Question

The average annual premium for automobile insurance in the United States is $1411. A representative sample of annual premiums for the state of Michigan is contained in the Excel Online file below. Assume the population is approximately normal. Construct a spreadsheet to answer the following questions.Open spreadsheeta. Provide a point estimate of the mean annual automobile insurance premium in Michigan.$ (to the nearest dollar)b. Develop a 95% confidence interval for the mean annual automobile insurance premium in Michigan.($ , $ ) (to the nearest cent)c. Does the 95% confidence interval for the annual automobile insurance premium in Michigan include the national average for the United States

Answer 1

Using confidence interval concepts, it is found that:

a) The point estimate is the sample mean.

b) The confidence interval is: $\overline{x} \pm T\frac{s}{n}$

c) If $1411 is between the bounds of the interval yes, otherwise no.

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• At item a, it asks to provide a point estimate for the population mean, which is the sample mean $\overline{x}$

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Item b:

• In the spreadsheet, it is possible to find the standard deviation for the sample, thus, the t-distribution is used.
• The confidence interval will be given by:

$\overline{x} \pm T\frac{s}{n}$

In which:

• $\overline{x}$ is the sample mean.
• T is the critical value, from the t-distribution, with a two-tailed area of $\frac{1 - 0.95}{2} = 0.025$ and n-1 degrees of freedom.
• s is the standard deviation for the sample.
• n is the sample size.

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Item c:

We have to check if 1411 is between $\overline{x} - T\frac{s}{n}$ and $\overline{x} +T\frac{s}{n}$.

• If it is, the interval includes the National Average, otherwise, it does not.

A similar problem is given at brainly.com/question/24232455