SOLUTION: The lifetime of a certain brand of battery is known to have a standard deviation of 10.5 hours. Suppose that a random sample of 120 such batteries has a mean lifetime of 40.9 hours

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Question 193657: The lifetime of a certain brand of battery is known to have a standard deviation of 10.5 hours. Suppose that a random sample of 120 such batteries has a mean lifetime of 40.9 hours. Based on this sample, find the 95% confidence interval for the true mean lifetime of all batteries of this brand.

Answer by stanbon(75887) (Show Source):
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The lifetime of a certain brand of battery is known to have a standard deviation of 10.5 hours. Suppose that a random sample of 120 such batteries has a mean lifetime of 40.9 hours. Based on this sample, find the 95% confidence interval for the true mean lifetime of all batteries of this brand.
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x-bar = 40.9 hours ; s = 10.5
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E = 1.96*10.5/sqrt(120) = 1.8787
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95% C.I: 40.9 - 1.8787 < u < 40.9 + 1.8787
95% C.I.: 39.02 < u < 42.78
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Comment: Some texts require you to use a t-distribution
when calculating "mean" C.I.'s and working Hypothesis tests.
If you use "t" to get your E value you get:
95% C.I.: 39.002 < p < 42.798
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Cheers,
Stan H.