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

Question

Thirty-three 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 44.3 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

SolutionA:

Z crit for 90%=1.645

sample mean=138.5

pop std dev=44.3

n=sampel size=33

90% confidence interval for the population mean annual number of reported larceny cases in such communities

sample mean-z crit(pop stddev/sqrt(n),sample mean+z crit(pop stddev/sqrt(n)

138.5-1.645*44.3/sqrt(33),138.5+1.645*44.3/sqrt(33)

125.8,153.6

lower limit=123.4,

upper limit=151.2

margin of error=1.645*44.3/sqrt(33)=12.7

Solutionb:

95% confidence interval for the population mean annual number of reported larceny cases in such communities

Z crit for 95%=1.96

95% confidence interval for the population mean annual number of reported larceny cases in such communities=

sample mean-z crit(pop stddev/sqrt(n),sample mean+z crit(pop stddev/sqrt(n)

138.5-1.96*44.3/sqrt(33),138.5+1.96*44.3/sqrt(33)

123.4,153.6

lower limit=123.4

upper limit=153.6

margin of error=1.96*44.3/sqrt(33)=15.1

Solutionc:

Z crit for 99%=2.576

99% confidence interval for the population mean annual number of reported larceny cases in such communities=

sample mean-z crit(pop stddev/sqrt(n),sample mean+z crit(pop stddev/sqrt(n)

138.5-2.576*44.3/sqrt(33),138.5+2.576*44.3/sqrt(33)

118.6.158.4

lower limit=118.6

uper limit=158.4

margin of error=2.576*44.3/sqrt(33)=19.9

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