Finding the probability of a false positive drug test from tabulated data

Intro

Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we're going to learn how to find the probability of a false positive drug test from tabulated data.  Here's our problem statement: 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 results and why?

Part 1

OK, the first part of this problem is asking us for the probability of a false positive.  We have the option to put this time-related data into StatCrunch or Excel.  I actually prefer Excel, and I'll show you why here in a moment because --- well, I actually have the data here in Excel already loaded.  So the reason why I love this in Excel is because I can just select the data here, and notice how here at the bottom of my Excel window, I've got all of these summary stats.  The sum is what we're looking for.  This is the whole that we're going to use to calculate our probability.  Remember the probability is the part over the whole.  Well, this makes calculating the whole very easy.

The part is just the false positive test result.  A false positive is someone who tests positive but doesn't use.  And that's this space right here.  So 15 is my part, and 107 is my whole.  So if I just take my calculator and take 15 divided by 107, I get my probability.  We're asked around to three decimal places.  And notice there's no percent sign here next to the answer field.  So they want us to submit our answer in decimal form.  Excellent!

Part 2

Now the second part of his problem asks, "Who would suffer from a false positive result and why?"  Well, let's look through our answer options here.  Answer option A says, "The employer would suffer because the person tested would not be suspected of using drugs when in reality he or she does use drugs."  Well, no, a false positive means that you're testing positive but you don't use.  So that can't be right.  Answer option B says, "The person tested will suffer because he or she would not be suspected of using drugs when in reality he or she does use drugs."  Again, that's the opposite of a false positive.  That's actually a false negative.  A false positive is where they're not using but they test positive.  So that's not what we want here.

Answer option C: "The employer will suffer because the person tested would be suspected of using drugs when in reality he or she does not use drugs."  Well, the second part of this statement is true, but how does the employer suffer from that?  I mean more of the suffering is going to be from the individual because someone who is subjected to a false positive drug test, they're going to be treated like a user even though they aren't.  And so in the very least, their reputation in the workplace is going to suffer.  You know, uh, you know, in most cases it's probably going to mean you're losing your job.  So it's really the person who's going to suffer more than the employer.

Answer option D says, "The person tested will suffer because he or she would be suspected of using drugs when in reality he or she does not use drugs."  That's what we're looking for.  Fantastic!

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