A randomized, placebo-controlled study of a diet drug (Meridia) was done on overweight or obese subjects and reported in the New England Journal of Medicine (James et al. 2010). The patients were all 55 years old or older with a high risk of cardiovascular events. Those who had a heart event had either a heart attack, a stroke, or death from heart-related factors. The table gives the counts.

a. Compare the rates of heart events for the drug group and for the placebo group.
b. Assuming the conditions are met (although we have random assignment and not a random sample), find a 95% confidence interval for the difference in proportions. In particular, does the interval capture 0, and what does that show?
c. Say you collected a new sample 10 times larger. Assuming the proportions came out the same, would the interval change? Would the new interval be narrower or wider?

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Drug Placebo 490 4408 4898 Heart Event 559 4347 4906 No Heart Event