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 σ is known to be 43.5cases 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.)
(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.)
(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.)
Solution :
Given that,
(a)
Sample size = n = 31
Z/2 = 1.645
Margin of error = E = Z/2* ( /n)
= 1.645 * (43.5 / 31)
Margin of error = E = 12.9
(b)
Sample size = n = 31
Z/2 = 1.96
Margin of error = E = Z/2* ( /n)
= 1.96 * (43.5 / 31)
Margin of error = E = 15.3
(c)
Sample size = n = 31
Z/2 = 2.576
Margin of error = E = Z/2* ( /n)
= 2.576 * (43.5 / 31)
Margin of error = E = 20.1
Thirty-one small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5...
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