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. Aquestionnaire sent to owners of one of the manufacturers 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 following data
show the actual number of miles driven for 50 vehicles at the time of transmission failure.
85,092 32,609 59,465 77,437 32,534 64,090 32,464 59,902
39,323 89,641 94,219 116,803 92,857 63,436 65,605 85,861
64,342 61,978 67,998 59,817 101,769 95,774 121,352 69,568
74,276 66,998 40,001 72,069 25,066 77,098 69,922 35,662
74,425 67,202 118,444 53,500 79,294 64,544 86,813 116,269
37,831 89,341 73,341 85,288 138,114 53,402 85,586 82,256
1. Use appropriate descriptive statistics to summarize the transmission failure data.
2. 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.
3. Discuss the implication of your statistical findings in terms of the belief that some owners of the automobiles experienced early transmission failures.
4. 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.
5. What other information would you like to gather to evaluate the transmission failure problem more fully?
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