SOLUTION: An automobile assembly line operation has a scheduled mean completion time of 14.7 minutes. The standard deviation of completion times is 1.7 minutes. It is claimed that, under ne
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Question 481265: An automobile assembly line operation has a scheduled mean completion time of 14.7 minutes. The standard deviation of completion times is 1.7 minutes. It is claimed that, under new management, the mean completion time has decreased. To test this claim, a random sample of 80 completion times under new management was taken. The sample had a mean of 14.2 minutes. Can we support, at the 0.01 level of significance, the claim that the mean completion time has decreased under new management? Assume that the standard deviation of completion times has not changed. The value of the test statistic (round to at least 3 decicmal places)? The p-value(round to at least 3 decimal places)?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
An automobile assembly line operation has a scheduled mean completion time of 14.7 minutes. The standard deviation of completion times is 1.7 minutes.
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It is claimed that, under new management, the mean completion time has decreased.
Ho: u = 14.7
H1: u < 14.7 (claim)
To test this claim, a random sample of 80 completion times under new management was taken. The sample had a mean of 14.2 minutes.
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Can we support, at the 0.01 level of significance, the claim that the mean completion time has decreased under new management? Assume that the standard deviation of completion times has not changed.
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The value of the test statistic (round to at least 3 decicmal places)?
t(14.2) = (14.2-14.7)/[1.7/sqrt(80)] = -2.6307
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The p-value(round to at least 3 decimal places)?
P-value = P(t< -2.6307 when df = 79) = 0.0051
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Conclusion: Since the p-value is less than 1%,
reject Ho. The test results support the new
management's claim.
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Cheers,
Stan H.
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