Question
Asked Dec 21, 2019
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In Exercises 17–20, refer to the accompanying table showing results from a Chembio test for hepatitis C among HIV-infected patients (based on data from a variety of sources).

Positive predictive value Find the positive predictive value for the test. That is, find the probability that a subject has hepatitis C, given that the test yields a positive result. Does the result make the test appear to be effective?

Positive Test Result
Negative Test Result
Hepatitis C
335
10
No Hepatitis C
1153
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Positive Test Result Negative Test Result Hepatitis C 335 10 No Hepatitis C 1153

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Expert Answer

Step 1

Event A: selecting a subject having hepatitis-c.

Event B: selecting a subject with positive result.

Then P (A/B) is the probability of selecting a having hepatitis-c given subject with positive result.

Step 2
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Given that, Positive result Negative result total Нерatitis C No hepatitis C 2 337 335 10 345 1155 1153 total 1163 1500

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Step 3

P (A∩B) =335/1500.

P ...

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P(AB) P(A/ B)= P(B) 335/1500 337/1500 335 337 = 0.9941

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