My NOtus Thirty-one small communities in Connecticut (population near 10,000 eac

Question

My NOtus Thirty-one small communities in Connecticut (population near 10,000 each) gave an average of x-138.5 reported cases of larceny per year. Assume that ? is known to be 45.1 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? (Round your answers to one decimal place.) lower limit upper limit 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? (Round your answers to one decimal place.) lower limit upper limit 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? (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 the confidence levels increase, do the margins of error increase? As the confidence level increases, the margin of error decreases. As the confidence level increases, the margin of error remains the same As the confidence level increases, the margin of error increases

Explanation / Answer

solution : Given that x-bar = 138.5 , ? = 45.1 , n = 31

(a) For 90% confidence interval , Z = 1.645

margin of error = Z*?/sqrt(n) = 1.645*45.1/sqrt(31) = 13.3

Lower limit = x-bar - margin of error = 138.5 - 13.3 = 125.2

upper limit = x-bar +margin of error = 138.5 + 13.3 = 151.8

(b) For 95% confidence interval , Z = 1.96

margin of error = Z*?/sqrt(n) = 1.96*45.1/sqrt(31) = 15.9

Lower limit = x-bar - margin of error = 138.5 - 15.9 = 122.6

upper limit = x-bar + margin of error = 138.5 + 15.9 = 154.4

(c) For 99% confidence interval , Z = 2.576

margin of error = Z*?/sqrt(n) = 2.576*45.1/sqrt(31) = 20.9

Lower limit = x-bar - margin of error = 138.5 - 20.9 = 117.6

upper limit = x-bar + margin of error = 138.5 + 20.9 = 159.4

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