The following 2x2 table reports data from a cross-sectional study on height and whether or not a student had ever been bullied. The goal is to compare the prevalence of being bullied based on height.

Height Ever bullied

Yes No

Short 42 50

Not short 30 87

a) Write down the null and alternative hypothesis. Carry out a hypothesis test and report your results and conclusion at significance level =0.05 using RStudio.

b) Calculate a point estimate and 95% confidence interval for the relative risk of having been bullied comparing short to not short students. Write one sentence that interprets the point estimate and confidence interval.

c) Calculate a point estimate and 95% confidence interval for the odds ratio that compares the odds of having been bullied for short students to the odds for students who are not short.

d) Now suppose that instead of a cross-sectional study we have just completed a prospective study in which a cohort of students were monitored for 2 years. We ascertain the bullying status (yes or no) of each cohort member at the beginning of the study and then again 2 years later. What statistical procedure would you use to test whether the current bullying prevalence for students who are not short is different from what it was 2 years ago?