Question 575430: Assume that a sample is drawn and z(α/2) = 1.65 and σ = 35. Answer the following questions:
(A) If the Maximum Error of Estimate is 0.05 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 larger?
(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) = 1.65 and σ = 35. Answer the following questions:
(A) If the Maximum Error of Estimate is 0.05 for this sample, what would be the sample size?
n = [z*s/ME]^2
n = [1.65*35/0.05]^2 = 1155^2 = 1,334,025
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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?
400 = [1.65*35/ME]^2
[1.65*35/ME = 20
ME = 1.65*35/20
ME = 2.89
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(C) What happens to the Maximum Error of Estimate as the sample size gets larger?
ME and n are inversely related.
As sample size increases the Maximum Error decreases.
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(D) What effect does the answer to C above have to the size of the confidence interval?
The confidence interval is ALWAYS 2 times ME.
If n increases ME decreases and the CI becomes smaller.
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Cheers,
Stan H.
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