Posts: 3,675,934
Threads: 734,342
Joined:
Sep 2021
Reputation:
5
The blood supply used by a local hospital for transfusions during surgical procedures is discovered to be infected with hepatitis C. To protect the blood supply from future contamination, all new donors are required to be screened for hepatitis C. The test used for this screening has a sensitivity of 95%, and a specificity of 90%. If this test is used on a sample of donors in which 10% are known to have hepatitis C, what is the chance that a donor who tests negative is actually free from the disease?
A. About 99%
B. About 95%
C. About 90%
D. About 85%
E. About 50%
F. About 45%
Posts: 3,675,934
Threads: 734,342
Joined:
Sep 2021
Reputation:
5
here is the answer and it's exp...
The correct answer is A. To answer this question you must construct a 2 x 2 table. Start with a sample of 1,000 because it is a nice, round number and, because screening tests are about ratios, it does not matter what sample size you use. The Table is then completed by computing 10% of 1,000 for the total number of diseased in the marginal (100), taking 95% of this 100 and 90% of the remaining 900 non-diseased part of the sample. With the table complete, Negative predictive value can be computed using the given numbers
Negative predictive value = 810/815 or just over 99%. Note that you should be able to estimate that without even actually completing the calculation. To complete the full set of calculations:
Note: the test has excellent negative predictive value, but a positive predictive value just slightly better than chance (50%).
