During the Physician's Health Study,n1= 11037 physicians were randomly assigned to take 325 mg of aspirin every other day;y1= 104 of them had heart attacks during the study. Anothern2= 11034 physicians were randomly assigned to take a placebo;y2= 189 of them had heart attacks. These data are shown in the table below.

Treatment

Heart attack Aspirin Placebo

Yes 104 189

No 10933 10845

Total 11037 11034

Letp1= Pr{heart attack|aspirin}, the probability of having heart attacks among those who take aspirin; and letp2= Pr{heart attack|placebo}, the probability of having heart attacks among those who take placebo.

1. Based on the data, computep1andp2, the sample proportions for each of the two groups. What is the difference in proportions?
2. Suppose that it is of interest to test whether having heart attack is statistically independent of taking aspirin. Establish the null and alternative hypotheses.
3. Complete the table below by computing theexpected cell countsassumingH0is true. Round your answers to two decimal places. (Hint: Take a look at Slides 14 and 15 from Lecture 19 notes.)

Treatment

heart attack aspirin placebo total

yes 293

no 21778

total 11037 11034 22071

4. Use the following R code to perform a2independence test.health = matrix(c(104,10933,189,10845),nrow=2,ncol=2)

 chisq.test(health) 293 21778 22071 

What is the P-value? What do you conclude at= 0.01 significance level?

1. Find a point estimate for the relative riskp1/p2then interpret.
2. Find a point estimate for the odds ratio
3. =p1/(1p1)p2/(1p2)

then interpret.