5. In the Framingham Study, serum cholesterol levels were measured for a large number of healthy males. The population was then followed for 16 years. At the end of this time, the men were divided into two groups: those who had developed coronary heart disease and those who had not. The distributions of the initial serum cholesterol levels for each group were found to be approximately normal. Among individuals who eventually developed coronary heart disease, the mean serum cholesterol level was 4d = 242 mg/100 ml and the standard deviation was o a = 50 mg/100 ml; for those who did not develop the disease, the mean serum cholesterol level was µnd = 215 mg/100 ml and the standard deviation was o nd = 41 mg/100 ml. (a) Suppose that an initial serum cholesterol level of 260 mg/100 ml or higher is used to predict coronary heart disease. What is the probability of correctly predicting heart disease for a man who will develop it? (b) What is the probability of predicting heart disease for a man who will not develop it? (c) What is the probability of failing to predict heart disease for a man who will develop it?

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5. In the Framingham Study, serum cholesterol levels were measured for a large number of healthy males. The
population was then followed for 16 years. At the end of this time, the men were divided into two groups:
those who had developed coronary heart disease and those who had not. The distributions of the initial
serum cholesterol levels for each group were found to be approximately normal. Among individuals who
eventually developed coronary heart disease, the mean serum cholesterol level was µd = 242 mg/100 ml and
the standard deviation was od = 50 mg/100 ml; for those who did not develop the disease, the mean serum
cholesterol level was µnd = 215 mg/100 ml and the standard deviation was o nd = 41 mg/100 ml.
(a) Suppose that an initial serum cholesterol level of 260 mg/100 ml or higher is used to predict coronary
heart disease. What is the probability of correctly predicting heart disease for a man who will develop
it?
(b) What is the probability of predicting heart disease for a man who will not develop it?
· a
(c) What is the probability of failing to predict heart disease for a man who will develop it?
(d) What would happen to the probabilities of false positive and false negative errors if the cutoff point for
predicting heart disease is lowered to 250 mg/100 ml?
(e) In this population, does initial serum cholesterol level appear to be useful for predicting coronary heart
disease? Why or why not?
Transcribed Image Text:5. In the Framingham Study, serum cholesterol levels were measured for a large number of healthy males. The population was then followed for 16 years. At the end of this time, the men were divided into two groups: those who had developed coronary heart disease and those who had not. The distributions of the initial serum cholesterol levels for each group were found to be approximately normal. Among individuals who eventually developed coronary heart disease, the mean serum cholesterol level was µd = 242 mg/100 ml and the standard deviation was od = 50 mg/100 ml; for those who did not develop the disease, the mean serum cholesterol level was µnd = 215 mg/100 ml and the standard deviation was o nd = 41 mg/100 ml. (a) Suppose that an initial serum cholesterol level of 260 mg/100 ml or higher is used to predict coronary heart disease. What is the probability of correctly predicting heart disease for a man who will develop it? (b) What is the probability of predicting heart disease for a man who will not develop it? · a (c) What is the probability of failing to predict heart disease for a man who will develop it? (d) What would happen to the probabilities of false positive and false negative errors if the cutoff point for predicting heart disease is lowered to 250 mg/100 ml? (e) In this population, does initial serum cholesterol level appear to be useful for predicting coronary heart disease? Why or why not?
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