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 + 104 26 130 Test Result − 21 49 70 Column Total 125 75 200 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 −).

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 +	104	26	130
Test Result −	21	49	70
Column Total	125	75	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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