Question 638003: Assume that a sample is drawn and z(α/2) = 1.96 and σ = 30. Answer the following questions:
(A) If the Maximum Error of Estimate is 0.04 for this sample, what would be the sample size?
(B) Given that the sample Size is 400 with this same z(α/2) and σ, what would be the Maximum Error of Estimate?
(C) What happens to the Maximum Error of Estimate as the sample size gets smaller?
(D) What effect does the answer to C above have to the size of the confidence interval?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Assume that a sample is drawn and z(α/2) = 1.96 and σ = 30. Answer the following questions:
(A) If the Maximum Error of Estimate is 0.04 for this sample, what would be the sample size?
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n = [z*s/E]^2
n = [1.96*30/0.04]^2 = 2,160,900
(B) Given that the sample Size is 400 with this same z(α/2) and σ, what would be the Maximum Error of Estimate?
400 = [1.96*30/E]^2
1.96*30/E = 20
E = 1.96*30/20
E = 2.94
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(C) What happens to the Maximum Error of Estimate as the sample size gets smaller?
n = [z*s/E]^2
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Notice that n and E are inversely related.
So, as n gets smaller, E get larger
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(D) What effect does the answer to C above have to the size of the confidence interval?
The width of the confidence interval is ALWAYS twice as large as the max. error.
So, as the sample size gets smaller, the CI gets wider.
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Cheers,
Stan H.
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