On December 15, 2020, the U.S. Food and Drug Administration approved the first at-home test for COVID-19. It can give results in about 15 minutes. This test has a 3% false positive rate and a 5% false negative rate. (a) Explain what this test's false positive rate and false negative rate mean in context. (b) Which do you think is more serious: a false positive or a false negative result? Justify your answer. Suppose that 5% of the U.S. population is infected with COVID-19 when the test is released, and that we give the test to a randomly selected person from the population. (c) If the person tests positive, what is the probability that they have COVID-19? How does this compare to the result in Ouestion 1(c)? (d) If the person tests negative, what is the probability that they don't have COVID-19?
On December 15, 2020, the U.S. Food and Drug Administration approved the first at-home test for
COVID-19. It can give results in about 15 minutes. This test has a 3% false positive rate and a 5% false
negative rate.
(a) Explain what this test's false positive rate and false negative rate mean in context.
(b) Which do you think is more serious: a false positive or a false negative result? Justify your answer.
Suppose that 5% of the U.S. population is infected with COVID-19 when the test is released, and that we
give the test to a randomly selected person from the population.
(c) If the person tests positive, what is the probability that they have COVID-19? How does this compare
to the result in Ouestion 1(c)?
(d) If the person tests negative, what is the probability that they don't have COVID-19?
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
