Fake news In a survey of 1002 U.S. adults in December 2016 by Pew Research (www.journalism.org/2016/12/15/many-americans-believe-fake-news-is-sowing-confusion/), 64% of adult respondents say they think that made-up “news” is causing a great deal of confusion about the basic facts of current issues and events.

1. Pew reports a margin of error of ±3.6% for this result. Explain what the margin of error means.

2. Pew reports that 39% of respondents are “very confident” that they can recognize fake news. Find a confidence interval for the true proportion who are very confident.

3. Pew reports that only 6% of respondents are not at all confident in their ability to detect fake news. Would a confidence interval for the proportion not confident be wider or narrower than the confidence interval for those who are very confident that you found in part b?