SOLUTION: A 20-minute Oil and Lube service claims that their average service time is no more than 20 minutes. A random sample of 40 service times was collected, and the sample mean was found

Question 386229: A 20-minute Oil and Lube service claims that their average service time is no more than 20 minutes. A random sample of 40 service times was collected, and the sample mean was found to be 21.3 minutes, with a sample standard deviation of 5.5 minutes. Is there evidence to reject the claim at the alpha = 0.05 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 20-minute Oil and Lube service claims that their average service time is no more than 20 minutes.
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A random sample of 40 service times was collected, and the sample mean was found to be 21.3 minutes, with a sample standard deviation of 5.5 minutes.
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Is there evidence to reject the claim at the alpha = 0.05 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 <= 20 min (claim)
Ha: u > 20 min
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test statistic:
t(21.3) = (21.3-20)/[5.5/sqrt(40)] = 1.4949
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p-value = P(t > 1.4949 when df=39) = 0.0715
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Since the p-value is greater than 5%, fail to reject Ho.
Conclusion: The test results support the claim.
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Cheers,
Stan H.

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