Question: Refer to the article discussed in Exercise. The article continued by reporting that of those who do believe the world will come to an end, 33% believe it will happen within either a few years or a few decades. Respondents were only asked that question if they answered yes to the question about the world coming to an end, so about 590 respondents would have been asked the question.

a. Consider only those adult Americans who believe the world will come to an end. For that population, compute a 95% confidence interval for the proportion who believe it will come to an end within the next few years or few decades.

b. Explain why you could not use the margin of error of 3% reported in the article to compute the confidence interval in part a.

Exercise: U.S. News and World Report (19 December 1994, pp. 62-71) reported on a survey of 1000 American adults, conducted by telephone on December 2-4, 1994, designed to measure beliefs about apocalyptic predictions. They reported that the margin of error was "3 percentage points."

a. Verify that the margin of error for a sample of size 1000 is as reported.

b. One of the results reported was that 59% of Americans believe the world will come to an end. Construct a 95% confidence interval for the true percentage of Americans with that belief, using the margin of error given in the article. Interpret the interval in a way that could be understood by a statistically naive reader.