Background: 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 revealed several complaints about early transmission problems. 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 in the Auto.xls file show the actual number of miles driven for a sample of 50 vehicles at the time of transmission failure.
Part 1: Descriptive Statistics and Interval Estimation
A. Using the miles in the bottom of this page use the Descriptive statistics function in Excel to summarize the following statistics for Miles Driven:
n ________________________
Mean ________________________
Standard Deviation ________________________
Standard Error ________________________
Min ________________________
Max ________________________
Q1 ________________________
Q3 ________________________
B. Develop a 95% confidence interval for the mean number of miles driven until transmission failure for the population of automobiles with transmission failure. Provide a managerial interpretation of the interval estimate in the context of the problem.
C. Discuss the implications of your statistical findings in parts A and B in terms of the belief that some owners of the automobiles experienced early transmission failures. Do you believe that there is a problem with early transmission failures based on this sample?
D. What other information would you like to gather to evaluate the transmission failure problem more fully? The only variable in this data set is Miles Driven, recommend three other variables that might provide useful information in evaluating this problem.
Part 2: Sample Size Determination
A. How many repair records should be sampled if the research firm wants the population mean number of miles driven until transmission failure to be estimated with a margin of error of 5000 miles? Use 95% confidence and show all your work, not just the final number. Remember, with sample size determination to always round up to the nearest whole number to oversatisfy the criteria.
Miles 85092 39323 64342 74276 74425 37831 77539 32609 89641 61978 66998 67202 89341 88798 59465 94219 67998 40001 118444 73341 77437 116803 59817 72069 53500 85288 32534 92857 101769 25066 79294 138114 64090 63436 95774 77098 64544 53402 32464 65605 121352 69922 86813 85586 59902 85861 69568 35662 116269 82256