When a test is conducted to determine whether or not someone is infected with a partic-
ular virus, an incorrect test result can occur in two
ways: an infected person may test negative, or a
noninfected person may test positive. The latter
is called a false positive test. It has been pointed
out that the social consequences of false positive
tests for the AIDS virus are particularly serious.
Such a false positive test will unnecessarily "stig.
matize and frighten many healthy people," be-
cause most people consider a positive AIDS test
to be a sentence to ghastly suffering and death."
Meyer and Pauker therefore assert that it is important that a patient who tests positive for the
AIDS virus have a high probability of really being
infected. In order to focus on the false positive rate
of the test, assume throughout this question that we are dealing with a test that properly identifies
all persons who really are infected with AIDS
virus.
a. Assume that 5% of a population to be tested
for the AIDS virus really is infected and that
the test has a false positive rate of .5%. Find
the probability that a person who tests positive
really is infected.
b. Would your answer to part (a) be higher or
lower if more than 5% of the population to
be tested were actually infected? Answer the
question by referring to the formula for con-
ditional probability without performing any
calculations.
c. Assume now that a low-risk population is to
be tested. Specifically, assume that .01% of the
population to be tested is actually infected with
the AIDS virus and that the test has a false
positive rate of .005% (which is unusually
low). Find the probability that a person who
tests positive really is infected,
d. What would your answer to part (c) be if you
assumed a false positive rate of .5%?
e. Summarize the implications of your findings
in parts (a) through (d),