The mean annual premium for automobile insurance in the United States is $1503 (insure.com 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.

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.

b. What is a point estimate of the difference between the mean annual premium in Pennsylvania and the national mean?

c. At α = .05, test for a significant difference. What is your conclusion?