I personally have used statistics in trying to challenge the reliability of drug testing results. Suppose the chance of a mistake in the taking and processing of a urine sample for a drug test is just 1 in 100. And your client has a “dirty” (i.e., positive) test result. Only a 1 in 100 chance that it could be wrong? Not necessarily. If the vast majority of all tests given— say 99 in 100—are truly clean, then you get one false dirty and one true dirty in every 100 tests, so that half of the dirty tests are false. T D = event that the test result is dirty T C = event that the test result is clean D = event that the person tested is actually dirty C = event that the person tested is actually clean P(T D|D) = 0.99 P(C) = 0.99 P(T D|C) = 0.01 P(D) = 0.01  What is the probability of a random test resulting in dirty?  What is the probability of person being clean given that their test re- sult is dirty? Is this consistent with the quote given?

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
Topic Video
Question

In an article that appears on the website of the American Statistical Asso-
ciation (www.amstat.org/meetings/jsm/2000 /usei/gunn.pdf, retrieved April 25, 2017),

Carlton Gunn, a public defender in Seattle, Washington, wrote about how he uses statis-
tics in his work as an attorney. He states:

I personally have used statistics in trying to challenge the reliability of drug
testing results. Suppose the chance of a mistake in the taking and processing
of a urine sample for a drug test is just 1 in 100. And your client has a “dirty”
(i.e., positive) test result. Only a 1 in 100 chance that it could be wrong? Not
necessarily. If the vast majority of all tests given— say 99 in 100—are truly
clean, then you get one false dirty and one true dirty in every 100 tests, so
that half of the dirty tests are false.
T D = event that the test result is dirty
T C = event that the test result is clean
D = event that the person tested is actually dirty
C = event that the person tested is actually clean
P(T D|D) = 0.99 P(C) = 0.99
P(T D|C) = 0.01 P(D) = 0.01
 What is the probability of a random test resulting in dirty?

 What is the probability of person being clean given that their test re-
sult is dirty? Is this consistent with the quote given?

Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Research Design Formulation
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
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