2 Drug testing Athletes are often ... [FREE SOLUTION]

91影视

The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset 91影视 Explanations$ Math

4th Edition 路 809 pages

ISBN: 9781319113339

Chapter 5: 2 (page 293)

Drug testing Athletes are often tested for use of performance-enhancing drugs. Drug tests aren鈥檛 perfect鈥攖hey sometimes say that an athlete took a
banned substance when that isn鈥檛 the case (a 鈥渇alse positive鈥�). Other times, the test concludes that the athlete is 鈥渃lean鈥� when he or she actually took a
banned substance (a 鈥渇alse negative鈥�). For one commonly used drug test, the probability of a false negative is 0.03.
(a) Interpret this probability as a long-run relative frequency.
(b) Which is a more serious error in this case: a false positive or a false negative? Justify your answer.

Short Answer

Expert verified

Part (a) As the sample size increases over the long-run relative frequency, the probability of getting a false negative will decrease.

Part (b) False-negative is considered to more serious error than allowing an athlete when the banned substance is taken.

Step by step solution

Part (a) Step 1 Explanation

It is given that the probability of getting a false negative is equal to 0.03. It means that 3% of the risk of failing to detect the significant difference is accepted. As the sample size increases over the long-run relative frequency, the probability of getting a false negative will decrease.

Part (b) Step 1. Justification

False-negative is considered to more serious error than allowing an athlete when the banned substance is taken. It results in the impact of the sports and will create biasness. But in case of false positives, not allowing an athlete who is eligible and didn鈥檛 take a banned substance will not affect the sports except for the biasness of an individual. More stringent action can be taken to avoid the selection of athlete who has taken the banned substance.