You wish to construct a 95% confidence interval to compare two proportions.If we wish to obtain a margin of error of at most 0.05,what sample size should we take from each group? Assume equal sample sizes.
A)769
B)1984
C)768
D)385
E)384

Question

Quizplus · Accepted Answer

The formula for the sample size for a two-proportion confidence interval is:n = (Z^2 * p * q) / e^2where:n is the sample sizeZ is the z-score for the desired confidence levelp is the estimated proportion in the first groupq is the estimated proportion in the second groupe is the margin of errorIn this case, we want a 95% confidence level, a margin of error of at most 0.05, and we assume equal sample sizes. The z-score for a 95% confidence level is 1.96. The estimated proportions are both 0.5, since we are assuming equal sample sizes. Plugging these values into the formula, we get:n = (1.96^2 * 0.5 * 0.5) / 0.05^2n = 768Therefore, the correct answer is A) 769.

You Wish to Construct a 95% Confidence Interval to Compare