The ELISA test is used to screen donated blood for the AIDS virus. It is estimated that 0.5% of the population is infected by the AIDS virus. The accuracy of the test is 97.7%; that is, a sample with...

The ELISA test is used to screen donated blood for the AIDS virus.  It is estimated that 0.5% of the population is infected by the AIDS virus.  The accuracy of the test is 97.7%; that is, a sample with the AIDS virus is correctly identified to be carrying the virus 97.7% of the time [P(POSITIVE | AIDS) = 0.977].  The specificity of the test is 92.6%; a healthy blood sample is correctly diagnosed 92.6% of the time [P(NEGATIVE | NO AIDS) = 0.926].

Starting with a population of 1,000,000 bottles of donated blood, find the number of bottles in each of the following four categories:

• AIDS Infected which tested POSITIVE


• AIDS Infected that tested NEGATIVE


• NO AIDS Infected that tested POSITIVE


• NO AIDS Infected that tested NEGATIVE.

Discuss the false positive and false negative results.  Should ELISA’s credibility be questioned?