4/7.4 points | Previous Answers My N Enzyme immunoassay tests are used to screen

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4/7.4 points | Previous Answers My N 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 antibod es are present 0.9925 0.0075 Given antibodies are absent 0.0080 0.9920 Suppose that 1% 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: antbodies 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 0099 Antibodies 925 Present Negative .0007 X Member of Population .99 Positive 0079 0080 Antibodies Absent Negative 9821 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? 0178 (c) Identify the test's sensitivity, specificity, and positive predictive valuc sensitivity 99.2004 X 99.2421 X positive predictive value 99.25 ×

Explanation / Answer

a) in diagram ; the error value: negative =0.01*0.0075 =0.0001

c)sensitivity =0.9925 (as test result + given present)

specificity =0.9920 (test result - given absent)

positive predictive value =(0.9925*0.01/(0.9925*0.01+0.99*0.0080)) =0.5562

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