Thirty small communities in Connecticut (population near 10,000 each) reported an average of  = 138.5 cases of larceny per year. Assume that σ is known to be 42.6 cases per year.
(a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error?
(b) Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error?
(c) Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error?
(d) Compare the margins of error for parts (a)–(c). As the confidence levels increase, do the margins of error increase?
(e) Compare the lengths of the confidence intervals for parts (a)–(c). As the confidence levels increase, do the confidence intervals increase in length?