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A 99 percent one-sample z-interval for a proportion will be created from the point estimate obtained from each of two random samples selected from the same population: sample R and sample S. Let R represent a random sample of size 1,000, and let S represent a random sample of size 4,000. If the point estimate obtained from R is equal to the point estimate obtained from S, which of the following must be true about the respective margins of error constructed from those samples?
(A) The margin of error for S will be 4 times the margin of error for R.
(B) The margin of error for S will be 2 times the margin of error for R.
(C) The margin of error for S will be equal to the margin of error for R.
(D) The margin of error for R will be 4 times the margin of error for S.
(E) The margin of error for R will be 2 times the margin of error for S.

Respuesta :

Answer:(E) The margin of error for R will be 2 times the margin of error for S.

Explanation: Apply the standard error formula which is [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]. Use .5 for p. Do it for sample S and sample R. The SE for S is 0.007906. The SE for R is 0.015811.  0.015811/0.007906=2. Since R is the smaller sample, it will have a higher margin of error. Thus, it is 2 times that of S. Mr. Crane.

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