Question

Enzyme immunoassay tests are used to screen blood specimens for the presence of antibodies to HIV, the virus that causes AIDS. Antibodies indicate the presence of the virus. The test is quite accurate but is not always correct. Here are approximate probabilities of positive and negative test results when the blood tested does and does not actually contain antibodies to HIV. Test Result Given antibodies are present 0.9975 0.0025 Given antibodies are absent 0.0060 0.9940 Suppose that 2% of a large population carries antibodies to HIV in its blood. (a) Draw a tree diagram representing the HIV status of a person from this population (outcomes: antibodies present or absent) and the blood test result (outcomes: test positive or negative). Notice that the probabilities provided for the test results are conditional probabilities. (Round your answers to four decimal places.) Positive Present and Positive Antibodies.9975 Present .0025 0.02 - Negativ Present and Negative Member of Population 0.98 Positive Absent and Positive .0060 Antibodies Absent 0.9940 - Negativ A bsent and Negative Note: To avoid rounding errors, do not use the already rounded values in the process of calculation. Complete the entire calculation then round it to 4 decimal places. (b) What is the probability that the test is positive for a randomly chosen person from this population? (c) Identify the test's sensitivity, specificity, and positive predictive value. sensitivity specificity positive predictive value

Answer 1

• Positive 0.0200 Present and Positive Antibodies.9975 Present .0025 0.02 Negativ 0.0000 Present and Negative Member of Population 0.98 Positive0.0059 Absent and Positive .0060 Antibodies Absent 0.9940 Negativ 0.9741 Absent and Negative

b)

P(tested positive) =0.02*0.9975+0.98*0.0060 =0.0258

c)

sensitivity =0.9975

specificity=0.9940

positive predicted value =0.02*0.9975/0.0258=0.7724