2) Provide a point estimate of the mean annual automobile insurance premium in Michigan (SHOW RESULTS but you may use Ext an der b) Develop a 95% confidence interval for the mean annual automobile insurance premium in Michigan (SHOW' WORK but you may use Excel for key calmulations: c) Does the 95% confidence interval for the annual automobile insurance premium in Michigan include the national average for the US What is your interpretation of the relationship between auto insurance premiums in Michigan and the national average?

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Author:Amos Gilat
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The average annual premium for automobile insurance in the U.S. is $1,503. The following annual premiums ($) are representative of the website’s findings for the state of Michigan:

\[
\begin{array}{cccccc}
1,905 & 2,370 & 2,184 & 2,981 \\
2,725 & 2,545 & 2,332 & 2,677 \\
2,677 & 2,529 & 3,112 & 2,857 \\
2,600 & 2,442 & 2,545 & 2,367 \\
2,962 & 2,312 & 2,525 & 2,115 \\
\end{array}
\]

Assume the population is approximately normal.

a) Provide a point estimate of the mean annual automobile insurance premium in Michigan (SHOW RESULTS, but you may use Excel).

b) Develop a 95% confidence interval for the mean annual automobile insurance premium in Michigan (SHOW WORK, but you may use Excel for calculations).

c) Does the 95% confidence interval for the annual automobile insurance premium in Michigan include the national average for the U.S.? What is your interpretation of the relationship between auto insurance premiums in Michigan and the national average?
Transcribed Image Text:The average annual premium for automobile insurance in the U.S. is $1,503. The following annual premiums ($) are representative of the website’s findings for the state of Michigan: \[ \begin{array}{cccccc} 1,905 & 2,370 & 2,184 & 2,981 \\ 2,725 & 2,545 & 2,332 & 2,677 \\ 2,677 & 2,529 & 3,112 & 2,857 \\ 2,600 & 2,442 & 2,545 & 2,367 \\ 2,962 & 2,312 & 2,525 & 2,115 \\ \end{array} \] Assume the population is approximately normal. a) Provide a point estimate of the mean annual automobile insurance premium in Michigan (SHOW RESULTS, but you may use Excel). b) Develop a 95% confidence interval for the mean annual automobile insurance premium in Michigan (SHOW WORK, but you may use Excel for calculations). c) Does the 95% confidence interval for the annual automobile insurance premium in Michigan include the national average for the U.S.? What is your interpretation of the relationship between auto insurance premiums in Michigan and the national average?
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