The Insure.com website reports that the mean annual premium for automobile insurance in the United States was $1,503 in March 2014. Being from Pennsylvania at that time, you believed automobile insurance was cheaper there and decided 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 $1,430 with a standard deviation of

s = $170.

(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.

H₀: = 1,503

H_a: 1,503

H₀: > 1,503

H_a: 1,503

H₀: 1,503

H_a: > 1,503

H₀: 1,503

H_a: < 1,503

H₀: < 1,503

H_a: 1,503

(b)

What is a point estimate in dollars of the difference between the mean annual premium in Pennsylvania and the national mean? (Use the mean annual premium in Pennsylvania minus the national mean.)

$

(c)

At

= 0.05,

test for a significant difference.

Find the value of the test statistic. (Round your answer to three decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

Do not reject H₀. We can conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.

Reject H₀. We cannot conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.

Reject H₀. We can conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.

Do not reject H₀. We cannot conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.