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 + 27 103 130 Test Result 25 70 45 Column Total 200 128 72 Assume the sample is representative of the entire population. For a person selected at random, compute the following probabilities. (Enter your answers as fractions.) P( condition present); this is known as the sensitivity of a test. (a) P( (b) 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. P(condition present and +); this is the predictive value of the test (e) (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 + 27 103 130 Test Result 25 70 45 Column Total 200 128 72 Assume the sample is representative of the entire population. For a person selected at random, compute the following probabilities. (Enter your answers as fractions.) P( condition present); this is known as the sensitivity of a test. (a) P( (b) 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. P(condition present and +); this is the predictive value of the test (e) (f) P(condition present and -).
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section: Chapter Questions
Problem 3P: Dividing a Jackpot A game between two pIayers consists of tossing coin. Player A gets a point if the...
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Transcribed Image Text: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 +
27
103
130
Test Result
25
70
45
Column Total
200
128
72
Assume the sample is representative of the entire population. For a person selected at random, compute the following probabilities. (Enter your answers as fractions.)
P( condition present); this is known as the sensitivity of a test.
(a)
P(
(b)
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.
P(condition present and +); this is the predictive value of the test
(e)
(f)
P(condition present and -).
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