The first test a doctor would order to determine whether a person is infected with HIV (the virus that causes AIDS) is the ELISA test. It detects antibodies and antigens for HIV. A study in Statistical Science by J. Gastwirth estimated that, if the person is actually infected with HIV, this test produces a positive result 97.7% of the time. If a person is not infected with HIV, the test result is negative 92.6% of the time. According the the US Centers for Disease Control (CDC), an estimated 1.1 million Americans out of a population of 321 million were infected with HIV in 2015. Using the information above, determine the probability that a randomly selected person whose ELISA test is positive actually is infected with HIV? a. What is the probability that a randomly selected American is infected with HIV? b. Using the answer to part (a) and the conditional probabilities of positive and negative ELISA test results, fill out the contingency table below: ELISA Test Result Positive Negative HIV Infected Not Infected c. What is the probability that a randomly selected person whose ELISA test is positive actually is infected with HIV? d. What is the probability that a randomly selected person whose ELISA test is positive actually is not infected with HIV? e. Based on the answer to (c) and (d) above, is the ELISA test effective?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

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The first test a doctor would order to determine whether a person is infected with HIV (the virus that causes AIDS) is the ELISA test. It detects antibodies and antigens for HIV. A study in Statistical Science by J. Gastwirth estimated that, if the person is actually infected with HIV, this test produces a positive result 97.7% of the time. If a person is not infected with HIV, the test result is negative 92.6% of the time. According the the US Centers for Disease Control (CDC), an estimated 1.1 million Americans out of a population of 321 million were infected with HIV in 2015. Using the information above, determine the probability that a randomly selected person whose ELISA test is positive actually is infected with HIV?
a.	What is the probability that a randomly selected American is infected with HIV?
b.	Using the answer to part (a) and the conditional probabilities of positive and negative ELISA test results, fill out the contingency table below:
		ELISA Test Result
		Positive	Negative
HIV	Infected
Not Infected

c.	What is the probability that a randomly selected person whose ELISA test is positive actually is infected with HIV?
d.	What is the probability that a randomly selected person whose ELISA test is positive actually is not infected with HIV?
e.	Based on the answer to (c) and (d) above, is the ELISA test effective?

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