10.124 Gap between rich and poor: 32>n margin

a. For comparisons of groups in which n1 = n2, with common value denoted by n, use the fact that the largest possible value of pn 11 - pn 2 occurs at pn = 0.5 to show that the margin of error for a large-sample 95% confidence interval for 1p1 - p22 can be no greater than 220.5>n = 22>n.

b. A 2014 survey by the Pew Research Center reported that the percentage of people who think the gap between the rich and the poor is a very big problem in their country is 46% in the United States, 47% in the U.K., 39% in Germany, 74% in Turkey and 72%

in Argentina. Assuming that each country had a random sample of 1000 people, use the 32>n bound to identify any pairs of countries for which the true percentages might not be different.