Question 701182: Assume that a sample is drawn and z(α/2) = 1.96 and σ = 25. Answer the following questions:
(A) If the Maximum Error of Estimate is 0.02 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?
please someone help me
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^2 = 25. Answer the following questions:
(A) If the Maximum Error of Estimate is 0.02 for this sample, what would be the sample size?
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ME = z*s/sqrt(n)
So, n = [z*s/E]^2
Your Problem:
n = [1.96*5/0.02'^2 = 240,100
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(B) Given that the sample Size is 400 with this same z(α/2) and σ, what would be the Maximum Error of Estimate?
ME = 1.96*5/20 = 0.49
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(C) What happens to the Maximum Error of Estimate as the sample size gets smaller?
ME and n are indirectly related.
As the sample size gets smaller ME gets larger.
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(D) What effect does the answer to C above have to the size of the confidence interval?
Since the confidence level always has width 2*ME,
the CI gets larger as the sample size gets smaller.
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Cheers,
Stan H.
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