Exercises Section 3.4: 8. Are students who attend private universities more likely to attend a school far from home? A study of first-year college students asked separate random samples of students from private and public universities the following question: "How many miles is this university from your permanent home?" Here is a two-way table summarizing the responses for these two groups of students. Weekly sauna bathing frequency Public Private Total Distance from Less than 500 miles 37,552 16,246 53,798 home More than 500 miles 5,811 9,486 15,297 Total 43,363 25,732 69,095 a. State the appropriate null and alternative hypotheses, using "equally likely" and "more likely" instead of same ability and greater ability. b. Calculate the difference (Private - Public) in percentage of students who attend school at least 500 miles from home. Then explain how the difference is evidence for the alternative hypothesis. c. Provide the two explanations for the evidence stated in part (b). d. Explain how to use note cards to simulate the difference (Private - Public) in percentage of students who attend school at least 500 miles from home, assuming that the students are equally likely to attend school at least 500 miles from home