Gonorrhea is a common infectious disease. In 1999, the rate of reported gonorrhea infections was 132.2 per 100,000 persons. A polymerase chain reaction (PCR) test for gonorrhea is known to have sensitivity 97% and specificity 98%. A sensitivity of 97% means that if someone has the disease, the probability of correctly testing positive is 97%, so the probability of testing negative (when someone has the disease) is 3%. A specificity of 98% means that if someone does not have the disease, the probability of correctly testing negative is 98%, so the probability of testing positive (when someone does not have the disease) is 2%.
a. Based on the information provided, complete a two-way table where the total count is 100,000; counts having gonorrhea or not are shown along the rows, and counts testing positive or negative are shown along the columns.
b. If a randomly chosen person in the United States is routinely screened for gonorrhea, and the test comes up positive, what is the probability of actually having the disease?
c. The probability you found in part (b) applies to a randomly chosen person being screened. If someone is screened because of exhibiting symptoms, would the probability of having the disease be higher or lower than your answer to part (b)?