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).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb22ae095-e7b8-4f23-aa9d-cf34ec8dd477%2F02d9adc5-587b-4948-8489-2f4ee6652d82%2F4kqx9pg_processed.jpeg&w=3840&q=75)
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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