8.63 Physical education requirements. In the 1920s, about 97% of U.S. colleges and universities required a physical education course for graduation. Today, about 40% require such a course. A recent study of physical education requirements included 354 institutions: 225 private and 129 public. Among the private institutions, 60 required a physical education course, while among the public institutions, 101 required a course.21

  1. (a) What are the explanatory and response variables for this exercise? Justify your answers.

  2. (b) What are the populations?

  3. (c) What are the statistics?

  4. (d) Use a 95% confidence interval to compare the private and the public institutions with regard to the physical education requirement.

  5. (e) Use a significance test to compare the private and the public institutions with regard to the physical education requirement.

  6. (f) For parts (d) and (e), verify that the guidelines for using the large-sample methods are satisfied.

  7. (g) Summarize your analysis of these data in a short paragraph.