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.
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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