# Mean, Variance, Standard Deviation

There are five (5) parts to completing your managerial report worth ten (10) points each. You will be using Excel’s functions to summarize and compute your sample statistics.  This assignment tests your knowledge on how Ito compute and interpret the sample mean, variance, standard deviation, interval estimate of a population mean and other methods you’ve learned on how to organize and interpret your data.

Metropolitan Research, Inc.

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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, 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 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

77.539 88.798

Managerial Report

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 vour 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?