Putting It Together: Women, Aspirin, and Heart Attacks In a famous study by the Physicians Health Study Group from Harvard University from the late 1980s, 22,000 healthy male physicians were randomly divided into two groups; half the physicians took aspirin every other day, and the others were given a placebo. Of the physicians in the aspirin group, 104 heart attacks occurred; of the physicians in the placebo group, 189 heart attacks occurred. The results were statistically significant, which led to the advice that males should take an aspirin every other day in the interest of reducing the chance of having a heart attack. Does the same advice apply to women?
In a randomized, placebo-controlled study, 39,876 healthy women 45 years of age or older were randomly divided into two groups. The women in group 1 received 100 mg of aspirin every other day; the women in group 2 received a placebo every other day. The women were monitored for 10 years to determine if they experienced a cardiovascular event (such as heart attack or stroke). Of the 19,934 in the aspirin group, 477 experienced a heart attack. Of the 19,942 women in the placebo group, 522 experienced a heart attack.

(a) What is the population being studied? What is the sample?

(b) What is the response variable? Is it qualitative or quantitative?

(c) What are the treatments? (d) What type of experimental design is this?

(e) How does randomization deal with the explanatory variables that were not controlled in the study?

(f) Determine whether the proportion of cardiovascular events in each treatment group is different using a two-sample Z-test for comparing two proportions. Use the  level of significance. What is the test statistic?

(g) Determine whether the proportion of cardiovascular events in each treatment group is different using a chi-square test for homogeneity of proportions. Use the  level of significance. What is the test statistic?

(h) Square the test statistic from part (f) and compare it to the test statistic from part (g). What do you conclude?

As part of a manufacturing process, a plastic container is supposed to be filled with 46 centilitres of saltwater solution. The plant has three machines that fi ll the containers. Managers are concerned that the machines might not be filling the containers with the same amount of saltwater solution, so they set up a randomized block design to test this concern. A pool of five machine operators operates each of the three machines at diff erent times. Company technicians randomly select five containers filled by each machine (one container for each of the five operators). The measurements are gathered and analysed. The Minitab output from this analysis follows. What was the structure of the design? How many blocks were there? How many treatment classifications? Is there a statistical difference in the treatment means? Are the blocking effects significant? Discuss the implications of the output.