Choosing sample sizes. For a single proportion the margin of error of a confidence interval is largest for any given sample size n and confidence level C when ˆp = 0.5. This led us to use p∗ = 0.5 for planning purposes. A similar result is true for the two-sample problem. The margin of error of the confidence interval for the difference between two proportions is largest when ˆp1 = ˆp2 = 0.5. Use these conservative values in the following calculations, and assume that the sample sizes n1 and n2 have the common value n. Calculate the margins of error of the 95% confidence intervals for the difference in two proportions for the following choices of n: 10, 25, 50, 100, 150, 200, 400, and 500. Present the results in a table and with a graph.

Summarize your conclusions.