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 $1,435 with a standard deviation of - $170. (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 H-1,503 H₁1,503 >1,503 Hs 1,503 How21,503 H: < 1,503 $1,503 H>1,503 Hg 1,503 M1,503 (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) x Find the p-value. (Round your answer to four decimal places) .

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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 $1,435 with a standard deviation of s= $170.
(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.
O
H1,503
H1,503
O
He: >1,503
H₁1,503
Ho: 21,503
H: <1,503
Hos 1,503
H> 1,503
M¹ <1,503
M21,503
(b) What is a point estimate in doilers 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.)
x
Find the p-value. (Round your answer four decimal places)
Pvalve-
o
Transcribed Image Text: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 $1,435 with a standard deviation of s= $170. (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. O H1,503 H1,503 O He: >1,503 H₁1,503 Ho: 21,503 H: <1,503 Hos 1,503 H> 1,503 M¹ <1,503 M21,503 (b) What is a point estimate in doilers 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.) x Find the p-value. (Round your answer four decimal places) Pvalve- o
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