Question - Planning a study to compare two means. Refer to Exercise, where we compared trustworthiness ratings for ads from two different publications. Suppose that you are planning a similar study using two different publications that are not expected to show the differences seen when comparing the Wall Street Journal with the National Enquirer. If we assume the same standard deviation and sample size for these two publications, the margin of error can be expressed as t*s√(2/n) with the degrees of freedom of t* = n - 1. Suppose that you want the margin of error for 95% confidence to be no more than 0.50 points. What sample size is required?

Exercise - Sample size and margin of error. In Section, we studied the effect of the sample size on the margin of error of the confidence interval for a single proportion. In this exercise we perform some calculations to observe this effect for the two-sample problem. Suppose that p^{^}₁ = 0.7 and p^{^}₂ = 0.6, and n represents the common value of n₁ and n₂. Compute the 95% margins of error for the difference in the two proportions for n = 40, 50, 80, 100, 400, 500, and 1000. Present the results in a table and with a graph. Write a short summary of your findings.