Question 633821: 1. A study was conducted to estimate the mean amount spent on birthday gifts for a typical family having two children. A sample of 180 was taken, and the mean amount spent was $219.76. Assuming a standard deviation equal to $41.77, find the 99% confidence interval for m, the mean for all such families (show all work).
2. Assume that a sample is drawn and z(α/2) = 1.65 and σ = 15. 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! 1. A study was conducted to estimate the mean amount spent on birthday gifts for a typical family having two children. A sample of 180 was taken, and the mean amount spent was $219.76. Assuming a standard deviation equal to $41.77, find the 99% confidence interval for m, the mean for all such families (show all work).
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x-bar = 219.76
E = 1.645*(41.77/sqrt(180)) = 5.1215
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90% CI: 219.76-5.12 < x < 219.76+5.12
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2. Assume that a sample is drawn and z(α/2) = 1.65 and σ = 15. Answer the following questions:
(A)If the Maximum Error of Estimate is 0.05 for this sample, what would be the sample size?
E = z*s/sqrt(n)
0.05 = 1.65*15/sqrt(n)
sqrt(n) = 1.65*15/0.05
sqrt(n) = 495
n = 22.25 = 22 when rounded down
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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?
Substitute for "n" and "z" and sigma.
Then solve for "E".
E = 1.2375
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(C) What happens to the Maximum Error of Estimate as the sample size gets larger?
E and sqrt(n) are indirectly related.
AS n get larger, E get smaller.
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(D) What effect does the answer to C above have to the size of the confidence interval?
The size of the CI is ALWAYS 2*E.
If n get larger, E get smaller, and the CI gets smaller (narrower).
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Cheers,
Stan H.
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