A For comparisons of groups in which n1 n2
a. For comparisons of groups in which n1 = n2, with common value denoted by n , use the fact that the largest possible value of p̂(1 - p̂) occurs at p̂ = 0.5 to show that the margin of error for a large-sample 95% confidence interval for (p1 - p2) can be no greater than 22√0.5/n = √22/n.
b. A 2003 report by the Pew Research Center reported that the percent of people who find religion very important in their life is 59% in the United States, 30% in Canada, 33% in Great Britain, 27% in Italy, 21% in Germany, and 11% in France. Assuming that each country had a random sample of 1000 people, use the 22/√n bound to identify any pairs of countries for which the true percentages might not be different.
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