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. In a recent article, a team of doctors discuss using a fever of 38°C or higher as a diagnostic indicator of postoperative atelectasis (collapse of the lung) as evidenced by x-ray observation. For fever ≥ 38°C as the diagnostic test, the results for postoperative patients are given below. Condition Present Condition Absent Row Total Test Result + 74 39 113 Test Result − 83 74 157 Column Total 157 113 270 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. In a recent article, a team of doctors discuss using a fever of 38°C or higher as a diagnostic indicator of postoperative atelectasis (collapse of the lung) as evidenced by x-ray observation. For fever ≥ 38°C as the diagnostic test, the results for postoperative patients are given below.
| Condition Present | Condition Absent | Row Total | |
| Test Result + | 74 | 39 | 113 |
| Test Result − | 83 | 74 | 157 |
| Column Total | 157 | 113 | 270 |
Assume the sample is representative of the entire population. For a person selected at random, compute the following probabilities. (Enter your answers as fractions.)
(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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