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A Screening Test for a Certain Disease Is Used in a Large

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A screening test for a certain disease is used in a large population of people of whom 1 in 1000 actually have the disease. Suppose that the false positive rate is 1% and the false negative rate is 0.5%. Thus a person who has the disease tests positive for it 99.5% of the time, and a person who does not have the disease tests negative for it 99% of the time.
(a) What is the probability that a randomly chosen person who tests positive for the disease actually has the disease?
(b) What is the probability that a randomly chosen person who tests negative for the disease actually has the disease?


Definitions:

Description

The act of detailing or representing something verbally or in written form to convey its characteristics, functions, or qualities.

Empirical Data Collection

The process of gathering information by direct or indirect observation or experience, without theoretical speculation.

Statistical Testing

A mathematical procedure to determine if there is a significant difference between groups or conditions in a study.

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