Thirty small communities in Connecticut (population near 10,000each) gave an average of x = 138.5 reported cases oflarceny per year. Assume that σ is known to be 40.3casesper year.
(a) Find a 90% confidence interval for the population meanannual number of reported larceny cases in such communities. Whatis the margin of error? (Round your answers to one decimalplace.)
| lower limit    | |
| upper limit    | |
| margin of error    | |
(b) Find a 95% confidence interval for the population mean annualnumber of reported larceny cases in such communities. What is themargin of error? (Round your answers to one decimal place.)
| lower limit    | |
| upper limit    | |
| margin of error    | |
(c) Find a 99% confidence interval for the population mean annualnumber of reported larceny cases in such communities. What is themargin of error? (Round your answers to one decimal place.)
| lower limit    | |
| upper limit    | |
| margin of error    | |
(d) Compare the margins of error for parts (a) through (c). As theconfidence levels increase, do the margins of error increase?
As the confidence level increases, the margin of errorincreases.
(e) Compare the lengths of the confidence intervals for parts(a) through (c). As the confidence levels increase, do theconfidence intervals increase in length?
As the confidence level increases, the confidenceinterval increases in length.
