Dennis Roberts wrote:
>
> At 06:14 PM 9/21/01 +0000, Jerry Dallal wrote:
> >I wrote:
> >
> > > Does anybody really care about the proportions of different colors
> > > in bags of M&Ms?
> >
> >because I surely didn't, but perhaps I should. Since the % blues
> >differ among plain and peanut (10 v 30, says WBW) there's probably a
> >good medical/epidemiology exercise to be had by relabeling
> >plain/peanut, blue/non-blue and handing out a bunch of bags to the
> >class. (Thanks also to LD).
>
> this may be true but ... in the overall scheme of things ... this has to be
> of trivial importance and interest ... there must be better "exemplars" to
> use that have more real life applications
>
> when m and ms go off the market, does this sort of problem have ANY
> relevance to anything?
>
> if we have to rely on m and m examples to capture their attention ... then
> no wonder we don't make much headway in our pursuit of teaching "fearful"
> students about statistics ...
My first comment "Does anyone really care..." was along these lines.
The problem of determining the proportions of M&Ms, to my mind,
trivializes the study of statistics. It might be useful to motivate
primary school students, but anyone older should be shown important
applications in areas that interest them.
I was rethinking the use of M&Ms because it was pointed out that plain
and peanut have substantially different proportions of blues. Every
once in a while, some of us use physical devices to demonstrate
sampling--I have a big jar with brown and white beads, for example--so I
thought, why not use M&M's to break the monotony? Plain and peanut might
represent smokers and non smokers, for example, while blue could
represent upper respiratory infection. The class could investigate
whether smokers were more likely than non smokers to develop URIs.
The more I think about it, the less I like it and find myself back where
Dennis is and I was originally. The reason for the second change of
heart has to do with whether the bagging of M&Ms reflects random
sampling. Does the company include a random sample of each color or does
it purposefully include close to a specific number of each for balance
(underdispersion). I could imagine studying different lot numbers and
different sized bags to determine whether the proportions of colors
behave like simple random samples, but that would put me back in
"'Studying M&Ms' Land". While it might have relevance to other problems
should M&Ms go off the marker, they aren't problems that interest me or
my students.
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