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# PT4.S1.Q23 - When 100 people who have not used cocaine

Legacy Member
edited June 2018 35 karma

Hi All,

Having a bit of trouble getting my head around this question. Originally chose B, but correct answer is C. Had a bit of a crack at it, anyone please elaborate or correct me on my thinking!

Basically, the argument is assuming what is true of the stats for the sample is true when the test is used for the general public. However, the argument does not provide any information/we do not have any way of confirming whether this is correct when applied to the general public, hence its flaw is '(C) fails to take into account what proportion of the population have used cocaine'.

Admin note: edited title

• Alum Member Sage
1861 karma

I think you pretty much got it!

We know for sure that B is wrong because it makes the same flaw C points out. We don't know what the properties of the average member of the population are, since we don't know the population itself. We're just given specific sample populations (100 people who have not used and 100 people who have), from which we're trying to make a broader (possibly incorrect) inference.

Like you reasoned, we can't be sure of the ratio of cocaine to non-cocaine users in the general population. What if the population consists of 3000 people, of which 2900 are not cocaine users and the remaining 100 are? According to our premises, of the 2900 people who are not cocaine users, 145 people will test positive. While of the remaining 100, 99 will test positive. So the conclusion of the argument no longer holds -- the majority of those who test positive will be people who have not used cocaine.
For the author's conclusion to hold, the author has to "take into account what proportion of the population that have used cocaine," as C states.

• Legacy Member
35 karma

Thanks for breaking it down like that, really cleared it up for me!