Question

Drug testing Athletes are often tested for use of performance-enhancing drugs. Drug tests aren’t perfect—they sometimes say that an athlete took a banned substance when that isn’t the case (a “false positive”). Other times, the test concludes that the athlete is “clean” when he or she actually took a banned substance (a “false negative”). 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

Part (a) The truth about $8\%$the time machine will say that the people are lying.

Part (b) The truth about $8\%$the time machine will say that the people are lying.

Step-by-step solution

Part (a) step 1. Given information

The probability of a false positive is $0.08$.

Part (a) Step 2. Concept Used 

Definition of relative frequency:-A relative frequency is the fraction of times an answer occurs that is the relative frequencies divide each frequency by the total number of students in the sample.

Part (a) Step 3. Calculation

A relative frequency is the fraction of times an answer occurs that is the relative frequencies divide each frequency by the total number of students in the sample.

That is $$\begin{gathered} =0.08\times 100 \\ =8\% \end{gathered}$$

This probability as a long-run relative frequency use a polygraph machine on many people who are all telling the truth about $8\%$the time machine will say that the people are lying.

Part (b) Step 1. Explanation 

A relative frequency is the fraction of times an answer occurs that is the relative frequencies divide each frequency by the total number of students in the sample. It seems that claiming someone is lying when telling the truth is a more serious error in this case a false positive or a false negative.