Suppose thirty communities gave an average of mc018-1.jpg = 142.6 reported cases of larceny per year. Assume that mc018-2.jpg is known to be 45.8 cases per year. Find a 75%, 85%, and 90% confidence interval for the population mean annual number of reported larceny cases in such communities. Compare the lengths of the confidence intervals. As the confidence levels increase, do the confidence intervals increase in length? Answer a. The 75% confidence level has a confidence interval length of 3.5; the 85% confidence level has a confidence interval length of 4.4; and the 90% confidence level has a confidence interval length of 5.0. As the confidence level increases, the confidence interval lengths increases. b. The 75% confidence level has a confidence interval length of 19.2; the 85% confidence level has a confidence interval length of 24.1; and the 90% confidence level has a confidence interval length of 27.5. As the confidence level increases, the confidence interval lengths increases. c. The 75% confidence level has a confidence interval length of 105.3; the 85% confidence level has a confidence interval length of 131.9; and the 90% confidence level has a confidence interval length of 150.7. As the confidence level increases, the confidence interval length increases. d. The 75% confidence level has a confidence interval length of 5.0; the 85% confidence level has a confidence interval length of 4.4; and the 90% confidence level has a confidence interval length of 3.5. As the confidence level increases, the confidence interval length decreases. e. The 75% confidence level has a confidence interval length of 150.7; the 85% confidence level has a confidence interval length of 131.9; and the 90% confidence level has a confidence interval length of 105.3. As the confidence level increases, the confidence interval lengths decreases.
