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Origins In a 1993 Gallup poll, \(47 \%\) of the respondents agreed with the statement "God created human beings pretty much in their present form at one time within the last 10,000 years or so." When Gallup asked the same question in \(2008,\) only \(44 \%\) of those respondents agreed. Is it reasonable to conclude that there was a change in public opinion given that the P-value is 0.17? Explain.

Revealing information 886 randomly sampled teens were asked which of several personal items of information they thought it okay to share with someone they had just met. \(44 \%\) said it was okay to share their e-mail addresses, but only \(29 \%\) said they would give out their cell phone numbers. A researcher claims that a twoproportion \(z\) -test could tell whether there was a real difference among all teens. Explain why that test would not be appropriate for these data.

Gender gap A presidential candidate fears he has a problem with women voters. His campaign staff plans to run a poll to assess the situation. They'Il randomly sample 300 men and 300 women, asking if they have a favorable impression of the candidate. Obviously, the staff can't know this, but suppose the candidate has a positive image with \(59 \%\) of males but with only \(53 \%\) of females. a) What sampling design is his staff planning to use? b) What difference would you expect the poll to show? c) Of course, sampling error means the poll won't reflect the difference perfectly. What's the standard deviation for the difference in the proportions? d) Sketch a sampling model for the size difference in proportions of men and women with favorable impressions of this candidate that might appear in a poll like this. e) Could the campaign be misled by the poll, concluding that there really is no gender gap? Explain.

Buy it again? A consumer magazine plans to poll car owners to see if they are happy enough with their vehicles that they would purchase the same model again. They'll randomly select 450 owners of American-made cars and 450 owners of Japanese models. Obviously, the actual opinions of the entire population couldn't be known, but suppose \(76 \%\) of owners of American cars and \(78 \%\) of owners of Japanese cars would purchase another. a) What sampling design is the magazine planning to use? b) What difference would you expect their poll to show? c) Of course, sampling error means the poll won't reflect the difference perfectly. What's the standard deviation for the difference in the proportions? d) Sketch a sampling model for the difference in proportions that might appear in a poll like this. e) Could the magazine be misled by the poll, concluding that owners of American cars are much happier with their vehicles than owners of Japanese cars? Explain.

Shopping A survey of 430 randomly chosen adults found that \(21 \%\) of the 222 men and \(18 \%\) of the 208 women had purchased books online. a) Is there evidence that men are more likely than women to make online purchases of books? Test an appropriate hypothesis and state your conclusion in context. b) If your conclusion in fact proves to be wrong, did you make a Type I or Type II error? c) Estimate this difference with a confidence interval. d) Interpret your interval in context.

Gender gap Candidates for political office realize that different levels of support among men and women may be a crucial factor in determining the outcome of an election. One candidate finds that \(52 \%\) of 473 men polled say they will vote for him, but only \(45 \%\) of the 522 women in the poll express support. a) Write a \(95 \%\) confidence interval for the percent of male voters who may vote for this candidate. Interpret your interval. b) Write and interpret a \(95 \%\) confidence interval for the percent of female voters who may vote for him. c) Do the intervals for males and females overlap? What do you think this means about the gender gap? d) Find a \(95 \%\) confidence interval for the difference in the proportions of males and females who will vote for this candidate. Interpret your interval. e) Does this interval contain zero? What does that mean? f) Why do the results in parts c and e seem contradictory? If we want to see if there is a gender gap among voters with respect to this candidate, which is the correct approach? Why?

\- Online activity checks Are more parents checking up on their teen's online activities? A Pew survey in 2004 found that \(33 \%\) of 868 randomly sampled teens said that their parents checked to see what Web sites they visited. In 2006 the same question posed to 811 teens found \(41 \%\) reporting such checks. Do these results provide evidence that more parents are checking?