16. An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000. (1) What is the upper end point in a 99% confidence interval for the average income? (2) What is the 90% confidence interval? 17. Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is put into a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of 8 private colleges in the United States revealed the following endowments (in millions of dollars): 60.2, 47.0, 235.1, 490.0, 122.6, 177.5, 95.4, and 220.0. (1) What value will be used as the point estimate for the mean endowment of all private colleges in the United States? (2) What is the standard deviation of the sample? (3) Calculate a 95% confidence interval for the mean endowment of all the private colleges in the United States assuming a normal distribution for the endowments. 18. As an aid to the establishment of personnel requirements, the director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The director randomly selects 64 different 24-hour periods and determines the number of admissions for each. For this sample, X-19.8 and s = 25. (1) Are there any assumptions such that "The population sampled from has an approximate normal distribution" or "The population sampled from has an approximate 1 distribution" necessary? (2) Estimate the mean number of admissions per 24-hour period with a 95% confidence interval.