Question: Have efforts to promote equality for women gone far enough in the United States? A poll on this issue by the cable network MSNBC contacted 1019 adults. A newspaper article about the poll said, “Results have a margin of sampling error of plus or minus 3 percentage points.”

(a) Overall, 54% of the sample (550 of 1019 people) answered “Yes” Find a 95% confidence interval for the proportion in the adult population who would say “Yes” if asked. Is the report’s claim about the margin of error roughly right? (Assume that the sample is an SRS.)

(b) The news article said the 65% of men, but only 43% of women think that efforts to promote equality have gone far enough. Explain why we do not have enough information to give confidence intervals for men and women separately.

(c) Would a 95% confidence interval for women alone have a margin of error less that 0.03, about equal to 0.03, or greater than 0.03? Why? You see that the news article’s statement about the margin of error for poll results is a bit misleading.