An economist working for a state university wanted to acquire information about salaries in publicly funded and private colleges and universities. She conducted a survey of 623 public- university faculty members and 592 private-university faculty members asking each to report his or her rank (instructor = 1, assistant professor = 2, associate professor = 3, and professor = 4) and current salary ($1,000).

a. Conduct a test to determine whether public colleges and universities and private colleges and universities pay different salaries when all ranks are combined.

b. For each rank, determine whether there is enough evidence to infer that the private college and university salaries differ from that of publicly funded colleges and universities.

c. If the answers to parts (a) and (b) differ, suggest a cause.

d. Conduct a test to determine whether your suggested cause is valid.