Thirty-five small communities in Connecticut (population near10,000 each) gave an average of x = 138.5 reported casesof larceny per year. Assume that ? is known to be 40.7cases per 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?

(a) As the confidence level increases, the margin of errordecreases.

(b) As the confidence level increases, the margin of errorremains the same.    

(c) 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 the confidenceintervals increase in length?

(a) As the confidence level increases, the confidence intervalremains the same length.

(b) As the confidence level increases, the confidence intervaldecreases in length.    

(c) As the confidence level increases, the confidence intervalincreases in length.