9.53 Time-Yankelovich surveys, regularly seen in the news magazine Time, report on telephone surveys of approximately 1,000 respondents. In December 1983, 60% of the respondents said that they worry about nuclear war. In a similar survey in June 1983, only 50% said that they worry about nuclear war. (See Time, January 2, 1984, p. 51.) The article reporting these figures says that when they are compared “the potential sampling error is plus or minus 4.5%.”

a Explain how the 4.5% is obtained and what it means.

b Estimate the true difference in these proportions in a 95% confidence interval.