1. The mean diastolic blood pressure for a random sample of 80 people was 100 millimeters of mercury. If the standard deviation of individual blood pressure readings is known to be 9 millimeters of mercury, find a 95% confidence interval for the true mean diastolic blood pressure of all people. Then complete the table below. What is the lower limit of the 95% interval? What is the upper limit of the 95% interval?
2. A union of restaurant and foodservice workers would like to estimate the mean hourly wage, mean , of foodservice workers in the U.S. The union will choose a random sample of wages and then estimate using the mean of the sample. What is the minimum sample size needed in order for the union to be 95% confident that its estimate is within $0.45 of? Suppose that the standard deviation of wages of foodservice workers in the U.S. is about$2.25.
3. Suppose that a random sample of 13 adults has a mean score of 78 on a standardized personality test, with a standard deviation of 6. (A higher score indicates a more personable participant.) If we assume that scores on this test are normally distributed, find a 99% confidence interval for the mean score of all takers of this test. What is the lower limit of the confidence interval? What is the upper limit of the confidence interval?
4. Twenty years ago, a very famous psychologist specializing in marriage counseling authored a book detailing the way in which she believed spouses should communicate. She is now interested in theproportion of all couples who bought her book who stayed together. For a random sample of 200 200couples who bought her book, she found that 164164 of them stayed together. Based on this, compute a 95%95% confidence interval for the proportion of all couples who bought her book who stayed together. What is the lower limit of the 95% confidence interval? What is the upper limit of the 95% confidence interval?