3.5.1 A medical research team wishes to assess the usefulness of a certain symptom (call it $) in the diagnosis of a particular disease. In a random sample of 775 patients with the disease, 744 reported having the symptom. In an independent random sample of 1380 subjects without the disease, 21 reported that they had the symptom.

(a) In the context of this exercise, what is a false positive?

(b) What is a false negative?

(e) Compute the sensitivity of the symptom.

(d) Compute the specificity of the symptom.

(e) Suppose it is known that the rate of the disease in the general population is .001. What is the predictive value positive of the symptom? (F) What is the predictive value negative of the symptom? (g) Find the predictive value positive and the predictive value negative for the symptom for the following hypothetical disease rates: .0001, .01, and .10.

(b) What do you conclude about the predictive value of the symptom on the basis of the results obtained in part g?