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Thirty small communities in Connecticut (population near 10,000each) gave an average of x = 138.5 reported cases of larceny peryear. Assume that ? is known to be 45.1 cases 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 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:

(c) Find a 99% 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:

(d) Compare the margins of error for parts (a) through (c). Asthe confidence levels increase, do the margins of errorincrease?

As the confidence level increases, the margin of errorincreases.

As the confidence level increases, the margin of error remainsthe same.

As the confidence level increases, the margin of errordecreases.

(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 confidence intervaldecreases in length.

As the confidence level increases, the confidence intervalremains the same length.

As the confidence level increases, the confidence intervalincreases in length.