Q23 - When 100 people who have

[pypark]

The stimulus presents us with two premises and then a conclusion. I don't understand how the answer choice is C as opposed to answer choice B.

[giladedelman]

Thanks for the question!

We're told that 5 out of 100 people who have not used cocaine will test positive anyway, whereas 99 out of 100 who have used it will test positive. From these facts, the argument concludes that when a randomly chosen group is tested, the vast majority of positive results will be from people who have used cocaine.

On the surface, this seems to make sense; after all, cocaine users are much more likely to test positive. But there's a gap in the logic: we need to know something about the relative frequency of cocaine use in the general population. Consider this:

Say 1000 people are tested for cocaine. 900 have used the drug, and 100 have not. According to the premises, 891 users will test positive, while only 5 non-users will. So far, so good.

But what if, out of our 1000 people, there are only 10 users, and 990 non-users? Then we would expect 9 or 10 positive results from users, and 49 or 50 positive results from non-users. So in this case, the majority of those who test positive are the people who have not used cocaine.

This is why (C) is the correct answer. The argument fails to take into account the proportion of the population that has (or has not) taken cocaine.

(B), the answer you chose, is actually out of scope. When does the argument talk about the "average member of the population"? And, what property does it attribute to everyone? As far as I can tell, the answers to these questions are "never" and "none."

As for the other answer choices,

(A) is out of scope. The argument makes no value judgment.

(D) is the opposite of the truth: the argument explicitly says that 99 out of 100 cocaine users test positive, which necessarily implies that 1 user out of 100 does not.

(E) is way out of scope. The argument never advocates for testing (or for anything else).

Does that clear things up for you? Please let me know if you're still having trouble with this one.

[eagerlawstudent]

I still don't see why the correct answer is "c."

[geverett]

Going to revive this thread. However first you must watch this clip: http://www.youtube.com/watch?v=9PR_rzF8ofw

Alright one more question for you Gilad. So let's say that we did know the proportion of the total population that used cocaine. Even with that information would we not still have trouble drawing the conclusion in this argument? The reason being what if by "randomly" selecting a group of people they got a higher proportion or a lower proportion of cocaine users then is representative of the population as a whole. Could not the results end up being skewed then?

Should this answer choice instead read this way "Fails to take into account what proportion of the randomly chosen group have used cocaine and whether this proportion is representative of the population as a whole."



Also, eager law student. Return to Gilad's explanation. Check out these examples once more:

If 5% of people that have not used cocaine still test positive, and 99% of those who have used cocaine test positive then let's apply it to this example:

A giant hand sweeps down and picks up a group of 1,010 people from the earth at random.

- 1,000 people are selected who have not used cocaine and 5% test positive which means 50 people test positive for cocaine even though they have not used cocaine.

- 10 people are selected who have used cocaine and 9 of them test positive.

- Out of the total group we have 59 people who have tested positive for cocaine. 50 people who do not use cocaine and 9 people who do use cocaine. In this case the vast majority of people selected do not use cocaine. So the conclusion in the author's argument would not follow. Please let me know if this doesn't make sense still.

I chose B when I did this question as well. It's definitely wrong. They are not trying to attribute the properties of the "average member" of society to ever single member of the population. There is not mention of "average" in the stimulus as Gilad has mentioned.


Hey Gilad, what do you think of my initial question up top?

[giladedelman]

Thanks for the explanation, and no, the correct answer does not need to be rewritten. First of all, just because an argument overlooks something doesn't mean that if we plug that something back in, the argument needs to be perfect. So it's fine if we still have issues even if we do take into account the relative proportions. And, anyway, I think it's okay for us to assume that a randomly selected group will represent the population as a whole. The LSAT doesn't usually care about sample-size problems, unless there's a strong hint that it wants to go in that direction.

[Mab6q]

I have a question about two of the incorrect answer choices here.

A: I've seen this answer choice a few times, is there a question on the LSAT where this flaw has actually happened? I'm just not sure what it would look like.

B. Is this answer choice a part to whole flaw or an over-generalization? I always get the two mixed up.

Thanks.

[maryadkins]

Thanks for your questions.

A: I've seen this answer choice a few times, is there a question on the LSAT where this flaw has actually happened? I'm just not sure what it would look like.

Yes! It does come up. Example:

Anna is tall. --> Anna should never wear high heels.

The premise is a fact. The conclusion is a value judgment. That doesn't work.

B. Is this answer choice a part to whole flaw or an over-generalization? I always get the two mixed up.

I would say between the two, this is more of an over generalization. The average member isn't a "part" so much as the average, based on the whole—an imaginary "part" for data purposes. But more importantly, it sounds like you're kind of trying to pigeon hole answer choices into certain sub-categories of "flaw." This isn't the best use of your time. Some flaws aren't going to fit into pre-defined sub-categories, and regardless, it doesn't really matter...the better question is, "Does this answer choice articulate what this argument is doing that makes it bad?"

[jones.mchandler]

Thanks for the question!

We're told that 5 out of 100 people who have not used cocaine will test positive anyway, whereas 99 out of 100 who have used it will test positive. From these facts, the argument concludes that when a randomly chosen group is tested, the vast majority of positive results will be from people who have used cocaine.

On the surface, this seems to make sense; after all, cocaine users are much more likely to test positive. But there's a gap in the logic: we need to know something about the relative frequency of cocaine use in the general population. Consider this:

Say 1000 people are tested for cocaine. 900 have used the drug, and 100 have not. According to the premises, 891 users will test positive, while only 5 non-users will. So far, so good.

