The ELISA test for the presence of HIV antibodies in blood samples gives the correct result about 99.7% of the time for blood samples that are known to be HIVpositive. The test is correct 98.5% of the time for blood samples that are known to be HIV -negative.
a. Suppose 100,000 blood samples contain 10% that are HIV-positive. All are tested with ELISA. Set up a two-way table to show what the outcomes of the tests are expected to look like. What proportion of the samples that test positive are really expected to be positive?
b. Repeat the instructions for part a for a set of 100,000 blood samples that are assumed to contain 20% that are HIV -positive. c. How do the results for parts a and b compare? Comment on the possible social implications of mass testing of blood samples.