Question: To estimate the prevalence of HIV, the State of New York implemented a policy of testing women who gave birth. The test that was used is known as ELISA; it is actually a test for the HIV antibody. Assume that ELISA has a sensitivity of 0.998 and a specificity of 0.998. (Both numbers are high; in particular ELISA gives more false positives than these numbers indicate.) An article in the American Journal of Public Health reports on the administration of the ELISA test to 108,562 women in rural upstate New York who gave birth between November of 1987 and March of 1990. Of these women, 82 tested positive. From this observation, the authors conclude that the prevalence of HIV among rural women in New York state is approximately 0.076% because (82)/(108,562) = 0.00076.

i. What error did the authors commit?

ii. Approximately how many false positives would this test produce based on the updated probability P(~HIV|+)?

iii. Based on your calculation, what would you conclude?