You may need to use the appropriatetechnologyto answer this question.The mean annual premium for automobile insurance in the United States is $1,503.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 $1,430with a standard deviation of

s= $160.

(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.

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

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