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.   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   Managerial Report Use appropriate descriptive statistics to summarize the transmission failure data. 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. Discuss the implication of your statistical findings in terms of the belief that some owners of the automobiles experienced early transmission failures. 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. What other information would you like to gather to evaluate the transmission failure problem more fully?

Question

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.

 

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

 

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 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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