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 $1,425 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. Ho: = 1,503 Ha: 1,503 Ho: > 1,503 H:HS 1,503 Ho: < 1,503 H: 21,503 Ho: 21,503 H: < 1,503 OHMS 1,503 H: > 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 a = 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. O Do not reject Ho. We can conclude that the population mean automobile premium in Pennsylvania is lower than the national mean. O Reject Ho. We can conclude that the population mean automobile premium in Pennsylvania is lower than the national mean. O Do not reject Ho. We cannot conclude that the population mean automobile premium in Pennsylvania is lower than the national mean. O Reject H. We cannot conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.

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