Question 630763: An automobile assembly line operation has a scheduled mean completion time,u, of 13.7 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 19 completion times under new management was taken. The sample had a mean of 13.4 minutes. Assume that the population is normally distributed. Can we support, at the 0.05 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.
Perform a one-tailed test.
Null hypothesis: ?
Alternative hypothesis: ?
Type of test statistic: ?
The value of the test statistic: ?
The p-value: ?
Can we support the claim that the mean completion time has decreased under new management?
Found 2 solutions by reviewermath, stanbon:
Answer by reviewermath(1029)   (Show Source):
You can put this solution on YOUR website! Null hypothesis: µ = 13.7
Alternative hypothesis: µ < 13.7 (Claim)
z Test
Test Statistic, z: -0.7692
Critical z: -1.6449
P-Value: 0.2209
Fail to Reject the Null Hypothesis
Sample does not provide enough evidence to support the claim that the mean completion time has decreased under new management
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,u, of 13.7 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 19 completion times under new management was taken. The sample had a mean of 13.4 minutes. Assume that the population is normally distributed. Can we support, at the 0.05 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.
Perform a one-tailed test.
Null hypothesis: u >= 13.7
Alternative hypothesis: u < 13.7 (claim)
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Type of test statistic: t-distribution
The value of the test statistic: t = -0.7692
The p-value: 0.2259
Can we support the claim that the mean completion time has decreased under new management?
Fail to reject Ho.
The test results do not support the claim.
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Cheers,
Stan H.
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