According to U.S. News & World Report's Business School Rankings, the median earnings for graduates of full-time, highly ranked MBA programs 4 years after graduating is $125,000. A random sample of 50 recent graduates from a particular highly ranked MBA program was mailed a questionnaire and asked to report their annual earnings. Fifteen usable responses were received; nine indicated earnings greater than $125,000 and six indicated earnings below $125,000.

a. Specify the null and alternative hypotheses that should be used in testing whether the median income of graduates of the MBA program is more than $125,000.

b. Conduct the test of part a using a = .05 and draw your conclusion in the context of the problem.

c. What assumptions must hold to ensure the validity of your hypothesis test?