An automated blood-pressure machine classifies people as having either high blood pressure (hypertension) or normal (healthy) blood pressure. In clinical trials on adults the machine classified 88% of hypertensives as having hypertension, and classified 22% of healthy people, i.e. without hypertension, as having hypertension. Health officials are considering using the machine for screening an adult population in which 18% of persons have hypertension.

(a) Structure the above information using a contingency table. Take care to complete the marginal totals as well as the body of the table.

(b) Estimate the proportion of people that the machine classifies as hypertensive that would actually have hypertension?

(c) Consider those who would be classified by the machine as having normal blood pressure. If we chose one of these people at random, what is the chance that the selected person would actually be hypertensive?

(d) What would the machine do better in this population: show who has hypertension, or show who doesn't have it? Justify your answer.