An automated blood-pressure machine correctly classifies 87% of hypertensives as having hypertension (high blood pressure), and also classifies 22% of healthy people as having hypertension. The machine is being considered for use in a blood pressure screening programme in an adult population in which 20% of persons have hypertension.
(a) Structure the above information using a contingency table. Take care to complete all marginal totals as well as the body of the table.
(b) What proportion of people that the machine classifies as hypertensive 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.