NOTE: THIS IS FOR AN NON-GRADED QUIZ.

COVID STATS QUESTION

Many epidemiologists believe that testing is the only approach to long-term virus control; even with the vaccine increasingly available around the world, new variants may emerge against which some or all of the vaccines are ineffective.But what can one learn from these tests?We examine this issue in the context of BOSTON, where the prevalence of COVID-19 is about 5,000 cases out of 1,000,000 people in the state (cumulative who are still infected from the last few months, not per day).Suppose that the test for detecting COVID-19 yields a positive test for 99 percent of those actually infected, and it yields a negative test for 95 percent of those actually not infected.(These are approximate rates for rapid tests.)

(a)Use Bayes' Rule to calculate the probability that a person who tests positive is infected (i.e. P(COVID | +)).This number is usually referred to as the positive predictive value of the test.

(b)Use Bayes' Rule to calculate the probability that a person who tests negative is not infected (i.e. P(NO COVID | - )). This number is usually referred to as the negative predictive value of the test.