SOLUTION: A 15-minute Oil and Lube service claims that their average service time is no more than 15 minutes. A random sample of 40 service times was collected, and the sample mean was found

Question 359879: A 15-minute Oil and Lube service claims that their average service time is no more than 15 minutes. A random sample of 40 service times was collected, and the sample mean was found to be 16.4 minutes, with a sample standard deviation of 3.2 minutes. Is there evidence to support, or to reject the claim at the alpha = 0.01 level? Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A 15-minute Oil and Lube service claims that their average service time is no more than 15 minutes. A random sample of 40 service times was collected, and the sample mean was found to be 16.4 minutes, with a sample standard deviation of 3.2 minutes.
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Is there evidence to support, or to reject the claim at the alpha = 0.01 level? Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results
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Ho: u <= 15
Ha: u > 15
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t(16.4) = (16.4-15)/[3.2/sqrt(40)] = 2.7670
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p-value = P(t> 2.7670 when df = 39) = tcdf(2.7670,100,39) = 0.0043
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Since the p-value is less than 1%, reject Ho.
The test results do not support the claim that u <=15 min.
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Cheers,
Stan H.
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