Question

1. “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 )

sample size increases than margin of error decrease