Assignment $3$

DATA $\frac{?}{\text{b}\text{a}\text{r}}($ file $)$

Autolnsurance

$20.$ The average annual premium for automobile insurance in the United States is $$1503($

Insure.com website, March $6,2014).$ The following annual premiums $($$$)$ are representative of the website's findings for the state of Michigan.

$\backslash$table$[[1905,3112,2312],[2725,2545,2981],[2677,2525,2627],[2600,2370,2857],[2962,2545,2675],[2184,2529,2115],[2332,2442,]]$

Assume the population is approximately normal.

a$.$ Provide a point estimate of the mean annual automobile insurance premium in Michigan.

b$.$ Develop a $95\%$ confidence interval for the mean annual automobile insurance premium in Michigan.

c$.$ Does the $95\%$ confidence interval for the annual automobile insurance premium in Michigan include the national average for the United States? What is your interpretation of the relationship between auto insurance premiums in Michigan and the national average?