Question 265560
A 99% confidence interval (in inches) for the mean height of a population is 65.44 < &#956; < 66.96.
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This result is based on a sample size of 144.
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If the confidence interval 65.65 < &#956; < 66.75 is obtained from the same sample data, what is the degree of confidence?
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a. You will first need to find the sample mean and sample standard deviation based on the confidence interval given.
The width of the confidence interval is 2E
2E = 66.96-65.44 = 1.52
E = 0.76
But E = z*s/sqrt(144) and z = invNorm(0.995) = 2.5758..
So 0.76 = 2.5758*[s/sqrt(144)]
And s = 3.54 (sample standard deviation)
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Since xbar-E = 65.44
xbar - 0.76 = 65.44
xbar = 66.2 (sample mean)
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b. Use the value you found in part a to determine the degree of confidence for the interval 65.65 < &#956; < 66.75 is based on.
66.2-E = 65.65
E = 0.55
But E = z*s/sqrt(144)
0.55 = z*3.54/sqrt(144)
z = 1.8644
normalcdf(-100,-1.8644) = 0.03
Therefore the degree of confidence is 94%
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Cheers,
Stan H.