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Often there are cheaper, less accurate tests for diagnosing the presence of some conditions in a person, along with more expensive, accurate tests. Suppose we have two cheap tests and one expensive test, with the following characteristics. All three tests are positive if a person has the condition (there are no "false negatives"), but the cheap tests give "false positives". Let a person be chosen at random, and let D = {person has the condition}. The three tests are Test 1: Test 2: Test 3: P (positive test D) = .05; test costs $5.00 P (positive test D) = .03; test costs $8.00 P (positive test |D) = 0; test costs $40.00 We want to check a large number of people for the condition, and have to choose among three testing strategies: (i) Use Test 1, followed by Test 3 if Test 1 is positive. (ii) Use Test 2, followed by Test 3 if Test 2 is positive. (iii) Use Test 3. Determine the expected cost per person under each of strategies (i), (ii) and (iii). We will then choose the strategy with the lowest expected cost. It is known that about .001 of the population have the condition (i.e. P(D) = .001, P(D) = .999).

Often there are cheaper, less accurate tests for diagnosing the presence of some conditions in a person, along with more expensive, accurate tests. Suppose we have two cheap tests and one expensive test, with the following characteristics. All three tests are positive if a person has the condition (there are no "false negatives"), but the cheap tests give "false positives". Let a person be chosen at random, and let D = {person has the condition}. The three tests are Test 1: Test 2: Test 3: P (positive test D) = .05; test costs $5.00 P (positive test D) = .03; test costs $8.00 P (positive test |D) = 0; test costs $40.00 We want to check a large number of people for the condition, and have to choose among three testing strategies: (i) Use Test 1, followed by Test 3 if Test 1 is positive. (ii) Use Test 2, followed by Test 3 if Test 2 is positive. (iii) Use Test 3. Determine the expected cost per person under each of strategies (i), (ii) and (iii). We will then choose the strategy with the lowest expected cost. It is known that about .001 of the population have the condition (i.e. P(D) = .001, P(D) = .999).

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section: Chapter Questions
Problem 8CR
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Often there are cheaper, less accurate tests for diagnosing the presence of some conditions in a person, along with more expensive, accurate tests. Suppose we have two cheap tests and one expensive test, with the following characteristics. All three tests are positive if a person has the condition (there are no "false negatives"), but the cheap tests give "false positives". Let a person be chosen at random, and let D = {person has the condition}. The three tests are Test 1: Test 2: Test 3: P (positive test D) = .05; test costs $5.00 P (positive test |D) = .03; test costs $8.00 P (positive test |D) = 0; test costs $40.00 We want to check a large number of people for the condition, and have to choose among three testing strategies: (i) Use Test 1, followed by Test 3 if Test 1 is positive. (ii) Use Test 2, followed by Test 3 if Test 2 is positive. (iii) Use Test 3. Determine the expected cost per person under each of strategies (i), (ii) and (iii). We will then choose the strategy with the lowest expected cost. It is known that about .001 of the population have the condition (i.e. P(D) = .001, P(D) = .999).
Transcribed Image Text:Often there are cheaper, less accurate tests for diagnosing the presence of some conditions in a person, along with more expensive, accurate tests. Suppose we have two cheap tests and one expensive test, with the following characteristics. All three tests are positive if a person has the condition (there are no "false negatives"), but the cheap tests give "false positives". Let a person be chosen at random, and let D = {person has the condition}. The three tests are Test 1: Test 2: Test 3: P (positive test D) = .05; test costs $5.00 P (positive test |D) = .03; test costs $8.00 P (positive test |D) = 0; test costs $40.00 We want to check a large number of people for the condition, and have to choose among three testing strategies: (i) Use Test 1, followed by Test 3 if Test 1 is positive. (ii) Use Test 2, followed by Test 3 if Test 2 is positive. (iii) Use Test 3. Determine the expected cost per person under each of strategies (i), (ii) and (iii). We will then choose the strategy with the lowest expected cost. It is known that about .001 of the population have the condition (i.e. P(D) = .001, P(D) = .999).
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