Question

2. “In attempting to determine the population mean annual automobile insurance premium, you draw a sample of 25 automobile insurance policies. This sample has a sample mean annual premium of $1440 and a sample standard deviation of s=$165. a. Construct a 99% confidence interval for the population mean annual automobile insurance premium. b. Assuming everything else is fixed, what happens to the margin of error as the sample size increases.

Answer 1

a. Construct a 99% confidence interval for the population mean annual automobile insurance premium.

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 1440

S = 165

n = 25

df = n – 1 = 24

Confidence level = 99%

Critical t value = 2.7969

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 1440 ± 2.7969*165/sqrt(25)

Confidence interval = 1440 ± 92.2990

Lower limit = 1440 - 92.2990 = 1347.70

Upper limit = 1440 + 92.2990 = 1532.30

Confidence interval = (1347.70, 1532.30)

b. Assuming everything else is fixed, what happens to the margin of error as the sample size increases.

Assuming everything else is fixed, the margin of error decreases as the sample size increases