At 03:57 PM 1/17/01 -0500, Rich Ulrich wrote:
> - Okay, here is my answer before I repeat the official ones.
>The "greatest possible difference" is *at least* one foot.
>If this is a dedicated math question, the aspect of roundoff should
>give "one foot (minimum)"; and any slightest introduction of realism
>implies some *error-in-measurement* to be added on.
ok ... even if so ... what is a reasonable error that could be added on to
come to the conclusion of answer D? this would have to imply that two
errors in the opposite direction occur simultaneously ... the error
overshoots truth one way ... hence you round up ... whereas the errors
undershoots truth the other way ... hence you round down ... this is not "
... slightest introduction of realism ... "
>Thus, the "greatest possible difference" is one-foot, plus the
>amounts on BOTH SIDES of the error distribution -- whether that is
>in quarter-inches or angstroms. => something more than 1 foot.
> - Now, look at the answers.
>
> > >
> > >A. One jump could be up to 1/4 foot longer than the other.
> > >B. One jump could be up to 1/2 foot longer than the other.
> > >C. One jump could be up to 1 foot longer than the other.
> > >D. One jump could be up to 2 feet longer than the other.
> > >
rich tries to clarify this problem but ... i don't think is successful IN
RELATION TO THE GIVEN ANSWERS
now, we are assuming aren't we that someone did the measuring WITH a
"qualified measuring rule ... we know of course that (just like the "chain"
for measuring first downs in a football game) it could be stretched more or
less taut ... but, what would be some reasonable limit for tautness or
UNtautness without the competitor screaming bloody murder??? thus, we could
say ... if the distance was measured withOUT error .. the greatest distance
would be 1 foot ...
given that there is no indication in this item of anything to do with
MEASUREMENT ERROR ... WE CANNOT ASSUME ANYTHING ABOUT THAT CONCEPT
i would suggest that given the way this item is stated ... that is, what is
said and what is not said ... we have to assume that whatever the
measurement was ... it was correct and, all that would be done given that
it is said "to the nearest foot" ... that either rounding up or down
according to the standard system of rounding ... would have to apply
it you are really arguing that this item is trying to "test" for more ...
then, this item is not a simple math item ... and i think you would have a
hard time saying that a person who answered D really knows more than the
person who answers C ... given what is said and implied in this item ...
however, if you answered A or B ... you do have a problem!
some might call this a classic trick item ... where it hopes that some will
not even consider measurement error ... or, read the item in such a way
that the thought of measurement error never even enters their mind ...
and, should it? not unless this is a test not about math so much but, about
measurement ...
> - I don't care if you want to obsess about whether "up-to" contains
>the exact margin [ even though: that is a separate fault that makes
>this an unprofessional question ]. With ANY scope at all for realism
>(i.e., measurement error), the exact margin has to be exceeded.
>So. What "best describes" the "greatest"?
>
>Choice (C) does a good job of describing "the difference" -- if that
>had been asked. But that was not in the question. The focus has been
>set on the "greatest." I think that the naive rater might rule out
>(C) because it answers the wrong question, and it is logically
>inconsistent with the correct answer.
>
>Answer (D) is also pretty poor, but it is not impossible.
>If you decide it is a math question, it is the only possible one.
>
>As Robert Dawson pointed out, the whole pretext/description is not
>realistic for the report of an actual track meet. Someone *could*
>say that, reasonably, if the two jumps were *very* close to the
>21-feet; otherwise, the whole comment is just totally stupid. So,
>someone who was reading this as a social question might decide that
>(A) is the only feasible answer. Realistically speaking.
>
>Those of us who are quite bright don't have any doubts though.
>We know, by the internal awkwardness, that this was not a subtle,
>sneaky, trick-logical question. We are quite a bit smarter than the
>idiot (relatively speaking) with 120 IQ who wrote the question, and we
>know the question/answer, even if he failed to ask it.
>
>
> > >
> > >ObPuzzle: Assume that the wording needs improvement. Assume that the
> > >concept to be tested is that "the range of real numbers for which the
> > >closest integer is 21 is the interval from 20.5 to 21.5 not including
> > >either endpoint, sometimes notated (20.5, 21.5)." What is a simple,
> > >natural wording in everyday language that would test someone's
> > >understanding of this concept while providing a single, unambiguously
> > >correct choice?
> >
>
>What simple, natural wording... ? Well, it is *not* a wording that
>brings in the distraction of "up to." It is not a wording that
>implies perfect precision in measurement, or requires great knowledge
>of track meets, or requires ignorance of track meets.
>
>--
>Rich Ulrich, [EMAIL PROTECTED]
>http://www.pitt.edu/~wpilib/index.html
>
>
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