But what if, out of our 1000 people, there are only 10 users, and 990 non-users? Then we would expect 9 or 10 positive results from users, and 49 or 50 positive results from non-users. So in this case, the majority of those who test positive are the people who have not used cocaine.

This is why (C) is the correct answer. The argument fails to take into account the proportion of the population that has (or has not) taken cocaine.

(B), the answer you chose, is actually out of scope. When does the argument talk about the "average member of the population"? And, what property does it attribute to everyone? As far as I can tell, the answers to these questions are "never" and "none."

As for the other answer choices,

(A) is out of scope. The argument makes no value judgment.

(D) is the opposite of the truth: the argument explicitly says that 99 out of 100 cocaine users test positive, which necessarily implies that 1 user out of 100 does not.

(E) is way out of scope. The argument never advocates for testing (or for anything else).

Does that clear things up for you? Please let me know if you're still having trouble with this one.

the stimulus states that whenever a "randomly selected group" is chosen, the majority of those who test positive will be those who have actually used cocaine. the above example seems to be a non-randomly selected group. can we disregard the actual frequency of cocaine use in the population because the stimulus never states what that frequency is?

[WaltGrace1983]

the stimulus states that whenever a "randomly selected group" is chosen, the majority of those who test positive will be those who have actually used cocaine. the above example seems to be a non-randomly selected group. can we disregard the actual frequency of cocaine use in the population because the stimulus never states what that frequency is?

I'm not sure if I totally get where you are coming from. I'll try my best to explain this one more.

I think you may be confusing "randomly-selected" with "proportionate." I could be wrong. The argument's reasoning has failed because it gives us two different groups (those that have used cocaine and those that haven't) and makes a judgment about the population those groups belong to (the general population of people).

If you have NOT used cocaine → 5% chance of testing positive
If you have used cocaine → 99% chance of testing positive

These are the premises, let's take these as fact.

Now we get to the conclusion, saying that if we pick a random group and tested those people, the "vast majority" of those who test positive will be people who have used cocaine.

The question is this: what is the makeup of this randomly selected group? Who is in this group?

I looked up some facts on Google. There are about 300 million people living in America and about 2 million cocaine users.

Thus, if you were to have a list of every single person in America and pick 100 random names, you would have a less than 1% chance at picking a crackhead.

However, you would have a 99% chance at picking a non-crackhead.

In addition, you know that about 5% of those people chosen will test positive for cocaine even if they haven't done it.

So basically, it is HIGHLY likely that this randomly selected group of people will include about 4-5 of those who have been INCORRECTLY charged with using cocaine.

The point is this: we cannot take two proportions of two different groups of people and assume that we know the proportions as a whole UNLESS we know how proportionate each group is to that whole (wow that was a mouthful).

Here's another analogy: 80/100 Manhattan students score a 165+ on the LSAT while 20/100 non-Manhattan students score a 165+ on the LSAT. Therefore, from a randomly chosen group of LSAT takers, we can assume that the vast majority those who have scored a 165+ are Manhattan students.

The problem is that there are tens of thousands of LSAT takers but only a few thousand (I'd assume) Manhattan scholars.

[jones.mchandler]

The point is this: we cannot take two proportions of two different groups of people and assume that we know the proportions as a whole UNLESS we know how proportionate each group is to that whole (wow that was a mouthful).

that's basically what I was asking--sorry for the poorly worded question. what I was getting at is this: the stimulus states that when a "randomly chosen group of people is tested..".

In the examples given ITT, the group is always self selected, where we are assuming 990 non users, 900 users, or some combination where we are determining what allocation of users is being selected. We can self select this group because the stimulus does not state the overall proportion of cocaine users in the population.

i think my issue was bringing in outside knowledge in a detrimental manner in this question. as C points out, we do not in fact know the proportion of cocaine users in the population (as it is not given in the stimulus).

[maryadkins]

Great discussion here! Thanks for helping each other out on this.

[HyunaJ903]

Hi all,

I'm finding it very difficult to see C as the correct answer (if I were to see this question on the test) because, as far as I understand it, that is the whole point of the randomized test. How is it a "reasoning error" when it is not possible to "take into account what proportion of the population have used cocaine" because the test is being conducted on a randomly chosen group of people? I've read the explanations and though I do agree that would make the conclusion more accurate, the way the conclusion was confuses me.

Thanks for any help in advance

[ohthatpatrick]

Maybe this metaphor will do it for you.

When 100 regular adults are challenged to dunk a basketball, only 5 can do it.
When 100 NBA players are challenged to dunk a basketball, 99 can do it.
---------------------
Thus, if you randomly grab a group of people and challenge them to dunk a basketball, the vast majority of the people who can dunk will be NBA players.


If you were to go outside right now and grab 100 random people and challenge them to dunk a basketball, do you think that the majority of the people who can dunk will be NBA players?

Of course not ... because you're assuming that if you go outside right now and grab 100 random people, you probably won't have grabbed any NBA players.

Since NBA players are so rare in the population, most random samples of people will include zero NBA players.

Hence, the conclusion we made above is incorrect.

By the same logic, we can say that the author's conclusion about cocaine users is vulnerable to the same type of objection, if it turns out that cocaine users are so rare in the general population that most random groups of people would include zero cocaine users.