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MY NOTES ASK YOUR TEACHER You may need to use the appropriate technology to answer this question. Insure.com reports that the mean annual premium for automobile insurance in the United States was $1,365 in 2018. Being from Pennsylvania, you believe automobile insurance is cheaper there, and you 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 $1,272 with a standard deviation of s = $160. (Use = 0.05.) (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. 1,365 Ha: < 1,365 Hoi A > 1,365 O Ha: 1,365 Hoi A = 1,365 Ha: 1,365 Ho: 1,365 Ha: > 1,365 O Ho: < 1,365 Ha: 1,365 (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) Find the value of the test statistic. (Round your answer to three decimal places.) What is the p-value? (Round your answer to four decimal places.) p-value = (d) At = 0.05, test for a significant difference. What is your conclusion? O Reject Ho. We cannot 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 Do not reject Ho. We can conclude that the population mean automobile premium in Pennsylvania is lower than the national mean. 0 MY NOTES ASK YOUR TEACHER You may need to use the appropriate technology to answer this question. Insure.com reports that the mean annual premium for automobile insurance in the United States was $1,365 in 2018. Being from Pennsylvania, you believe automobile insurance is cheaper there, and you 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 $1,272 with a standard deviation of s = $160. (Use = 0.05.) (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. 1,365 Ha: < 1,365 Hoi A > 1,365 O Ha: 1,365 Hoi A = 1,365 Ha: 1,365 Ho: 1,365 Ha: > 1,365 O Ho: < 1,365 Ha: 1,365 (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) Find the value of the test statistic. (Round your answer to three decimal places.) What is the p-value? (Round your answer to four decimal places.) p-value = (d) At = 0.05, test for a significant difference. What is your conclusion? O Reject Ho. We cannot 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 Do not reject Ho. We can conclude that the population mean automobile premium in Pennsylvania is lower than the national mean. 0
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