Background: Metropolitan Research Inc. a consumer research organization, conduct
ID: 3046844 • Letter: B
Question
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
Data set:
Using the Auto Web file attached to this Lab 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 proble
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?
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 82256Explanation / Answer
Solution:
Part a
Here, we have to find the descriptive statistics for the miles at failure for the given sample data. Required descriptive statistics by using excel are summarized as below:
Miles at failure
Mean
73340.3
Median
72705
Mode
#N/A
Minimum
25066
Maximum
138114
Range
113048
Variance
619946014.0510
Standard Deviation
24898.7151
Coeff. of Variation
33.95%
Skewness
0.2601
Kurtosis
0.1671
Count
50
Standard Error
3521.2101
Minimum
25066
Q1
59902
Q2
72705
Q3
86813
Maximum
138114
Part b
Here, we have to find 95% confidence interval for population mean.
Confidence interval = Xbar -/+ t*S/sqrt(n)
From given data, we have
Xbar = 73340.3
S = 24898.71511
Sample size = n = 50
Confidence level = 95%
Degrees of freedom = n – 1 = 49
Critical t value = 2.0096
(by using t-table)
Confidence interval = 73340.3 -/+ 2.0096*24898.71511/sqrt(50)
Confidence interval = 73340.3 -/+ 2.0096*3521.210059
Confidence interval = 73340.3 -/+ 7076.1364
Lower limit = 73340.3 - 7076.1364 = 66264.16
Upper limit = 73340.3 + 7076.1364 = 80416.44
We are 95% confident that the average miles at failure will between 66264.16 and 80416.44.
Part c
From above parts A and B, it is observed that the average mile at failure is given as 73340.3 with standard deviation of 24898.71511. Also, we are 95% confident that the average miles at failure will between 66264.16 and 80416.44. According to the values of skewness, Q1 and Q3, it is observed that there is a problem of early transmission failures as the data shows positive skewed nature.
Miles at failure
Mean
73340.3
Median
72705
Mode
#N/A
Minimum
25066
Maximum
138114
Range
113048
Variance
619946014.0510
Standard Deviation
24898.7151
Coeff. of Variation
33.95%
Skewness
0.2601
Kurtosis
0.1671
Count
50
Standard Error
3521.2101
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