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. Source: Shalley Branch, "MBAs: What Do They Really Want," Fortune (March 16, 1998), p.167.
a) Assuming that a random sample was selected, construct a 98% confidence interval for the proportion of all U.S. MBA students who expect to stay at their first job five years or more.
b) Based on the interval from a), can you conclude that there is strong evidence that less than one-fourth of all U.S. MBA students expect to stay? Explain why.