In: Statistics and Probability
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 43.7 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 |
Given that
Given that,
= 138.5
= 43.7
n = 31
a ) At 90% confidence level the z is ,
= 1 - 90% = 1 - 0.90 = 0.10
/ 2 = 0.10 / 2 = 0.05
Z/2 = Z0.05 = 1.645
Margin of error = E = Z/2* (/n)
= 1.645 * (8.8 / 31 )
= 12.9
Margin of error = 12.9
At 90% confidence interval estimate of the population mean is,
- E < < + E
138.5 - 12.9< < 138.5 + 12.9
125.6 < < 151.1
Lower limit =125.6
Upper limit =151.1
b ) At 95% confidence level the z is ,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2 = 0.05 / 2 = 0.025
Z/2 = Z0.025 = 1.960
Margin of error = E = Z/2* (/n)
= 1.960 * (8.8 / 31 )
= 15.4
Margin of error =15.4
At 95% confidence interval estimate of the population mean is,
- E < < + E
138.5 - 15.4 < < 138.5 + 15.4
123.1 < < 153.9
Lower limit =153.9
Upper limit =123.1
c ) At 99% confidence level the z is ,
= 1 - 99% = 1 - 0.99 = 0.01
/ 2 = 0.01 / 2 = 0.005
Z/2 = Z0.005 = 2.576
Margin of error = E = Z/2* (/n)
= 2.576 * (8.8 / 31 )
= 20.2
Margin of error =20.2
At 99% confidence interval estimate of the population mean is,
- E < < + E
138.5 - 20.2 < < 138.5 +20.2
118.3 < < 65.2
Lower limit =118.3
Upper limit =158.7