Question
In: Statistics and Probability
The average annual premium for automobile insurance in the United States is $1520. A representative sample...
The average annual premium for automobile insurance in the United States is $1520. 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.
a. 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?
We would be ___?__% confident that auto insurance premiums in Michigan are __?__ the national average.
| Annual Premium |
| 1906 |
| 3139 |
| 2317 |
| 2786 |
| 2558 |
| 2977 |
| 2682 |
| 2540 |
| 2656 |
| 2670 |
| 2319 |
| 2817 |
| 2917 |
| 2540 |
| 2664 |
| 2196 |
| 2549 |
| 2189 |
| 2398 |
| 2471 |
Solutions
Expert Solution
I used Excel to solve this question.
Step.1 First enter data in excel.
Step.2 Go to 'Data' ---> 'Data Analysis' ---> Select 'Descriptive Statistic'
Step.3 New window pop-up on screen. Enter input range and output range. you will get folling output:
| Annual Premium | Annual Premium | |||
| 1906 | ||||
| 3139 | Mean | 2564.55 | ||
| 2317 | Standard Error | 65.90221923 | ||
| 2786 | Median | 2553.5 | ||
| 2558 | Mode | 2540 | ||
| 2977 | Standard Deviation | 294.7236842 | ||
| 2682 | Sample Variance | 86862.05 | ||
| 2540 | Kurtosis | 0.24152367 | ||
| 2656 | Skewness | -0.203487349 | ||
| 2670 | Range | 1233 | ||
| 2319 | Minimum | 1906 | ||
| 2817 | Maximum | 3139 | ||
| 2917 | Sum | 51291 | ||
| 2540 | Count | 20 | ||
| 2664 | Confidence Level(95.0%) | 137.9349298 | ||
| 2196 | ||||
| 2549 | Lower limit = mean - Confidence Level(95.0%) | 2426.61507 | ||
| 2189 | Upper limit = mean + Confidence Level(95.0%) | 2702.48493 | ||
| 2398 | ||||
| 2471 |
a.
The point estimate of the mean annual automobile insurance premium in Michigan is 2565
b.
95% confidence interval is ( 2426.62 , 2702.48 )
c.
The 95% confidence interval for the annual automobile insurance premium in Michigan does not include the national average for the United States.
We would be 95% confident that auto insurance premiums in Michigan are not equal to the national average.
orchestra answered 2 years agoRelated Solutions
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automobile insurance premium, you draw a sample of 25 automobile
insurance policies. This sample has a sample mean annual premium of
$1440 and a sample standard deviation of s=$165.
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annual automobile insurance
premium.
b. Assuming everything else is fixed, what happens to the margin
of error as the sample size increases.
“In attempting to determine the population mean annual automobile insurance premium, you draw a sample of...
“In attempting to determine the population mean annual
automobile insurance premium, you draw a sample of 25 automobile
insurance policies. This sample has a sample mean annual premium of
$1440 and a sample standard deviation of s=$165.
a. Construct a 99% confidence interval for the population mean
annual automobile insurance
premium.
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of error as the sample size increases.
“In attempting to determine the population mean annual automobile insurance premium, you draw a sample of...
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confidence interval for the population mean annual automobile
insurance premium. b. Assuming everything else is fixed, what
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