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- owing-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.

a) Pew reports a margin of error of ± 3.6% for this result.

b) 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.
c) 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?