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
icon
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).
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).
Expert Solution
steps

Step by step

Solved in 6 steps with 5 images

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman