Question

Thirty small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5 reported cases of larceny per year. Assume that σ is known to be 41.9 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

Answer 1

Mean () = 138.5
Sample size (n) = 30
Standard deviation (s) = 41.9
Confidence interval (in %) = 90
z @ 90% = 1.645
Since we know that

Required confidence interval = (138.5-12.584, 138.5+12.584)
Required confidence interval = (125.916, 151.084)

b) Confidence interval(in %) = 95
z @ 95% = 1.96
Since we know that

Required confidence interval = (138.5-14.9937, 138.5+14.9937)
Required confidence interval = (123.5063, 153.4937)

c) Confidence interval(in %) = 99
z @ 99% = 2.576
Since we know that

Required confidence interval = (138.5-19.706, 138.5+19.706)
Required confidence interval = (118.794, 158.206)
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