Thirty-one small communities in Connecticut (population near 10,000 each) gave a

Question

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 sigma is known to be 40.9 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

Explanation / Answer

here std error =std deviation/(n)1/2 =7.346

a) fro 90% CI; z=1.28

hence lower limit =sample mean -z*std error =126.4

upper limit =sample mean +z*std error =150.6

margin of error =z*std error =12.1

b) for 95% CI, z=1.96

hence lower limit =124.1

upper limit =152.9

margin of error=14.4

c) for 99% CI, z=2.5758

lower limit =119.6

upper limit=157.4

margin of errror =18.9

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