An article in the Los Angeles Times (24 December 1994, p. A16) announced that a new test for detecting HIV had been approved by the Food and Drug Administration (FDA). The test requires the person to send a saliva sample to a lab. The article described the accuracy of the test as follows: The FDA cautioned that the saliva test may miss one or two infected individuals per 100 infected people tested, and may also result in false positives at the same rate in the uninfected. For this reason, the agency recommended that those who test positive by saliva undergo confirmatory blood tests to establish true infection.
a. Do you think it would be wise to use this saliva test to screen blood donated at a blood bank, as long as those who test positive were retested as suggested by the FDA? Explain your reasoning.
b. Suppose that 10,000 students at a university were all tested with this saliva test and that, in truth, 100 of them were infected. Further, suppose the false positive and false negative rates were actually both 1 in 100 for this group. If someone tests positive, what is the probability that he or she is infected?