Question

In Exercises 21–24, refer to the sample data in Table 4-1, which is included with the Chapter Problem. Assume that 1 of the 555 subjects included in Table 4-1 is randomly selected.

	Positive Test Result (Test shows drug use)	Negative Test Result (Test shows no drug use)
Subject Uses Drugs	45 (True Positive)	5 (False Negative)
Subject Does Not Use drugs	25 (False Positive)	480 (True Negative)

Drug Testing Job Applicants Find the probability of selecting someone who got a result that is a false negative. Who would suffer from a false negative result? Why?

Short answer

The probability of selecting a person who got a false negative result is 0.00901.

The employer will suffer from a false negative result because of the risk of hiring a person who uses drugs.

Step-by-step solution

Given information

Data are given in 4 categories depending on the true condition versus the test results for a sample of 555 people.

Define probability

Probability is the number of outcomes that result in an event (E) divided by the total number of outcomes.

It is computed using the formula

$P\left(E\right)=\frac{\text{Number}\text{of}\text{favourable}\text{outcomes}\text{of E}}{\text{Total}\text{number}\text{of}\text{outcomes}}$

Calculate the probability for a randomly selected individual

Let A be the event of selecting a person who got a false negative result.

The total number of persons who were tested is 555.

The number of persons who got a false negative test result is 5.

The probability of event A is

$$\begin{gathered} P\left(A\right)=\frac{Numberofpersonswhotestedfalsenegative}{Totalnumberofpersons} \\ =\frac{5}{555} \\ =0.00901 \end{gathered}$$

Therefore, the probability of selecting a person who got a false negative test result is 0.00901.

Explain the impact of the result

It can be concluded that the employer will suffer from a false negative test result.

The randomly selected person would test negative for the use of drugs when he actually uses them.

For such a subject, the employer would be at the risk of hiring a person who continues to use drugs.