Question 4. A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid.

a) Use a 90% confidence interval to estimate the true proportion of students who receive financial aid. Explain/show how you obtain your answer. (15 pts.)

b) If the dean wanted to estimate the proportion of all students receiving financial aid to within 3% with 99% reliability, how many students would need to be sampled? Explain/show how you obtain your answer. (5 pts.)

Question 5. A sales and marketing management magazine conducted a survey on salespeople cheating on their expense reports and other unethical conduct. In the survey on 200 managers, 58% of the managers have caught salespeople cheating on an expense report, 50% have caught salespeople working a second job on company time, 22% have caught salespeople listing a "strip bar" as a restaurant on an expense report, and 19% have caught salespeople giving a kickback to a customer.

a) Construct a 95% confidence interval estimate of the population proportion of managers who have caught salespeople cheating on an expense report. Explain/show how you obtain your answer. (10 pts.)

b) What is the sampling error of a 95% confidence interval estimate of the population proportion of managers who have caught salespeople cheating on an expense report? Explain/show how you obtain your answer. (6 pts.)

c) True or False: It is possible that the 95% confidence interval calculated from the data will not contain the sample proportion of managers who have caught salespeople cheating on an expense report. Explain/show how you obtain your answer. (2 pts.)

d) True or False: It is possible that the 95% confidence interval calculated from the data will not contain the population proportion of managers who have caught salespeople cheating on an expense report. Explain/show how you obtain your answer. (2 pts.)