A university health services physician is concerned about how much sleep freshman are getting. She asks a simple random sample of 50 students if they got at least 8 hours of sleep the previous night. Then she constructs a 95% confidence interval for the true proportion of all freshman college students who got at least 8 hours of sleep the previous night. (a) Explain what would happen to the width of the interval if the confidence level were decreased to 90%.
(b) Explain what you would expect to happen to the width of the interval if the sample size was increased to 200 students.
(c) After calculating the interval, the physician realizes that the sample was drawn from only the 70% of freshman who had turned in their health forms by the time they arrived on campus. Can she adjust the confidence interval to take this undercoverage into account? If so, how? If not, why not?