Question 449396: A manufacturer claims that the mean lifetime, M, of its light bulbs is 52 month. The standard deviation of these lifetimes is 5 months. Eighty bulbs are selected at random, and their mean lifetime is found to be 51 months. Can we conclude, at the 0.05 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 52 months?
Perform a two-tailed test.
I am having a lot of trouble with this. Can someone hep me?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A manufacturer claims that the mean lifetime, M, of its light bulbs is 52 months. The standard deviation of these lifetimes is 5 months.
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Eighty bulbs are selected at random, and their mean lifetime is found to be 51 months.
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Can we conclude, at the 0.05 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 52 months?
Perform a two-tailed test.
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Ho: u = 52 months
Ha: u is not 52 months (claim)
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x-bar = 51 months
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t(51) = (51-52)/[5/sqrt(80)] = -1.7889
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p-value = 2*P(t < -1.7889 when df = 79) = 2*tcdf(-100,-1.7889,79) = 0.0775
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Since the p-value is greater than 5%, fail to reject Ho.
The test results do not support the claim.
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Cheers,
Stan H.
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