Part (a) of this exercise is also given Exercise. Using given Case Study on pages as an example:

a. Explain the difference between a population and a sample.

b. Use the proportion of placebo takers who had heart attacks, which was .017, to explain the difference between a population parameter and a sample statistic.

Exercise
Using given Case Study as an example, explain the difference between a population and a sample.

Case Study
Does Aspirin Reduce Heart Attack Rates?

In 1988, the Steering Committee of the Physicians' Health Study Research Group released the results of a 5-year randomized experiment conducted using 22,071 male physicians between the ages of 40 and 84. The purpose of the experiment was to determine whether or not taking aspirin reduces the risk of a heart attack. The physicians had been randomly assigned to one of the two treatment groups. One group took an ordinary aspirin tablet every other day, while the other group took a placebo. None of the physicians knew whether he was taking the actual aspirin or the placebo. The results, shown in Table 1.1, support the conclusion that taking aspirin does indeed help to reduce the risk of having a heart attack. The rate of heart attacks in the group taking aspirin was only about half the rate of heart attacks in the placebo group. In the aspirin group, there were 9.42 heart attacks per 1000 participating doctors, while in the placebo group, there were 17.13 heart attacks per 1000 participants.

Because the men in this experiment were randomly assigned to the two conditions, other important risk factors such as age, amount of exercise, and dietary habits should have been similar for the two groups. The only important difference between the two groups should have been whether they took aspirin or a placebo. This makes it possible to conclude that taking aspirin actually caused the lower rate of heart attacks for that group. In a later chapter, you will learn how to determine that the difference seen in this sample is statistically significant. In other words, the observed sample difference probably reflects a true difference within the population. To what population does the conclusion of this study apply? The participants were all male physicians, so the conclusion that aspirin reduces the risk of a heart attack may not hold for the general population of men. No women were included, so the conclusion may not apply to women at all. More recent evidence, however, has provided additional support for the benefit of aspirin in broader populations.

Moral of the Story: Unlike with observational studies, cause-and-effect conclusions can generally be made on the basis of randomized experiments.

Definitions: A randomized experiment is a study in which treatments are randomly assigned to participants. A treatment is a specific regimen or procedure assigned to participants by the experimenter. A random assignment is one in which each participant has a specified probability of being assigned to each treatment. A placebo is a pill or treatment designed to look just like the active treatment but with no active ingredients. A statistically significant relationship or difference is one that is large enough to be unlikely to have occurred in the sample if there was no relationship or difference in the population.