The Physicians’ Health Study is a very large, randomized study designed to “test the effects of low-dose aspirin… in the prevention of cardiovascular disease (CVD).” The subjects were 22,071 U.S. male physicians (aged 40–84 years, in the year 1982), who were randomly assigned to be in either the low-dose aspirin group or the placebo group. Each participant was required to take the assigned pill every other day for five years. Th e study was double blind. Of the 11,034 physicians who took the placebo, 189 suffered heart attacks during the study. Of the 11,037 physicians who took aspirin, 104 had heart attacks.
a. Is this an experiment or an observational study? Explain how you are deciding.
b. Identify the explanatory and response variables. Also, identify whether each is categorical or quantitative.
c. Explain what it means for a study to be “double blind.” Also, explain the purpose of using “double blinding” in this study.
d. Organize the counts in a well-labeled 2 × 2 table.
e. Find the observed difference in proportion of heart attack cases between the physicians who took aspirin and those who took the placebo.
f. State the appropriate null and alternative hypotheses in words.
g. Use an appropriate applet to use a simulation-based approach to find a p-value to test the hypotheses stated.

h. Evaluate the strength of evidence based on the p-value.

i. Explain why it would be okay to use the theory-based method (that is, normal distribution based method) to find a p-value for this study.
j. Use an appropriate applet to find and report the following from the data:
• The standardized statistic
• The theory-based p-value
k. How do the simulation-based and theory-based p-values compare?