Insure.com reports that the mean annual premium for automobile insurance in the United States was $1365 in 2018. 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 $1302 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 a = .05, test for a significant difference. What is your conclusion?