#30 ## Positive Predictive Value Calculation for Drug Test### Scenario Description:A person is working for a company with a mandatory drug-testing policy. It is estimated that 2% of the employees use a certain drug. The company administers a drug test that is 96% accurate in identifying drug users. ### Problem Statement:Calculate the positive predictive value (PPV) for the drug test.### Explanation:The Positive Predictive Value (PPV) is the probability that subjects with a positive screening test are truly drug users. ### Formula:\[ \text{PPV} = \frac{\text{true positives}}{\text{true positives} + \text{false positives}} \]- True Positive: The test correctly identifies someone as a drug user.- False Positive: The test incorrectly identifies someone as a drug user.### Given Data:- Prevalence of drug use (P(D)) = 2% or 0.02- Sensitivity of the test (P(T+|D)) = 96% or 0.96### Calculation:Assuming a population size of 1000 employees for simplicity:- Expected number of drug users: \( 1000 \times 0.02 = 20 \)- Expected number of non-users: \( 1000 - 20 = 980 \)- True Positives: \( 20 \times 0.96 = 19.2 \)- False Positives: \( 980 \times (1 - 0.96) = 39.2 \)Using the PPV formula:\[ \text{PPV} = \frac{19.2}{19.2 + 39.2} \approx 0.329 \]Thus, the positive predictive value is approximately **32.9%**.### Input Area:The positive predictive value is [ ].*(Type an integer or decimal rounded to three decimal places as needed.)*---In an educational context, learners should understand the relationship between prevalence, sensitivity, and PPV. Practical application of these concepts helps in interpreting test results accurately.

Positive predictive value (PPV):The positive predictive value is the probability that following a…

Assume that a person is working for a company that has a mandatory drug-testing policy. It is estimated that 2% of the employees use a certain drug, and the company is giving a test that is 96% accurate in identifying users of this drug. Calculate the positive predictive value for the drug test. The positive predictive value is (Type an integer or decimal rounded to three decimal places as needed.)

Assume that a person is working for a company that has a mandatory drug-testing policy. It is estimated that 2% of the employees use a certain drug, and the company is giving a test that is 96% accurate in identifying users of this drug. Calculate the positive predictive value for the drug test. The positive predictive value is (Type an integer or decimal rounded to three decimal places as needed.)

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks