Diagnostic tests of medical conditions can have several types of results. The te
ID: 2946351 • 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 (ndicates 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 Test Result + Test Result Column Total Condition Present 105 18 Condition Absent 25 52 Row Total 130 70 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. 0.853 (b) P(- | condition present): this is known as the false-negative rate 0.146 Enter a fraction, integer, or exact decimal. Do not a (c) P(- condition absent); this is known as the specificity of a test. 0.675 (d) P(+ condition absent); this is known as the false-positive rate 0.324 (e) P(condition present and +); this is the predictive value of the test. 0.525 (f) P(condition present and -) 0.125 Need Help? Talk to a TutorExplanation / Answer
Solution:
(a) P(+ | condition present) = P (+ and condition present)/P (condition present)
P (+|condition present) = 105/123
(b) P(? | condition present) = P (- and condition present)/P (condition present)
P (-|condition present) = 18/123 or 0.146
(c) P(? | condition absent) = P (- | condition absent)/ P (condition absent)
P (- | condition absent) = 52/77
(d) P(+ | condition absent) = P (+|condition absent)/ P (condition absent)
P (+ |condition absent) = 25/77
(e) P(condition present and +) = 105/200
(f) P (condition present and -) = 18/200