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# When 100 people who have not used cocaine are tested for

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Manager
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When 100 people who have not used cocaine are tested for [#permalink]  26 Oct 2005, 09:06
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When 100 people who have not used cocaine are tested for cocaine use, on average only 5 will test positive. By contrast, of every 100 people who have used cocaine 99 will test positive. 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.
A reasoning error in the argument is that the argument
(A) attempts to infer a value judgment from purely factual premises
(B) attributes to every member of the population the properties of the average member of the population
(C) fails to take into account what proportion of the population have used cocaine
(D) ignores the fact that some cocaine users do not test positive
(E) advocates testing people for cocaine use when there is no reason to suspect that they have used cocaine
Current Student
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I would have to sgo with B on this one.

OA?

FACT: Some Japanese "energy drinks" contain trace amounts of Coca leaf extracts that give people a jolt of energy for about \$8 a pop.
Manager
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some more inputs & then the OA
Current Student
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B makes sense ...it questions the validity of the sample or study ...are the 100 people representitive of the vast majority
Director
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E is irrelevant. A is not correct since any value is given in the conclusion. D is not correct because the argument does take into account the fact that some cocaine users do not test positive. It is said in the conclusion "the vast majority". Between C and B I choose C. Imagine you take 1010 people: 1000 of whom having used cocaine, and 10 of whom not having used cocaine. If we test the group of people not having used cocaine, we will have, on average, 50 positive tests. On the other group, we will have aprox. 9 positive test. Therefore, we will have 59 positive test, 50 from the non-users group and 9 from the users group. The vast majority in this case is not coming from the people who have used cocaine.

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A?
Director
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I vote for (B).

A sample group of 100 people cannot represent the whole population.
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Manager
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go C go..
Director
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automan wrote:
E is irrelevant. A is not correct since any value is given in the conclusion. D is not correct because the argument does take into account the fact that some cocaine users do not test positive. It is said in the conclusion "the vast majority". Between C and B I choose C. Imagine you take 1010 people: 1000 of whom having used cocaine, and 10 of whom not having used cocaine. If we test the group of people not having used cocaine, we will have, on average, 50 positive tests. On the other group, we will have aprox. 9 positive test. Therefore, we will have 59 positive test, 50 from the non-users group and 9 from the users group. The vast majority in this case is not coming from the people who have used cocaine.

Very good explanation.

However, (C) would be better if it was about "test groups", not "the population".

(C) fails to take into account what proportion of the population have used cocaine
(C') fails to take into account what proportion of the test group have used cocaine

What do you think?
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Director
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Re: CR : cocaine [#permalink]  27 Oct 2005, 05:58
i'll pick (C) on this one.

Here's why: if the proportion of the population that is tested have 99% people who have not taken cocaine, then you will have results where a majority of those will not have taken cocaine. (Argument falls apart)

On the other hand, if you reverse the proportion to 99% (take coke), then the argument will be true.

So, we need to know what the true proportion of the population is. But we dont have a clue.

Reason for dumping (B): The statement says 'vast majority' (and not EVERY INSTANCE) and therefore does not seem to attribute to every member of the population the properties of the average member of the population. (B) off.
Manager
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thanks...OA is C
Manager
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Re: CR : cocaine [#permalink]  27 Oct 2005, 08:05
C for me coz we don't know the how big the cocaine polulation in this society is. So maybe the fact is not representative at all.
Director
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gamjatang, the properties of the test group shold be the same that the properties of the population since the test group is randomly chosen.
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got this one wrong.
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hey ya......

Director
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automan wrote:
gamjatang, the properties of the test group shold be the same that the properties of the population since the test group is randomly chosen.

Well...true true.
I missed that point.
Thanks for reminding me.
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