The article "Rethinking Calcium Supplements" (U.S. Airways Magazine, October 2010) describes a study investigating whether taking calcium supplements increases the risk of heart attack. Consider the following four study descriptions. For each study, answer the following five questions:

Question 1: Is the described study an observational study or an experiment?

Question 2: Did the study use random selection from some population?

Question 3: Did the study use random assignment to experimental groups?

Question 4: Based on the study description, is it reasonable to conclude that taking calcium supplements is the cause of the increased risk of heart attack?

Question 5: Is it reasonable to generalize conclusions from this study to some larger population? If so, what population?

Study 1: Every heart attack patient and every patient admitted for an illness other than a heart attack during the month of December at a large urban hospital was asked if he or she took calcium supplements. The researchers found that the proportion of heart attack patients who took calcium supplements was significantly higher than the proportion of patients admitted for other illnesses who took calcium supplements.

Study 2: Two hundred people were randomly selected from a list of all people living in Minneapolis who receive Social Security. Each person in the sample was asked whether or not they took calcium supplements. These people were followed for 5 years, and whether or not they had a heart attack during the 5-year period was noted. The researchers found that the proportion of heart attack victims in the group taking calcium supplements was significantly higher than the proportion of heart attack victims in the group not taking calcium supplements.

Study 3: Two hundred people were randomly selected from a list of all people living in Minneapolis who receive Social Security. Each person was asked to participate in a statistical study, and all agreed to participate. Those who had no previous history of heart problems were instructed to take calcium supplements. Those with a previous history of heart problems were instructed not to take calcium

supplements. The participants were followed for 5 years, and whether or not they had a heart attack during the 5-year period was noted. The researchers found that the proportion of heart attack victims in the calcium supplement group was significantly higher than the proportion of heart attack victims in the no supplement group.

Study 4: Four hundred people volunteered to participate in a 10-year study. Each volunteer was assigned at random to either group 1 or group 2. Those in group 1 took a daily calcium supplement. Those in group 2 did not take a calcium supplement. The proportion who suffered a heart attack during the 10-year study period was noted for each group. The researchers found that the proportion of heart attack victims in group 1 was significantly higher than the proportion of heart attack victims in group 2.