A “Mediterranean diet” (high in fish, olive oil, red wine, etc.) has been touted as a key to a long life. A study by Trichopoulou et al. (2005) looked at the death rates of people according to whether their diet had a low component, a medium component, or a high component of foods that characterize a Mediterranean diet. In these kinds of studies, it is important to look for other confounding variables, such as smoking, that might be correlated with the main variable under study. For each person in the study, therefore, the team also recorded whether the person was a current smoker, a former smoker, or had never smoked. We want to know if there is an association between diet and smoking. The data for men in the study are as follows, where the numbers represent the number of men in each category:

a. Draw a mosaic plot of these data. What is the pattern?

b. Test whether there is an association between diet and smoking.

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Never smoked Never smoked Former smokerFormer smoker Current smoker Current smoker Low Med. diet 25162516 36573657 20122012 Medium Med. diet 29202920 46534653 16271627 High Med. diet 24172417 34493449 12941294