A shop manual gives 6.5 hours as the average time required to perform a 30,000 mile major maintenance service on a Porsche 911. Last month a mechanic performed 11 such services, and his required times were as follows.

 

We want to determine if there is sufficient evidence to conclude that the mechanic can perform this service in less time than specified by the service manual.

a.) If you are to construct a confidence interval estimate for the mean time of services performed by the mechanic for the 30,000 mile major maintenance service on a Porsche 911, what distribution are you going to apply and explain why?

b.) Construct a 98% confidence interval estimate for the population mean time for the entire 30,000-mile-major-maintenance service performed by the mechanic.

c.) Would you think that the mechanic can perform this service in less time than specified by the service manual? Explain.

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