBA programs would you expect to observe in each star rating category if there are no differences in the category proportions in the population of all MBA programs?

c. Specify the null and alternative hypotheses for testing whether there are differences in the star rating category proportions in the population of all MBA programs.

d. Calculate the x2 test statistic for testing the hypotheses in part

c. e. Give the rejection region for the test using a = .05.

f. Use the results, parts d and

e, to make the appropriate conclusion. g. Find and interpret a 95% confidence interval for the proportion of all MBA programs that are ranked in the three-star category.