Probability Question

Question

Refer to the sample data for​ pre-employment drug screening shown below. If one of the subjects is randomly​ selected, what is the probability that the test result is a false​ positive? Who would suffer from a false positive​ result? Why?

Pre-Employment Drug Screening Results	Positive test result	Negative test result
	Drug Use Is Indicated	Drug Use Is Not Indicated
Subject Uses Drugs	46	10
Subject Is Not a Drug User	18	28

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Part 1

The probability of a false positive test result is

enter your response here.

​(Round to three decimal places as​ needed.)

Answer 1

Pr(false positive)

=18/(18+46+10+28)

= 18/102

=about .176470588

= 17.647%

If this is a DUI test, the driver or pilot gets falsely arrested and loses. The towing company

makes some money towing & storing the vehicle. the car owner loses their car, the

passengers get delayed and inconvenienced.

if this is a drug test given to a parolee or probationer, they get falsely arrested

and lose, but so does everyone else involved "lose," for wasting their time.

the chemist or lab technician lose some credibility when or if the false results are discovered

If this is a sports, school or employment test, the athlete, student or employee unfairly loses

their Olympic gold medal, gets suspended from school or loses their job

A false positive is a Type I error, for mistakenly rejecting the true null hypothesis

Pr(false positive/positive)

= probability a postive test result is a false positive

= 18/46

= .3913043

= 39.130%

Pr(positive)

= (18+46)/102

=64/102

=.62745098

= 67.451%

Pr(false negative)

=10/102

=.098039215

=9.804%

A false negative is a Type II error

for falsely rejecting a True null hypothesis

A true negative is correcctly failing to reject a true null hypothesis

A true positive is correctly rejecting a false null hypotheis