Question

Negative Test Result Positive Test Result 335 Hepatitis C No Hepatitis C DIR (a) (2 points) Find the probability of selecting a subject with a positive test result, given that the subject does not have hepatitis C Why is this case problematic for test subjects? (b) (2 points) Find the probability of selecting a subject with a negative test result, given that the subject does not have hepatitis C. What would be an unfavorable consequence of this error? (c) (2 points) Find the positive predictive value for the test. That is, find the probability that a subject has hepatitis C, given that the test yield positive results. Does the result make the test appear to be effective? (d) (2 points) Find the negative predictive value for the test. That is, find the probability that a subject does not have hepatitis C given that the test yield negative results. Does the result make the test appear to be effective?

Answer 1

a)
A = has Hepatitis C
B =test is positive

P(B|A') = P(B and A')/P(A') = 2/(2 + 1153) =0.00173

b)
P(B' | A') = 1153/1155
= 0.998268

c)
P(A|B) = 335/(335 + 2) = 335/337
= 0.994065

d)
P(A'|B') = 1153/(1153+10)
= 0.99140154