Qms 3311- Case Study 2

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...