Thirty small communities in Connecticut (population near 10,000each) gave an average of x = 138.5 reported cases oflarceny per year. Assume that ? is known to be 44.9 casesper 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.As the confidence level increases, the margin of errorremains the same.    As the confidence levelincreases, the margin of error decreases.

(e) Compare the lengths of the confidence intervals for parts (a)through (c). As the confidence levels increase, do the confidenceintervals increase in length?

As the confidence level increases, the confidence intervalremains the same length.As the confidence level increases, theconfidence interval decreases in length.    Asthe confidence level increases, the confidence interval increasesin length.