Thirty-one small communities in Connecticut (population near 10,000 each) gave a
ID: 3222580 • Letter: T
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 is known to be 40.5 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.)
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 or 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 or error=
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 or 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 or error=
Explanation / Answer
a) here std error =std deviation/(n)1/2 =7.274
for 90% CI, z=1.645
hence margin of errror =z*std error =11.9647
lower limit =xbar -margin of error =126.5353
upper limit=xbar +margin of error =150.4647
b)for 95% CI, z=1.96
hence margin of errror =z*std error =14.2568
lower limit =xbar -margin of error =124.2432
upper limit=xbar +margin of error =152.7568
c) for 99% CI, z=2.5758
hence margin of errror =z*std error =18.7366
lower limit =xbar -margin of error =119.7634
upper limit=xbar +margin of error =157.2366
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