Reference no: EM132312999

Project

Rules:

1) Post one set of solutions with names of all participating students in the group to the Canvas course website.

2) The one file needs to be in either an MS Word format or PDF format

3) Graphs should be neat, clean and well-labeled.

4) "Explanations" and answers should be given in the form of complete sentences.

Diagnostic tests of medical conditions can have several results.

1) The patient has the condition and the test is positive (+)

2) The patient has the condition and the test is negative (-) - Known as "false negative"

3) The patient doesn't have the condition and the test is negative (-)

4) The patient doesn't have the condition and the test is positive (+) - Known as "false positive"

Consider the following:

Enzyme immunoassay (EIA) tests are used to screen blood specimens for the presence of antibodies to HIV, the virus that causes AIDS. Antibodies indicate the presence of the virus. The test is quite accurate but is  not always correct. Suppose that 1% of a large population carries antibodies to HIV in their blood.

Of  those that carry the HIV antibodies in their blood, 99.85% will have a positive test result and 0.15% will  have a false-negative test result. Of those that do not carry the HIV antibodies in their blood, 99.4% will  have a negative test result and 0.60% will have a false-positive test result.

a) Draw a tree diagram for selecting a person from this population and testing his or her blood.

Take a look in the example on page 398 of the class text book for an example of a tree diagram.

b) Construct a probability table that shows the probabilities for individuals in this population with respect to the presence of antibodies and test results.

Take a look in the example on page 394 of the class text book for an example of a probability table.

c) What is the probability the EIA is positive for a randomly chosen person from this population?

d) In words, define the sensitivity of a test like this. Define the sensitivity in the context of this test using conditional probability notation. Calculate the sensitivity of this test? (you may need to look up what this term means for this context)

Take a look at the last equation/calculation in the right hand column of the example on page 398 of the class textbook for an example of the conditional probability notation.

e) In words, define the specificity of a test like this. Define specificity in the context of this test using conditional probability notation. Calculate the specificity of this test? (you may need to look up what this term means for this context)

Take a look at the last equation/calculation in the right hand column of the example on page 398 of the class textbook for an example of the conditional probability notation.

f) In words, define the positive predictive value of a test like this. Define positive predictive value in the contest of this test using conditional probability notation. Calculate the positive predictive value of this test? (you may need to look up what this term means)

Take a look at the last equation/calculation in the right hand column of the example on page 398 of the class textbook for an example of the conditional probability notation.

g) In words, define the negative predictive value of a test like this. Define negative predictive value in the context of this test using conditional probability notation. Calculate the negative predictive value of this test? (you may need to look up what this term means)

Take a look at the last equation/calculation in the right hand column of the example on page 398 of the class textbook for an example of the conditional probability notation.