One of the tests that is available to determine if someone has the human immunod

Question

One of the tests that is available to determine if someone has the human immunodeficiency virus (HIV) is called the Single Use Diagnostic System (SUDS). This test will give a positive result in approximately 97.9% of the cases where someone has the virus and 5.5% of those who do not have the virus. The latter is called a false positive. Suppose you are living in a city of 100,000 people. It is estimated that approximately 0.3% of the United States population is infected with HIV. We will assume that this percentage is true for the hypothetical city you are living in as well. From the numbers given above, what is a. P(someone has HIV) b. P(test positive I have HIV) c. P(test positive I don't have HIV) Create a two-way table using "Have HIV" and "Don't Have HIV" as columns and Test Positive" and "Test Negative" for the rows. Fill In the entries indicating how many citizens would be in each category. Be sure to include the totals for each row/column like we did in class. The total at the bottom right should be 100,000. To create a table in Word, use "Insert" then "Table". Suppose you live in this city and tested positive for HIV. What is the probability that you actually have the disease? a. Write this in terms of P(E_1|E_2), i.e. like #1bc above. b. Calculate your probability. c. Discuss the difference between your answers in (3b) and in (1b). Why are they so different? Why is the probability so much lower than P(test positive I have HIV)? One erroneous result is a false positive. Another is a false negative. Given the accuracy of the test and the other data given, what is the probability that a person who tests negative for the virus actually has HIV? a. Write this in terms of P(E_1|E_2), i.e. like #1bc above. b. Calculate your probability.

Explanation / Answer

1)Population 100,000

0.3% infected by HIV

97.9% in positive cases and 5.5% falsepositivr

a)P(someone has HIV) = total number of people with / total population

= 0.3

b) P(test positive / have HIV) =P(tested positive and have HIV)/P(have HIV) = 0.979

c) P(test positive /doesn't have HIV) = 0.055

2)

Have HIV Doesn;t Have HIV

Test positive 294 5484

Test Negative 6 94216

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