In article <[EMAIL PROTECTED]>,
Alan McLean <[EMAIL PROTECTED]> wrote:
>Hi to all.
>A friend of mine has a problem. The following is my understanding of the
>problem.
>She has a box of, say, 50 physically identical (to the eye, anyway)
>objects, but they vary in chemical composition - there may be half a
>dozen or so different compositions in the box. She has another of these
>objects, physically similar to those in the box. She needs to test the
>objects in the box to determine if the single object came from, or could
>have come from, this box. If one of the box objects matches the single
>object in chemical composition (presumably this match is within some
>level of precision) then she will be able to say that the object
>(probably) came from the box (or could have come from the box). If none
>of the box objects matches the single object, then the latter could not
>have come from the box.
>She has been asked to give a statistical formula to identify the sample
>size she will need to take to answer the question.
>The problem is not very clear - I think the people asking for the
>formula are not statisticians, but managers who think that anything that
>can possibly be quantified should be quantified. But maybe someone cna
>come up with a suggestin I can pass on.
The worst situation is that in which all 50 are different.
In that case, if there is a match, the match is equally
likely to come at each trial. To answer the question with
certainty, it will be necessary to test all of the objects
in the box.
Other distributions of objects make it easier. If one knows
that there are only two kinds of objects there, to be certain
would require testing objects until two different types occur.
Other scenarios, and making probability statements, will
require other assumptions.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
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