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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“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...
“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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automobile insurance premium, you draw a sample of 25 automobile
insurance policies. This sample has a sample mean annual premium of
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confidence interval for the population mean annual automobile
insurance premium. b. Assuming everything else is fixed, what
happens to the margin of error as the sample size increases.
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