When 100 people who have not used cocaine are tested for cocaine use, on average only 5 will test positive. By contr...

AllisonJ on April 1, 2021

Explanation

I can see how the answer choice is C but could I have a further explanation?

Replies

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Victoria on April 13, 2021

Hi @AllisonJ,

Happy to help!

The argument concludes that, when a randomly chosen group of people is tested for cocaine use, the vast majority of those who test positive will be people who have used cocaine.

Why? Because 99 out of every 100 people who have used cocaine will test positive and 5 out of every 100 people who have not used cocaine will usually falsely test positive.

What is the error here? The argument fails to account for the proportion of the population who have actually used cocaine.

As an example, let's say that we test 1000 people for cocaine use. Out of these 1000 people, let's say that 990 have used cocaine and 10 have not. Based on the proportions above, we can expect that 980 users will test positive whereas maybe 1 non-user will test positive.

However, what if we flip this? What if we test 1000 people for cocaine use, but only 10 of them have actually used cocaine? Based on the proportions above, we could expect that at least 9 users would test positive and at least 49 non-users would falsely test positive. In this case, the vast majority of those who tested positive are people who have not used cocaine, contradicting the conclusion drawn in the stimulus.

Hope this helps! Please let us know if you have any further questions.

RileyDelRey on September 23, 2022

Can you please provide more clarification why not A

Abigail-Okereke on November 14, 2022

I'm sorry, I still don't understand the flaw in this stimulus or why c is correct. I chose a like Riley; can someone please explain why A doesn't work?

Emil-Kunkin on November 17, 2022

A tells us the argument is flawed because it contains a value judgement. However, the argument does not have a value judgement. A value judgement is to say that something is good or bad. However the argument is purely descriptive. It is not saying that cocaine use is bad or good, just talking about the relative incidence of false negatives or positives.

C is correct because the author concludes that most positives are true. However, if 1 million people have never used it, and 100 have, and all are tested, there will be 99 true positives, and 50,000 false positives. So, C shows why the conclusion does not have to be true.