Task:
Discuss the below:
In a study, serum cholesterol levels were measured for a large number of healthy males. The population was then followed for 16 years. Afterwards 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 249 mg/100 ml with the standard deviation of 44 mg/100 ml; for those who did not develop the disease, the mean serum cholesterol level was 207 mg/100 ml with the standard deviation of 26 mg/100 ml.
Suppose that an initial serum cholesterol level of 260 mg/100 ml or higher is used to predict coronary heart disease.
a) What is the probability of predicting heart disease for a man who will not develop it (i.e. the probability of false positive)?
b) What is the probability of failing to predict heart disease for a man who will develop it (i.e. the probability of false negative)?