Question

2. “In attempting to determine the population mean annual automobile insurance premium, you draw a sample...

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.

Homework Answers

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.

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