Dogs are being trained to detect lung cancer by smelling the breath of patients. 1286 patientswith known cancer status are tested. 708 patients without cancer were given a negative result,and 4 patients without cancer were given a positive result. 10 patients with cancer were givena negative result, and 564 patients with cancer were given a positive result.
(a) Create a table to organize the above information and help solve the problems below.
(b) Find the probability of a positive test for a patient with cancer (the sensitivity).
(c) Find the probability of a negative test for a patient without cancer (the specificity).
(d) Find the probability of having cancer for a patient getting a positive result (the positivepredictive value) for this test on this sample.
(e) Assume that the sensitivity and specificity are always the same. Find the positive predictivevalue of this test when used on a population where 7% of people have lung cancer.