You may need to use the appropriatetechnologyto answer this question.

The Insure.com website reports that the mean annual premium for automobile insurance in the United States was $1,503 inMarch 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 of25 automobileinsurance policies from the state of Pennsylvania showed a mean annual premium of $1,435with a standard deviation ofs= $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 thep-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

RejectH₀. We can conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.

Do not rejectH₀. We cannot conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.

RejectH₀. We cannot conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.

Do not rejectH₀. We can conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.