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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 a medical condition and some of whom do not. Results of a new diagnostic test for a condition are shown.
Condition Present Condition Absent Row Total
Test Result 108 22 130
Test Result − 23 47 70
Column Total 131 69 200
Assume the sample is representative of the entire population. For a person selected at random, compute the following probabilities. (Enter your answers as fractions.)
(a)
P(+ | condition present); this is known as the sensitivity of a test.
(b)
P(− | condition present); this is known as the false-negative rate.
(c)
P(− | condition absent); this is known as the specificity of a test.
(d)
P(+ | condition absent); this is known as the false-positive rate.
(e)
P(condition present and +); this is the predictive value of the test.
(f)
P(condition present and −).
 
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