In March 16, 1998, issue of Fortune magazine, the results of a survey of 2,221 MBA students from across the United States conducted by the Stockholm-based academic consulting firm Universum showed that only 20 percent of MBA students expect to stay at their first job five years or more.

a) Set up the null and alternative hypotheses to test whether the proportion of MBA students who expect to stay at their first job five years or more is less than one-fourth of all U.S. MBA students.

b) Perform the hypothesis test with a significance level of 0.02.

c) Based on the interval from b), can you conclude that there is strong evidence that less than one-fourth of all U.S. MBA students expect to stay? describe why.