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"Metropolitan Research, Inc., a consumer...
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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 reviewed several complaints about early transmission problems. Nationwide, the populations 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 the sample data support the conclusion that the mean mileage of vehicles produced by this manufacturer is lower than the national average mileage at transmission failure. Be sure to clearly state your hypotheses. Use the p-value approach to conduct the hypothesis test using α = .005. Include the test statistic, p-values, rejection rule, and conclusions in your answer.

5. Assuming 95% confidence, what is the recommended sample size if the desired margin of error is 1,000 miles? Would it be reasonable to obtain this sample size? Why/why not?
Auto.xlsx

Column1
Confidence Level(95.0%)

7076.1364065679

Data

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

mean
median
standard deviation
min
max
standard error of the mean

73340.3
72705
24898.7151084352
25066
138114
3521

Column1
Confidence Level(95.0%)

Column1
Mean
Standard Error
Median
Mode
Standard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count

73340.3
3521.2100592013
72705
#N/A
24898.7151084352
619946014.05102
0.1671262116
0.2601179743
113048
25066
138114
3667015
50

Page 2

7076.136407

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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,...

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