Question

The mean annual premium for automobile insurance in the United States is $1503 (Insure website, March 6, 2014). Being from Pennsylvania, you believe automobile insurance is cheaper there and wish to develop statistical support for your opinion. A sample of 25 automobile insurance policies from the state of Pennsylvania showed a mean annual premium of $1440 with a standard deviation of s = $165. If required, enter negative values as negative numbers.

a. Develop a hypothesis test that can be used to determine whether the mean annual premium in Pennsylvania is lower than the national mean annual premium. H 0: μ H a: μ
b. What is a point estimate of the difference between the mean annual premium in Pennsylvania and the national mean (to the nearest dollar)? $ c. At = .05, test for a significant difference by completing the following. Calculate the value of the test statistic (to 2 decimals). The p-value is What is your conclusion?

Answer 1

It is not evident the mean annual premium in Pennsylvania is lower than the national mean annual premium

Explanation:

Given that annual premium for automobile insurance in the United States (Insure website, March 6, 2014), are as follows:

Mean 1440.00

SD 165.00

SEM 33.00

N 25

a)
`H_0: \bar x = 1503\\H_a: \bar x <1503`

(left tailed test at 5% level)

b) a point estimate of the difference between the mean annual premium in Pennsylvania and the national mean

=
`1440-1503\\=-103`

c) df = 24

standard error of difference = 33.000

t = 1.9091

The 95% confidence interval of this difference:

From -131.11 to 5.11

p value = 0.0683

Since p >0.05, we accept H0

It is not evident the mean annual premium in Pennsylvania is lower than the national mean annual premium