A paper demonstrated the application of Bayes's Rule for making inferences about testosterone abuse among athletes. In a population of 1000 athletes, suppose 150 are illegally using testosterone Of the users, suppose 75 would test positive for testosterone. Of the nonusers, suppose 17 would test positive. a. Given that the athlete is a user, find the probability that a drug test for testosterone will yield a positive result. (This probability represents the sensitivity of the drug test.) (Simplify your answer.) b. Given the athlete is a nonuser, find the probability that a drug test for testosterone will yield a negative result. (This probability represents the specificity of the drug test.) 0.98 c. If an athlete tests positive for testosterone, use Bayes's Rule to find the probability that the athlete is really doping. (This probability represents the positive predictive value of the drug test.) (Round to three decimal places as needed.)
A paper demonstrated the application of Bayes's Rule for making inferences about testosterone abuse among athletes. In a population of 1000 athletes, suppose 150 are illegally using testosterone Of the users, suppose 75 would test positive for testosterone. Of the nonusers, suppose 17 would test positive. a. Given that the athlete is a user, find the probability that a drug test for testosterone will yield a positive result. (This probability represents the sensitivity of the drug test.) (Simplify your answer.) b. Given the athlete is a nonuser, find the probability that a drug test for testosterone will yield a negative result. (This probability represents the specificity of the drug test.) 0.98 c. If an athlete tests positive for testosterone, use Bayes's Rule to find the probability that the athlete is really doping. (This probability represents the positive predictive value of the drug test.) (Round 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...
Related questions
Question
Please work out c) and explain in detail
Transcribed Image Text:A paper demonstrated the application of Bayes's Rule for making inferences about testosterone abuse among athletes. In a population of 1000 athletes, suppose 150 are illegally using testosterone.
Of the users, suppose 75 would test positive for testosterone. Of the nonusers, suppose 17 would test positive.
a. Given that the athlete is a user, find the probability that a drug test for testosterone will yield a positive result. (This probability represents the sensitivity of the drug test.)
1
(Simplify your answer.)
b. Given the athlete is a nonuser, find the probability that a drug test for testosterone will yield a negative result. (This probability represents the specificity of the drug test.)
0.98
c. If an athlete tests positive for testosterone, use Bayes's Rule to find the probability that the athlete is really doping. (This probability represents the positive predictive value of the drug test.)
(Round to three decimal places as needed.)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON