Question 83903: Please help me with this statistical problem.
A manufacturer claims that the mean lifetime, u , of its light bulbs is 53 months. The standard deviation of these lifetimes is 8 months. Seventy bulbs are selected at random, and their mean lifetime is found to be 54 months. Can we conclude, at the 0.05 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 53 months?
Thanks!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A manufacturer claims that the mean lifetime, u , of its light bulbs is 53 months. The standard deviation of these lifetimes is 8 months. Seventy bulbs are selected at random, and their mean lifetime is found to be 54 months. Can we conclude, at the 0.05 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 53 months?
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Ho: mu = 53
Ha: mu does not equal 53
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Critical values for alpha = 5% = +-1.96
Test Statistic: z(54) = (54-53)/[8/sqrt70] = 1/0.9562=1.0458
p-value is 0.2956..
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Conclusion: Since p is greater than alpha=5%, Fail to Reject Ho.
The mean lifetime is 53 months.
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Cheers,
Stan H.
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