AP Statistics / Mr. Hansen
Test 3, Chapters 5 and 6, 12/7/2000 (contd.)

Name: __________________________

28.

A new test for hepatitis C is developed that has sensitivity and specificity both equal to 98%. In other words, the test is 98% accurate in avoiding both false negative readings and false positives. Assume that 1% of the population has hepatitis C.

(a, b)
(3 pts. on take-home)

State the sensitivity (0.98) and specificity (also 0.98) in terms of conditional probabilities. No work needed.

(c)
(4 pts.)

If you select 54 people randomly and independently, compute the probability that at least one of them truly has hepatitis C. (Note: This question has nothing to do with test results.) Show work.

(d)
(5 pts.)

Make a probability tree diagram and circle the probability that a randomly selected person would receive a false negative reading. (If you prefer to use a tree of numbers of people, still compute and circle the probability of a false negative.)

(e)
(4 pts.)

Compute the probability that a person actually has hepatitis C, given that the person has a positive test result for the disease. Show a little bit of work.