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Date Submitted: 11/27/2012 08:01 PM
QMS 3311 –Summer 2012
Case Study 2
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 fullsized
cars reviewed several complaints about early transmission problems. Nationwide, the
population 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...