Suppose that a screening test for SARS-CoV2 infection has 90% sensitivity and 95% specificity. Assume 1% of the population being screened truly has SARS-CoV2 infection.

1. If you really are infected, what is the probability that the test says you are?

2. If you really are not infected, what is the probability that the test says you are?

3. The screening test is applied to a total of 15 people; 2 who really are infected and 13 who are not. What is the probability that it gets all of the screens correct? (That is, the two people who are infected get a positive result on the screen and the 13 who are not get a negative result).

4. You just tested positive. What is the probability that you really are infected, given your test result?

5. The same screening test is applied in another city that has a 2% incidence of infection among people who might get screened. Will the positive predictive value be higher or lower in the other city? How about the negative predictive value?