1) The CDC reports statistics and data about the amount of time that people sleep and the consequences of more or less sleep. This information informs people's personal choices, doctors' medical advice, and public policies about a number of programs (including the start of the school day for children). The average teenager, for example, needs about 9.5 hours of sleep' a night; however, the CDC reports that many US high school students get far less than that. a. A survey was done among 50 high schoolers to test the average amount of sleep that they get. The survey reported students are getting an average of 7.5 hours of sleep, with a variance of 1.65 hours. Based on this survey, what would you estimate for the average amount of sleep for the entire population of high school students and the standard error? [10 points] b. A second survey of a random sample of 4,600 U.S. high school students found that the average number of hours of sleep reported by these students was 7 hours, with a variance of 1.44 hours.' i. A high schooler is defined as having "short sleep duration" if they get less than 8 hours of sleep per night. If the number of hours of sleep is normally distributed and using the results of the survey mentioned above, what is the probability a high school student who took the survey would be classified as having a "short sleep duration"? [10 points] ii. Assuming hours of sleep is normally distributed and using the results of the survey mentioned above, what is the probability a high school student who took the survey sleeps between 8 and 10 hours a night? [15 points] C. A third survey of a random sample of 3,500 US high school students and found that the average hours of sleep was 8.5 hours, with a variance of 1.01 hours.* Evaluate the hypothesis that the average hours of sleep is different between surveys (15 points) d. Someone criticizes your use of these data by saying that even the two large surveys combined contain only 8,100 high school students out of approximately 17 million' high school students in the United States. How would you defend your use of these samples to understand the population of high school students? [5 points]