This exercise deals with a comparison between Mediterranean diet and low-fat diet recommended by the American Heart Association in the context of risks for illness or death among patients that survived a heart attack. This case study is taken from the Rice Virtual Lab in Statistics. More details on this case study can be found in the case study Mediterranean Diet and Health that is presented in that site.
β1β
De Lorgeril, M., Salen, P., Martin, J., Monjaud, I., Boucher, P., Mamelle, N. (1998). Mediterranean Dietary pattern in a Randomized Trial. Archives of Internal Medicine, 158, 1181-1187.
The subjects, 605 survivors of a heart attack, were randomly assigned follow either (1) a diet close to the βprudent diet step 1β of the American Heart Association (AHA) or (2) a Mediterranean-type diet consisting of more bread and cereals, more fresh fruit and vegetables, more grains, more fish, fewer delicatessen food, less meat.
The subjectsβ diet and health condition were monitored over a period of four-year. Information regarding deaths, development of cancer or the development of non-fatal illnesses was collected. The information from this study is stored in the file
diet.csv. The file diet.csv contains two factors: health that describes the condition of the subject, either healthy, suffering from a non-fatal illness, suffering from cancer, or dead; and the type that describes the type of diet, either Mediterranean or the diet recommended by the AHA. The file can be found on the internet at http://pluto.huji.ac.il/~msby/StatThink/Datasets/diet.csv. Answer the following questions based on the data in the file:
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Produce a frequency table of the two variable. Read off from the table the number of healthy subjects that are using the Mediterranean diet and the number of healthy subjects that are using the diet recommended by the AHA.
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Test the null hypothesis that the probability of keeping healthy following an heart attack is the same for those that use the Mediterranean diet and for those that use the diet recommended by the AHA. Use a two-sided alternative and a 5% significance level.
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Compute a 95% confidence interval for the difference between the two probabilities of keeping healthy.
