The data presented in section 16.1 investigating the association between smoking and aortic stenosis are saved on your disk under the data set stenosis. Smoking status is saved under the variable name smoke and the presence of aortic stenosis under the name disease and gender under the name sex. Show equations/work and use R statistical software.

smoke disease sex yes yes male yes yes male yes yes male yes yes male yes yes male yes yes male yes yes male yes yes male yes yes male yes yes male yes yes male yes yes male yes yes male yes yes male yes yes male yes yes male yes yes male yes yes male yes yes male yes yes male yes yes male yes yes male yes yes male yes yes male yes yes male yes yes male yes yes male yes yes male yes yes male yes yes male yes yes male yes yes male yes yes male yes yes male yes yes male yes yes male yes yes male no yes male no yes male no yes male no yes male no yes male no yes male no yes male no yes male no yes male no yes male no yes male no yes male no yes male no yes male no yes male no yes male no yes male no yes male no yes male no yes male no yes male no yes male no yes male no yes male no yes male yes no male yes no male yes no male yes no male yes no male yes no male yes no male yes no male yes no male yes no male yes no male yes no male yes no male yes no male yes no male yes no male yes no male yes no male yes no male yes no male yes no male yes no male yes no male yes no male no no male no no male no no male no no male no no male no no male no no male no no male no no male no no male no no male no no male no no male no no male no no male no no male no no male no no male no no male no no male yes yes female yes yes female yes yes female yes yes female yes yes female yes yes female yes yes female yes yes female yes yes female yes yes female yes yes female yes yes female yes yes female yes yes female no yes female no yes female no yes female no yes female no yes female no yes female no yes female no yes female no yes female no yes female no yes female no yes female no yes female no yes female no yes female no yes female no yes female no yes female no yes female no yes female no yes female no yes female no yes female no yes female no yes female no yes female no yes female no yes female no yes female yes no female yes no female yes no female yes no female yes no female yes no female yes no female yes no female yes no female yes no female yes no female yes no female yes no female yes no female yes no female yes no female yes no female yes no female yes no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female no no female 

a. Construct a 2 x 2 table of smoking status vs aortic stenosis for males only. Estimate the odds of developing disease for smokers relative to nonsmokers.

b. Construct the same 2 x 2 table for females. Again, estimate the odds ratio.

c. Within each gender group, are the odds of being diagnosed with aortic stenosis higher for smokers or nonsmokers?

d. Conduct a test of homogeneity to determine whether it is appropriate to combine the information for males and females using the Mantel-Haenszel method.

e. Compute a point estimate for the summary odds ratio.

f. At the 0.05 level of significance, test the null hypothesis that there is no association between smoking status and aortic stenosis. What do you conclude?