Certain businesses and professions have reputations for being somewhat dishonest when dealing with customers. One area of concern is the honesty of auto repair shops. Many provinces require emissions checks; a vehicle that doesn’t pass the check must be repaired. In one province, the Department of Transport (DT) has been receiving numerous complaints about a particular auto repair chain. The province decided to check the shops to determine whether they were unlawfully issuing “no pass” reports in order to charge customers unnecessary repair fees. The province procured eight vehicles. Each was first tested on department emissions equipment, and then the eight vehicles were randomly sent to auto repair shops for testing on emissions. As part of the check for accuracy, the hydrocarbon (HC) emissions in parts per million (ppm) were compared:

a) Is there a difference between the measured HC levels taken from the auto shop and the DT measurements? Find a suitable confidence interval.

b) Do you think the DT has evidence that the auto shop readings differ from the department readings? Perform the appropriate test.

c) If you found the test results to be significant, can the DT automatically assume the auto shop is cheating its customers? What other possible explanations could cause the differences in readings?

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Vehicle 3 4 6 7 8 DT HC Level Auto Shop HC Level 3 5 8 42 10 30 20 | 11 7 10 15