#23 - When 100 people who have not used cocaine are tested

[abajaj]

Hi,

I'm unable to understand any aspect of the correct answer choice of this question (C). The last two choices I had left were B and C. I feel like I can refute answer choice C because, according to my understanding, it doesn't matter what the proportion of the population has used cocaine because the conclusion of the passage says "the vast majority of those who test positive will be people who have used cocaine". So the mix of the population doesn't really matter in my head because the cocaine test will determine that?

Could someone please explain this one to me? Thank you!!!

[Nikki Siclunov]

Here's what we have: the cocaine test has a false positive rate of 5% (out of 100 non-users, 5 test positive) and a false negative rate of 1% (out of 100 users, 1 tests negative).

This information alone does not allow us to conclude that in a random group of people, most of those who test positive will be actual cocaine users. Here's why: Let's imagine that the "randomly chosen group of people" contains virtually no cocaine users to begin with (Scenario 1). In that case, 5 out of every 100 people will test positive even though they are clean. Even if 3 out of those 100 people were actual users (Scenario 2) and all 3 test positive for cocaine, given the high false-positive rate of 5% we can expect that 5 of the remaining 97 non-users would test positive as well. Again, the majority of those who test positive would not be actual users.

Now, let's imagine you drew your sample from a group of investment bankers, half of whom have used cocaine (Scenario 3). You'll probably get 2-3 false negatives, but the vast majority of those who test positive will be cocaine users. In this scenario, the conclusion would be reasonable.

As you can see, the author fails to take into account what proportion of the population tested used cocaine: if that percentage is negligible (as in Scenarios 1 and 2), then the conclusion makes no sense. On the other hand, if the percentage is significant (Scenario 3), the conclusion makes a lot more sense.

Hope this clears things up!

[abajaj]

Thank you! This clears up my question.

[yrivers]

Can someone explain this problem and answer pls? It's the LSAT problem re: cocaine use among people.

[Dave Killoran]

Hey Y,

As a starter, here is an explanation of a portion of this problem that you might find useful: lsat/viewtopic.php?t=2436&p=6254

Thanks!

[s_takesonLSAT]

I did not end up choosing C because I thought to myself, even if the stimulus had included that one person out of a million abuses cocaine then that's still a considerable amount of people. Therefore the proportion of the population that uses cocaine would not help with the conclusion.
I did read another explanation that referred to who was being sampled, teachers vs investment bankers, but I didn't feel like the answer choice was referring to the sample but the population as a whole. Who was being tested would help, but how was I supposed to understand that from C. When I read "proportion of the population" I thought of a ratio but was it referring to job positions, prisoners, young adults, etc?

My thought process on the other answer choices:
A. I disagreed with this one because I didn't feel like a value judgment was made but I ended up choosing it. Looking back this is a worse answer choice I should have gone with C, but I just strongly disagreed with C.
B. The average member of the population that abuses cocaine was not discussed
C. explained above
D. Irrelevant
E. Nope

[Luke Haqq]

Hi s_takesonLSAT!

Thanks for the question, and happy to explain answer (C) more in-depth.

We know from the question stem that this is a flaw in the reasoning question. Answer choice (C) states that the author of the stimulus "fails to take into account what proportion of the population have used cocaine."

The stimulus provides information about two different groups who are tested--the first group being 100 people who have not used cocaine (out of which there will be 5 falsely testing positive), the second group being 100 who have used it (99 out of 100 accurately testing positive). From information about these two groups, the author reaches the conclusion, "Thus, 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."

This conclusion is problematic because we don't know more about the population that the "randomly chosen group" is taken from--for example, it might be taken out of a population that has no cocaine users at all. In that case, the information provided about the first group suggests 5% of this group will falsely test positive. Given that, it wouldn't be warranted to conclude that in any randomly chosen group, "the vast majority of those who test positive will be people who have used cocaine."

Suppose the randomly chosen group is of a 100 people, and testing reveals 5 positive results for cocaine use. The information in the stimulus is saying that it is possible that all 100 people were not cocaine users and those 5 results were false positives, or it might instead be the case that one or more of those 5 results were accurate. Without more information about the population being tested, we simply don't know how to interpret positive test results--e.g., whether they are false positives or accurate measurements. This is what answer choice (C) addresses--we don't know what proportion of the population from which the group is taken uses cocaine, which makes the author's conclusion flawed.

[ahorita]

How can we recognize this flaw in such a short time given? Is there any tips to notice a hint while reading down the stimulus for stimulus like this?

[KelseyWoods]

Hi ahorita!

The way to get faster at anything on the LSAT is to practice. Studying for the LSAT is like learning a language--it takes time to become fully fluent. At first you will be slow, and as your familiarity with LSAT language increases, you will become gradually faster. All Flaw questions boil down to the premises given do not fully prove the conclusion as stated. So your first task in identifying any flaw is simply to identify the conclusion, identify the premises, and ask yourself why the premises given do not fully prove the conclusion as stated. These numbers and percentages flaws are fairly common the test. So the more familiar you are with them, the faster you will become at spotting them. Study this flaw so that you will recognize it and similar flaws more quickly in the future.

So keep practicing! LSAT mastery takes time and repetition.

Hope this helps!

Best,
Kelsey

[ashpine17]

If we take the flawed conclusion at face value, is it assuming the majority of people tested in the "randomly selected group" are actual cocaine users?