Another outcome of interest in the Physicians’ Health Study was whether the subjects developed ulcers or not. Of the 11,034 physicians who took the placebo, 138 developed ulcers during the study. Of the 11,037 physicians who took aspirin, 169 developed ulcers.
a. Identify the explanatory and response variables. Also, identify whether each is categorical or quantitative.
b. Organize the counts in a well-labeled 2 × 2 table.
c. Find the observed difference in proportion of ulcer cases between the physicians who took aspirin and those who took the placebo.
d. State the appropriate null and alternative hypotheses in words.
e. Use an appropriate applet to use a simulation-based approach to find a p-value to test the hypotheses stated.
f. Based on this p-value, how strong is the evidence against the null hypothesis.
g. 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.
h. Use an appropriate applet to fi nd and report the following from the data:
• The standardized statistic
• The theory-based p-value
i. How do the simulation-based and theory-based p-values compare?