The prevalence of a disease in the general population is 0.2%. A diagnostic test is developed that correctly predicts the disease state of a sick person 90% of the time and of a healthy person 95% of the time. a. Draw the Venn diagram for the problem and indicate the number of people out of 10,000 people total that fall into the diagram's four bins. The bins should be defined by disease state (D+/D-) and test result (T/T) where + indicates you have the disease and indicates that you do not. b. What is the probability that a person with a positive test result actually has the disease? c. What is the probability that a person with a negative test result does not have the disease? d. Does the test have practical value for detecting people with the disease and why?
The prevalence of a disease in the general population is 0.2%. A diagnostic test is developed that correctly predicts the disease state of a sick person 90% of the time and of a healthy person 95% of the time. a. Draw the Venn diagram for the problem and indicate the number of people out of 10,000 people total that fall into the diagram's four bins. The bins should be defined by disease state (D+/D-) and test result (T/T) where + indicates you have the disease and indicates that you do not. b. What is the probability that a person with a positive test result actually has the disease? c. What is the probability that a person with a negative test result does not have the disease? d. Does the test have practical value for detecting people with the disease and why?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 23PPS
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Transcribed Image Text:The prevalence of a disease in the general population is 0.2%. A diagnostic test is developed that
correctly predicts the disease state of a sick person 90% of the time and of a healthy person 95% of the
time.
a. Draw the Venn diagram for the problem and indicate the number of people out of 10,000 people
total that fall into the diagram's four bins. The bins should be defined by disease state (D+/D¯) and
test result (T+/T) where + indicates you have the disease and indicates that you do not.
b. What is the probability that a person with a positive test result actually has the disease?
c. What is the probability that a person with a negative test result does not have the disease?
d. Does the test have practical value for detecting people with the disease and why?
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