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 + 103 27 130 Test Result − 21 49 70 Column Total 124 76 200 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 −).
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 + | 103 | 27 | 130 |
| Test Result − | 21 | 49 | 70 |
| Column Total | 124 | 76 | 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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