AIDS testing

In a recent column in Parade magazine, Marilyn Vos Savant raised the following question:

Suppose we assume that 5%of people are drug-users. A test is 95%accurate, which we'll say means that if a person is a user, the result is positive 95%of the time; and if she or he isn't, it's negative 95%of the time. A randomly chosen person tests positive. Is the individual highly likely to be a drug-user?

Marilyn's answer was:

Given your conditions, once the person has tested positive, you may as well flip a coin to determine whether she or he is a drug-user. The chances are only 50-50. But the assumptions, the makeup of the test group and true accuracy of the tests themselves are additional considerations.

Discussion

1. How can Marilyn's answer be correct?

2. What does she mean by saying that the makeup of the test group is an additional consideration?

Journal assignment

As reported in CHANCE magazine, in June of 1987 (former) Secretary of Health and Human Services Otis Bowen suggested taking blood samples from 45,000 randomly selected Americans and testing for the presence of HIV antibodies.

1. Suppose that if a person has the antibodies, the probability of a positive test is 99.9%, and that if the person does not have the antibodies the probability of a negative test is 99%. Assume that 1.5 million out of 250 million Americans have HIV antibodies. If a subject tests positive for the HIV antibodies, what is the probability that he or she actually has HIV antibodies.

2. Should there be mandatory HIV testing? For whom?

Homework assignment due Thursday 10 April

Read Part I of FPPA (Chapter 1 and 2) and do review exercises 2,4,5,7,8,10,11 at the end of Chapter 2.