High cholesterol levels have for some time been implicated as predictors of future heart attacks. The problem is that other factors such as age, smoking, weight and family history enter into the picture and the different factors are difficult to separate out. Suppose we isolate a group of 100 men who have "high" cholesterol levels and can predict, on the basis of other factors, that 10% of these men will have a heart attack in the next 5 years. How large a sample would we need to have an 80% chance of finding a significant difference if the true rate of heart disease in this group is 13%?