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Column1 Confidence Level(95.0%) 7076.1364065679 Data Miles 85092 39323 64342 74276 74425 37831 77539 32609 89641 61978 66998 67202 89341 88798 59465...

"Metropolitan Research, Inc., a consumer research organization, conducts surveys designed to evaluate a wide variety of products and services available to consumers. In one particular study, Metropolitan looked at consumer satisfaction with the performance of automobiles produced by a major Detroit manufacturer. A questionnaire sent to owners of one of the manufacturer’s full-sized cars reviewed several complaints about early transmission problems. Nationwide, the populations mean mileage, µ, is 80,000 miles, with a population standard deviation, σ, of 18,000 miles.

To learn more about the transmission failures, Metropolitan used a sample of actual transmission repairs provided by a transmission repair firm in the Detroit area. The data are shown in the CD file named “Auto” (Chapter 8 datasets). Use this data set to address the following questions.

1. Using the data provided above, what is the standard error of the mean? Calculate the probability that a simple random sample of 50 vehicles that will provide an estimate of the population mean mileage at transmission failure within +/- 4,000 miles of the population mean, µ. Clearly state your conclusions based on this information.

2. Use sample data contained in the dataset to develop point estimates of the population mean and the population standard deviation for mileage at transmission failure. Do these sample statistics contain any sampling error? If so, how large are the errors? Is there any way the research firm can limit the amount of sampling error when selecting a sample of vehicles?

3. At 95% confidence, what is the margin of error? What is the 95% confidence interval estimate of the population mean? Clearly state your conclusions based on this information. What would happen to the confidence interval if you increased the sample size to 200? Why? What are the new margin of error and confidence interval?

4. Use hypothesis testing to determine whether the sample data support the conclusion that the mean mileage of vehicles produced by this manufacturer is lower than the national average mileage at transmission failure. Be sure to clearly state your hypotheses. Use the p-value approach to conduct the hypothesis test using α = .005. Include the test statistic, p-values, rejection rule, and conclusions in your answer.

5. Assuming 95% confidence, what is the recommended sample size if the desired margin of error is 1,000 miles? Would it be reasonable to obtain this sample size? Why/why not?
Column1 Confidence Level(95.0%) 7076.1364065679
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Data Page 2 Miles 85092 39323 64342 74276 74425 37831 77539 32609 89641 mean 73340.3 61978 median 72705 66998 standard deviation 24898.7151084352 67202 min 25066 89341 max 138114 88798 standard error of the mean 3521 59465 Column1 94219 67998 Confidence Level(95.0%) 7076.136407 40001 118444 73341 Column1 77437 116803 Mean 73340.3 59817 Standard Error 3521.2100592013 72069 Median 72705 53500 Mode #N/A 85288 Standard Deviation 24898.7151084352 32534 Sample Variance 619946014.05102 92857 Kurtosis 0.1671262116 101769 Skewness 0.2601179743 25066 Range 113048 79294 Minimum 25066 138114 Maximum 138114 64090 Sum 3667015 63436 Count 50 95774 77098 64544 53402 32464 65605 121352 69922 86813 85586 59902 85861 69568 35662 116269 82256
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Metropolitan Research, Inc., a consumer research organization, conducts surveys designed to
evaluate a wide variety of products and services available to consumers. In one particular study,...

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