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

Solution :

a) degrees of freedom = n - 1 = 25 - 1 = 24

t/2,df = t0.005,24 = 2.797

Margin of error = E = t/2,df * (s /n)

= 2.797 * (165 / 25)

Margin of error = E = $92

The 99% confidence interval estimate of the population mean is,

  ± E

$1440  ± 92

= $ 1348, $ 1532)

b) The sample size increases, margin of error decreases.