Format Inf for Cat Data EOCEs

ch_inference_for_props/TeX/ch_inference_for_props_ex.tex

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 \eoce{\qt{Bullying in schools} A 2012 Survey USA poll asked Florida residents how big of a problem they thought bullying was in local schools. 9 out of 191 18-34 year olds responded that bullying is no problem at all. Using these data, is it appropriate to construct a confidence interval using the formula $\hat{p} \pm z^\star \sqrt{ \hat{p}(1-\hat{p})/n }$ for the true proportion of 18-34 year old Floridians who think bullying is no problem at all? If it is appropriate, construct the confidence interval. If it is not, explain why.
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 \eoce{\qt{Choose a test} We would like to test the following hypotheses:
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 \eoce{\qt{The Egyptian Revolution} A popular uprising that started on January 25, 2011 in Egypt led to the 2011 Egyptian Revolution. Polls show that about 69\% of American adults followed the news about the political crisis and demonstrations in Egypt closely during the first couple weeks following the start of the uprising. Among a random sample of 30 high school students, it was found that only 17 of them followed the news about Egypt closely during this time. \footfullcite{data:egypt}
 
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 \item Below is a histogram showing the distribution of $\hat{p}_{sim}$ in 10,000 simulations under the null hypothesis. Estimate the p-value using the plot and determine the conclusion of the hypothesis test.
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 \eoce{\qt{Assisted Reproduction} Assisted Reproductive Technology (ART) is a collection of techniques that help facilitate pregnancy (e.g. in vitro fertilization). A 2008 report by the Centers for Disease Control and Prevention estimated that ART has been successful in leading to a live birth in 31\% of cases \footfullcite{web:art}. A new fertility clinic claims that their success rate is higher than average. A random sample of 30 of their patients yielded a success rate of 40\%. A consumer watchdog group would like to determine if this provides strong evidence to support the company's claim.
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 \eoce{\qt{Social experiment, Part II} Exercise~\ref{socExp} introduces a ``social experiment" conducted by a TV program that questioned what people do when they see a very obviously bruised woman getting picked on by her boyfriend. On two different occasions at the same restaurant, the same couple was depicted. In one scenario the woman was dressed ``provocatively" and in the other scenario the woman was dressed ``conservatively". The table below shows how many restaurant diners were present under each scenario, and whether or not they intervened.
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 \eoce{\qtq{Is yawning contagious} An experiment conducted by the \textit{MythBusters}, a science entertainment TV program on the Discovery Channel, tested if a person can be subconsciously influenced into yawning if another person near them yawns. 50 people were randomly assigned to two groups: 34 to a group where a person near them yawned (treatment) and 16 to a group where there wasn't a person yawning near them (control). The following table shows the results of this experiment. \footfullcite{data:yawn}
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