Suppose forty communities have an average of x1347reported c

Suppose forty communities have an average of x=134.7reported cases of larceny per year. Assume that s is known to be 39.7 cases per year. Find an 85%, 90%, and 98% confidence interval for the population mean annual number of reported larceny cases in such communities. Compare the margins of error. As the confidence level increase, do the margins of error increase?

a. The 85% confidence level has a margin of error of 92.5; the 90% confidence level has a margin of error of 65.3; and the 98% confidence level has a margin of error of 57.2. As the confidence level increases, the margins of error decrease.

b. The 85% confidence level has a margin of error of 14.6; the 90% confidence level has a margin of error of 10.3; and the 98% confidence level has a margin of error of 9.0. As the confidence level increases, the margins of error decrease.

c. The 85% confidence level has a margin of error of 9.0; the 90% confidence level has a margin of error of 10.3; and the 98% confidence level has a margin of error of 14.6. As the confidence level increases, the margins of error increase.

d. The 85% confidence level has a margin of error of 1.4; the 90% confidence level has a margin of error of 1.6; and the 98% confidence level has a margin of error of 2.3. As the confidence level increases, the margins of error increase.

e. The 85% confidence level has a margin of error of 57.2; the 90% confidence level has a margin of error of 65.3; and the 98% confidence level has a margin of error of 92.5. As the confidence level increases, the margins of error increase.

Solution

Solution:

c. The 85% confidence level has a margin of error of 9.0; the 90% confidence level has a margin of error of 10.3; and the 98% confidence level has a margin of error of 14.6. As the confidence level increases, the margins of error increase.

Explanation:

1) For 85% confidnce interval:

Critical value Zc = 1.44

Margin of error E = Zc * (sigma / sqrt(n) ) = 1.44 * ( 39.7 / sqrt(40)) = 9.04

Confidence Interval CI = (134.7 - 9.04 , 134.7 +9.04) = (125.66 , 143.74)

2) For 90% confidnce interval:

Critical value Zc = 1.645

Margin of error E = Zc * (sigma / sqrt(n) ) = 1.645 * ( 39.7 / sqrt(40)) = 10.325

Confidence Interval CI = (134.7 -10.325 , 134.7 +10.325) = (124.37 , 145.02)

3) For 98% confidnce interval:

Critical value Zc = 2.33

Margin of error E = Zc * (sigma / sqrt(n) ) = 2.33 * ( 39.7 / sqrt(40)) = 14.625

Confidence Interval CI = (134.7 -14.625 , 134.7 +14.625) = (120.07 , 149.32)