Question 265560: Can someone please help me understand this question?
A 99% confidence interval (in inches) for the mean height of a population is 65.44 < μ < 66.96. This result is based on a sample size of 144. If the confidence interval 65.65 < μ < 66.75 is obtained from the same sample data, what is the degree of confidence?
a. You will first need to find the sample mean and sample standard deviation based on the confidence interval given.
b. Use the value you found in part a to determine the degree of confidence for the interval 65.65 < μ < 66.75 is based on.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A 99% confidence interval (in inches) for the mean height of a population is 65.44 < μ < 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 < μ < 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
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 < μ < 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.
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