On Tue, 16 Jan 2001 14:14:36 GMT, [EMAIL PROTECTED] (J. Williams)
concluded:
> Maybe, I am missing something, but think the original question and
> response items are quite clear and concise. I see nothing
> particularly "loose" about it. The essentials of a class interval
> used in frequency distributions seem apparent although it is subtle.
> For me, this appears to be an excellent question. Of course, I was
> not an English major either :-)
Well, I think anyone with advanced math courses can answer it because
we jump to conclusions. We know what the only "real" question is,
that is likely to be asked in this format. We have seen approximately
the same question a number of times -- and, if it was not asked right,
there was no one complaining.
... back to the question ...
< snip, my intro, other intro ... >
> >37. When Matt's and Damien's broad jumps were measured accurately to
> >the nearest foot, each measurement was 21 feet. Which statement best
> >describes the greatest possible difference in the lengths of Matt�s
> >jump and Damien's jump?
- 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.
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.
> >
- 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
=================================================================
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
http://jse.stat.ncsu.edu/
=================================================================
