# A Reasoning Error?

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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.

What do you think answer is?

I would pick 'a'. Could you explain 'b'?

Thank you
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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. "

This is true, although that is not true that the test will permit by neglect a 6% margin of error.

There will be drug consumers and innocents in unknown proportion.

If the vast majority is positive, this cannot be put down to errors that the test allows(error margin is narrow).

It means the majority of positives is really positive.

"attributes to every member of the population the properties of the average member of the population"

This is not necessarily true. The average members do not take drugs. The margin of error is close to 5%.
I don't see any value judgments nor any mention of advocating that people be tested, so I would eliminate A and E immediately.

CJ
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I pick "c".

S.
I pick "c".
That choice seems to have a lot to recommend it, doesn't it!

CJ
"fails to take into account what proportion of the population have used cocaine."

You do not have to take into account the proportion. The result and the narrow margin of error of the tests reveal the truth.
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"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."

Whether the red part is true is solely determined by the narrow margin of error of tests when innocents are proven addicts, and the precision (95%) of tests when addicts are proven addicts. The result is independent of what the constitution of the group is so why take it into account.

The vast majority of positives = it implies there are many positives, which means the proportion has to mean there are much more addicts in the tests.

But we do not have to take the proportion into account. the result speaks for itself and for the proportion
What is your choice, Peter? A, B, C, D, or E?

CJ
When I was learning about "false positives" I think we talked about this - C seems to be the one that fits my recollection of how it was explained to me.
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