webassignet Test Result Given antibodies are present Given antibodies are absent
ID: 3042832 • Letter: W
Question
webassignet Test Result Given antibodies are present Given antibodies are absent 0.9985 0.0015 0.0040 0.9960 Suppose that 4% of a large population caries 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 Notice that the probabilities provided for the test results are conditional probabities. (Round your answers to four decimal places.) positive or negetive), Positive0.00994 Antibodies 0.9985 Present 00015 Negative 0.00006 0.04 Member of 0.96 Positive 000384 0.0040 Antibodies Absent 0 9960 Negative 0.95616 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? 0044 (c) Identity the test's sensitivity, specificity, and positive predictive value. 0.9985 positive predictive value 0.9960 MacBook ProExplanation / Answer
(b)
The probability that test is positive for a ranomly chosen person is
P(positive) = P(positive and antibodies present)+ P(positive and antibodies absent) = 0.00384 + 0.03994 = 0.04378
Answer: 0.0438
(c)
Specificity: The probability of a person testing negative given that (s)he does not have the disease.
Specificity = P(negative| antibodies absent) = 0.9960
Positive predictive value given the probability that a person actually have diseases among those for whom test gives positive result.
Positive predictivity = P(antibodies present | positive) = P(antibodies present and positive) / P(positive) = 0.03994 / 0.04378 = 0.9123
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