This assignment involves events some years ago involving the drug Vioxx. So why are we talking about drugs in a Business Statistics class? Well, drugs are BIG business in America and the fallout of actions that are based on statistical analysis can be immense. Although approved by the FDA as a painkiller (primarily for arthritis pain), a later study linked Vioxx to an increased risk of heart attack and stroke. The end result was that the drug company Merck & Co. took the action of pulling the drug from the market despite annual sales of 2.5 billion dollars. In addition, they agreed to pay $4.85 billion to settle roughly 47,000 lawsuits by patients harmed by the drug, and saw their stock price fall by 40%. Certainly, shareholders were thrilled was this outcome.

The action by Merck to withdraw the drug from the market implies that the conclusion was reached that Vioxx was associated with an increase in the population proportion of patients who will experience heart attacks or strokes when compared to the population proportion of patients having a heart attack or stroke when not using the drug. The conclusion was based on a study in which researchers observed a higher heart attack and stroke risk in patients on Vioxx. Consider the following definitions:

p1 = the population proportion of patients experiencing a heart attack or stroke when using Vioxx, and

p2 = the population proportion of patients experiencing a heart attack or stroke when not using Vioxx.

For our purposes Ive used sample sizes that might be considered large as I was not able to find the exact numbers. So we will suppose that the study involved a random sample of 1300 subjects who were using Vioxx, and 1300 subjects who were given a placebo (sugar pill) that has no effect on the subjects. It was reported that after a period of time, 3.5% of the subjects on Vioxx had suffered a heart attack or stroke, compared to 1.9% of the subjects on the placebo having a heart attack or stroke.

1. (10 points) Use an appropriate hypothesis test to analyze the data provided at a level of significance of a = .01. Your objective is to determine if you agree with the conclusion that the results should be considered significant evidence that using Vioxx results in an increase in the population proportion of patients who will have a heart attack or stroke when compared with patients not using the drug (that is to say, the drug is considered to increase the risk of heart attack or stroke). Also state whether the action to pull the drug from the market was the appropriate action in light of the evidence provided by this study. State your conclusions in clear English sentences. Provide ALL RELEVANT INFORMATION AND COMPUTATIONS required to perform the test and reach a conclusion. (Please note: The conclusion Reject H_o or Do not reject H_o by itself is not considered an English sentence that indicates what you are concluding in the context of this problem.)

2. (4 points) Complete the following statement: If it is true that there is no difference in the population proportions of patients who suffer heart attacks and strokes when using Vioxx as compared to those patients who are not using the drug, the probability of observing a difference in the sample proportions as large, or larger, as the difference observed in this study is _______________________.
3. (4 points) Suppose that an independent analyst analyzed the same set of data from the study cited above, and her conclusion was that the results of the study do not provide significant evidence of an increase in the population proportion of heart attacks and strokes in patients using Vioxx. This would contradict the conclusion that was evidently reached by Merck & Co. Is it possible that an analyst could make this claim and justify it as being statistically appropriate? If so, how? Explain and BE SPECIFIC.

4. (4 points) In the context of this analysis, describe in English what event would correspond to a Type I Error.

5. (4 points) If your concern is protecting the public from using potentially harmful drugs, should you choose a value for the level of significance for the test above that is relatively large (say.05), or should you choose a value for the level of significance for this test that is relatively small (say .005)? Circle your answer.

I should choose a relatively large value for . I should choose a relatively small value for .

6. (4 points) If you work for Merck and your goal is to get a potentially harmful drug on the market in spite of the possible danger to the patients, should you choose a value for the level of significance for the test above that is relatively large (say.05), or should you choose a value for the level of significance for this test that is relatively small (say .005)? Circle your answer.

I should choose a relatively large value for . I should choose a relatively small value for .