Question

Statistics - Diagnostic tests of medical conditions.

Rules:

Turn in one set of solutions with names of all participating students in the group.

Graphs should be neat, clean and well-labeled. Explain how you arrived at the conclusions (functions/formulas used in calculations.)

“Explanations” and answers should given be given in the form of complete sentences.Since I give partial credit on the projects you should show your work so that some partial credit can be assigned if your answer is incorrect.

**Part 1:**

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.

d) What is the sensitivity of the test? (you may need to look up what this term means for this context)

e) What is the specificity of the test? (you may need to look up what this term means for this context)

f) Given that the EIA test is negative, what is the probability that a person has the antibody?

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?

Answer #1

Disease | ||||

Test | Present | % | Absent | % |

Positive | True Positive, a | 99.85 | False Positive, c | 0.6 |

Negative | False Negative, b | 0.15 | True Negative, d | 99.4 |

d) The sensitivity is define as the result will be positive when the disease is present.

e) The specificity is define as the result will be negative when the disease is not present.

f) The probability that the result will be positivetive given the disease is not present.

g) The Negative predictive value is the probability that the disease is not present when the test is negative,

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...

Part 1:
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...

Diagnostic tests of medical conditions can have several types of
results. The test result can be positive or negative, whether or
not a patient has the condition. A positive test (+) indicates that
the patient has the condition. A negative test (−) indicates that
the patient does not have the condition. Remember, a positive test
does not prove the patient has the condition. Additional medical
work may be required. Consider a random sample of 200 patients,
some of whom have...

Diagnostic tests of medical conditions have several results. The
rest result can be positive or negative. A positive test (+)
indicates the patient has the condition. A negative test (–)
indicates the patient does not have the condition. Remember, a
positive test does not prove the patient has the condition.
Additional medical work may be required. Consider a random sample
of 201 patients, some of whom have a medical condition and some of
whom do not. Results of a new...

Elisa Test
The standard test for the HIV virus is the Elisa
test, which tests for the presence of HIV antibodies. If an
individual does not have the HIV virus, the test will come
back negative for the presence of HIV antibodies 99.8% of
the time and will come back positive for the presence of
HIV antibodies 0.2% of the time (a false positive). If an
in-
dividual has the HIV virus, the test will come back positive
99.8% of...

The probability that a person has a certain disease is 2%.
Medical diagnostic tests are available to determine whether the
person actually has the disease. If the disease is actually
present, the probability that the medical diagnostic tests will
give a positive result (correct diagnosis) is 95%. If the disease
is not actually present, the probability of a positive test result
(incorrect diagnosis) is 0.5%. Suppose that the medical diagnostic
test shows a positive result, (a) What is the probability...

The probability that a person has a certain disease is 0.03
Medical diagnostic tests are available to determine whether the
person actually has the disease. If the disease is actually
present, the probability that the medical diagnostic test will give
a positive result (indicating that the disease is present) is
0.92
If the disease is not actually present, the probability of a
positive test result (indicating that the disease is present) is
0.02
a. If the medical diagnostic test has...

The probability that a person has a certain disease is 0.03
Medical diagnostic tests are available to determine whether the
person actually has the disease. If the disease is actually
present, the probability that the medical diagnostic test will give
a positive result (indicating that the disease is present) is
0.88 If the disease is not actually present, the probability of a
positive test result (indicating that the disease is present) is
0.02
a. If the medical diagnostic test has...

1. If the heights of ice hockey goalies are normally distributed
with the mean μ=72μ=72 inches and the standard deviation σ=5.4σ=5.4
inches. What is the percentage of hockey players that have the
height between 66.666.6 and 77.477.4 inches?
a. 68%
b. 50%
c. 32%
d. 95%
2. Diagnostic tests of medical conditions can have several types
of results. The test result can be positive or negative, whether or
not a patient has the condition. A positive test (+) indicates that...

9-7. Diagnostic Testing: Baseball Fever
A researcher at Javier Lopez University developed a new test for
detecting baseball fever. The new test was evaluated in a
population of 10,000 people, 21% of whom were definitely known to
have baseball fever. The number of negative tests was 8,162. The
positive predictive value was discovered to be 91.4%.
Use the information provided above to fill in the following 2 x
2 table:
Baseball Fever
Present
Absent
Test Result
Positive ...

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