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LiRa [457]
3 years ago
15

The average annual premium for automobile insurance in the United States is $1411. A representative sample of annual premiums fo

r 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
Mathematics
1 answer:
Harrizon [31]3 years ago
7 0

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.

--------------

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

--------------

Item b:

  • In the spreadsheet, it is possible to find the <em>standard deviation for the sample</em>, 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.

--------------

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

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