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b. Consider a patient in the "at risk" population. Of those with HIV, what percentage test positive? Of those who test positi what percentage have HIV? Explain why these two percentages are different. Of the patients in the "at risk" population with HIV,% test positive. Of the patients in the "at risk" population who test positive, % have HIV. (Type an integer or decimal rounded to the nearest tenth as needed.)

b. Consider a patient in the "at risk" population. Of those with HIV, what percentage test positive? Of those who test positi what percentage have HIV? Explain why these two percentages are different. Of the patients in the "at risk" population with HIV,% test positive. Of the patients in the "at risk" population who test positive, % have HIV. (Type an integer or decimal rounded to the nearest tenth as needed.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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24. answer part b

 

--- ### HIV Detection Rates and Incidence in Different Populations The Department of Health of a certain state estimates a 10% rate of HIV for the "at-risk" population and a 0.3% rate for the general population. Tests for HIV are 95% accurate in detecting both true negatives and true positives. Random selection of 5000 "at-risk" people and 20,000 people from the general population results in the following table. Use the table below to complete parts (a) through (e). #### Table: HIV Testing Results | Population | Test Positive | Test Negative | Test Positive | Test Negative | |--------------------|---------------|---------------|---------------|---------------| | | At-Risk | | General | | | Infected | 465 | 35 | 47 | 13 | | Not Infected | 221 | 4279 | 998 | 18,942 | --- #### Analysis Questions **a. Verify that incidence rates for the general and "at risk" populations are 0.3% and 10%, respectively. Also, verify that detection rates for the general and "at risk" populations are 95%. How would you verify the incidence rates?** *Multiple Choice Options:* A. Divide the number of infected patients by the number of uninfected patients. B. Divide the number of uninfected patients by the total number of patients. C. **Divide the number of infected patients by the total number of patients. (Correct Answer)** D. Divide the number of uninfected patients by the number of infected patients. *How would you verify the detection rates?* A. Divide the total number of false negatives by the total number of patients. B. Divide the total number of true negatives by the total number of patients. C. **Divide the total number of true positives by the total number of patients. (Correct Answer)** D. Divide the total number of false positives by the total number of patients. **b. Consider a patient in the "at-risk" population. Of those with HIV, what percentage test positive? Of those who test positive, what percentage have HIV? Explain why these two percentages are different.** *Question Prompts:* - Of the patients in the "at-risk" population with HIV, **93.0%** test positive. - Of the patients
Transcribed Image Text:--- ### HIV Detection Rates and Incidence in Different Populations The Department of Health of a certain state estimates a 10% rate of HIV for the "at-risk" population and a 0.3% rate for the general population. Tests for HIV are 95% accurate in detecting both true negatives and true positives. Random selection of 5000 "at-risk" people and 20,000 people from the general population results in the following table. Use the table below to complete parts (a) through (e). #### Table: HIV Testing Results | Population | Test Positive | Test Negative | Test Positive | Test Negative | |--------------------|---------------|---------------|---------------|---------------| | | At-Risk | | General | | | Infected | 465 | 35 | 47 | 13 | | Not Infected | 221 | 4279 | 998 | 18,942 | --- #### Analysis Questions **a. Verify that incidence rates for the general and "at risk" populations are 0.3% and 10%, respectively. Also, verify that detection rates for the general and "at risk" populations are 95%. How would you verify the incidence rates?** *Multiple Choice Options:* A. Divide the number of infected patients by the number of uninfected patients. B. Divide the number of uninfected patients by the total number of patients. C. **Divide the number of infected patients by the total number of patients. (Correct Answer)** D. Divide the number of uninfected patients by the number of infected patients. *How would you verify the detection rates?* A. Divide the total number of false negatives by the total number of patients. B. Divide the total number of true negatives by the total number of patients. C. **Divide the total number of true positives by the total number of patients. (Correct Answer)** D. Divide the total number of false positives by the total number of patients. **b. Consider a patient in the "at-risk" population. Of those with HIV, what percentage test positive? Of those who test positive, what percentage have HIV? Explain why these two percentages are different.** *Question Prompts:* - Of the patients in the "at-risk" population with HIV, **93.0%** test positive. - Of the patients
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