Re: web page for revision

7 Jan 2006 00:42:28 GMT from Ian Johnston
<ian.groups@xxxxxxxxxxxxxx>:
> Anyone watch "Catch Me if You Can" the other night? I was moved to
> investigate how the hero passed the Louisiana Bar Exam at 17, with no
> legal training. The answer, apparently, is that you could take it as
> many times as you like, only resitting the bits you got wrong, so he
> was able to iterate to a pass on the third attempt.

In my statistics class, I asked my students to calculate the
probability of passing a 10-question multiple-choice test by pure
guessing, assuming four alternatives for each question and a passing
grade of 60.[1]

Then I pointed out that, for most questions, students don't actually
have to guess randomly because even if they slept through class they
know _something_, and anyway most m-c questions have at least one
answer that's obviously wrong if you think about it. I then had my
students re-calculate he probability of passing if you can eliminate
one or two of the wrong answers.[2] "That's why I never give
multiple-choice tests," I said.

(It's a legitimate objection that an few m-c final exam would most
likely be longer than 10 questions. But that's a reasonable length
for an in-class quiz.

[1] It's a binomial distribution with p = 0.25, n = 10, x >= 6. The
probability is 1.97%.

[2] p = 1/2.5 = 0.4. The probability is now 26%. This means that more
than a quarter of students who know essentially nothing of the course
material will pass such a test. The standard deviation, by the way,
is 1.55.

--
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
http://OakRoadSystems.com/
"Do I smell the revolting stench of self-esteem?"
-- Jon Lovitz, in /The Producers/ (2005)
.

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