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?

Let X denote the annual premium for automobile insurance (in $)The national average of X for the US is μ=$1,503The sample data on X for the state of Michigan is given asx=1905,2370,2184,2981,2725,2545,2332,2627,2677,2529,3112,2857,2600,2442,2545,2675,,2962,2312,2525,2115The number of observations in x is, n=20 To find:a) The point estimate of the mean of x.b) The 95% confidence interval for the population mean.c) Deciding whether the confidence interval contains μ or nota) To find the point estimate of the mean annual automobile insurance premium in Michigan, it is required to compute the sample mean of the given data.The formula to compute the sample mean (x¯) is given asThe point estimate of the mean annual premium for the state of Michigan is $2,551b)The defined confidence level is (1−α)=0.95Hence the level of significance is α=0.05The formula to compute the 95% confidence interval for the mean is given byConsider the following calculations for computing s x(xi−x¯)2190541731623703276121841346892981184900272530276254536233247961262757762677158762529484311231472128579363626002401244211881254536267515376296216892123125712125256762115190096∑(xi−x¯)2=1724940Hence the sample standard deviation isAlso, the t-score can be computed using the EXCEL function =T.INV.2T(α,df)Here, α=0.05df= the number of degrees of freedom =n−1=19The EXCEL output for the t-score is as followsHence the confidence interval isThe 95% confidence interval for the mean annual premium for the state of Michigan is ( $2409.983669,$2692.016331 ).c) Interpretation:The above confidence interval suggests that there can be 95% confidence that the true mean annual premium for automobile insurance in the state of Michigan falls between $2,409.98 and $2,692.02.The national average for the US is $1,503.Conclusion:Since $1503 is not within the range of the confidence interval, based on the given data, it can be concluded that the 95% confidence interval for the mean annual automobile insurance premium in Michigan does not include the national average for the US.a) The point estimate of the mean annual premium for the state of Michigan is $2,551.b) The 95% confidence interval for the mean annual premium for the state of Michigan is ( $2409.983669,$2692.016331 )c)Interpretation:The above confidence interval suggests that there can be 95% confidence that the true mean annual premium for automobile insurance in the state of Michigan falls between $2,409.98 and $2,692.02.The national average for the US is $1,503.Conclusion:Since $1503 is not within the range of the confidence interval, based on the given data, it can be concluded that the 95% confidence interval for the mean annual automobile insurance premium in Michigan does not include the national average for the US.