Refer to the table which summarizes the results of testing for a certain disease. If one of the results is randomly selected, what is the probability that it is a false negative (test indicates the person does not have the disease when in fact they do)? What does this probability suggest about the accuracy of the test? Positive Test Negative Test 만 Subject has the disease Subject does not have the disease Result 111 11 Result 4 172 A. 0.0348 ; The probability of this error is low so the test is fairly accurate. B. 0.0369 ; The probability of this error is low so the test is fairly accurate. C. 0.591 ; The probability of this error is high so the test is not very accurate. D. 0.0134 ; The probability of this error is low so the test is fairly accurate. does not have the disease when in fact they do? What does this probability suggest about the accuracy of the test? Positive Test Negative Test Result Result Subject has the disease 111 4 Subject does not have the disease 11 172 O A.0.0348;The probability of this error is low so the test is fairly accurate O B.0.0369;The probability of this error is low so the test is fairly accurate OC.0.591;The probability of this error is high so the test is not very accurate O D.0.0134;The probability of this error is low so the test is fairly accurate
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From the table, this would be represented by the "Negative Test Result" column intersecting with "Subject has the disease" row. Show more…
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Find the indicated probability: Refer to the table which summarizes the results of testing for a certain disease. Positive Test Result Negative Test Result Subject has the disease 120 4 Subject does not have the disease 13 172 If one of the results is randomly selected, what is the probability that it is a false negative (test indicates the person does not have the disease when in fact they do)? What does this probability suggest about the accuracy of the test? 0.0421; The probability of this error is low, so the test is fairly accurate. 0.570; The probability of this error is high, so the test is not very accurate. 0.0323; The probability of this error is low, so the test is fairly accurate. 0.0129; The probability of this error is low, so the test is fairly accurate.
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Find the indicated probability. Refer to the table which summarizes the results of testing for a certain disease. If one of the results is randomly selected, what is the probability that it is a false positive (test indicates the person has the disease when in fact they don't)? What does this probability suggest about the accuracy of the test? 1) 0.0220; The probability of this error is low, so the test is fairly accurate. 2) 0.0952; The probability of this error is high, so the test is not very accurate. 3) 0.146; The probability of this error is high, so the test is not very accurate. 4) 0.421; The probability of this error is high, so the test is not very accurate.
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Suppose that a certain disease is present in $10 \%$ of the population, and that there is a screening test designed to detect this disease if present. The test does not always work perfectly. Sometimes the test is negative when the disease is present, and sometimes it is positive when the disease is absent. The table below shows the proportion of times that the test produces various results. a. Find the following probabilities from the table: $P(D), P\left(D^{c}\right), P\left(N \mid D^{c}\right), P(N \mid D)$ b. Use Bayes' Rule and the results of part a to find $P(D \mid N)$ c. Use the definition of conditional probability to find $P(D \mid N)$. (Your answer should be the same as the answer to part b.) d. Find the probability of a false positive, that the test is positive, given that the person is disease-free. e. Find the probability of a false negative, that the test is negative, given that the person has the disease. f. Are either of the probabilities in parts $\mathrm{d}$ or e large enough that you would be concerned about the reliability of this screening method? Explain.
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Bayes’ Rule
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