Question 492311: A confidence interval estimate for the population mean is given to be (45.37, 53.91). If the standard deviation is 12.604 and the sample size is 58, answer each of the following (show all work):
(A) Determine the maximum error of the estimate, E.
(B) Determine the confidence level used for the given confidence interval.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A confidence interval estimate for the population mean is given to be (45.37, 53.91). If the standard deviation is 12.604 and the sample size is 58, answer each of the following (show all work):
(A) Determine the maximum error of the estimate, E.
The width of the confidence interval is ALWAYS 2E
2E = (53.9-45.37)
2E = 8.53
E = 4.265
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(B) Determine the confidence level used for the given confidence interval.
ME = z*s/sqrt(n)
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4.265 = z*12.604/sqrt(58)
12.604*z = 4.265*sqrt(58)
z = 2.5771
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Find the right tail for z = 2.5771
normalcdf(2.5771,100) = 0.005
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The confidence level = 2*0.005 = 1%
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Cheers,
Stan H.
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