Diagnostic tests of medical conditions can have several types of results. The te
ID: 3228075 • Letter: D
Question
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 the condition are shown.
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 ).
Explanation / Answer
a) P(+ | condition present) = 108/129 = 36/43
b) P( | condition present) = 21/129 = 7/43
c) P( | condition absent) = 49/71
d) P(+ | condition absent) = 22/71
e) P(condition present and +) = 108/200 = 27/50
f) P(condition present and ) = 21/200