Question

“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

Given that,

= 1440

s =165

n = 25

Degrees of freedom = df = n - 1 = 25- 1 = 24

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2  df = t0.005, 24=2.797 ( using student t table)

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

= 2.797* (165 / 25) = 92.3010

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

- E < < + E

1440 - 92.3010< < 1440+ 92.3010

1347.6990 < < 1532.3010

( 1347.6990 , 1532.3010 )

(B)sample size increases when margin of error is decrease