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Topic: M&M's
Replies: 0

 Bob Hayden Posts: 2,384 Registered: 12/6/04
M&M's
Posted: Sep 17, 1996 8:04 PM

----- Forwarded message from Timothy Brown -----

I haven't used m & ms at the beginning of the year, but last year I
used them when we began hypothesis-testing... We found
that there was *enormous* variation in proportions of each color
between manufacturing lots. So if you buy all your bags from the
same carton in the same store, you might get tons of yellows and
almost no greens. The same goes for buying one 2-pound bag. So you
ms from a "random" selection of stores!

----- End of forwarded message from Timothy Brown -----

This only hides the problem. You will now get a lot more variability
than sampling theory would suggest. Despite their claims to the
contrary, Mars does not mix the candies thoroughly enough for them to
be considered a random sample from a fixed population. I think they
are great for demonstrating sampling variability (especially when they
exaggerate it!) but not for any inference procedure based on random
sampling, i.e., not for any inference procedure in an introductory
course.

Here's one intuitive way to think about the problem. If the bags were
random samples, the sampling distribution of the proportion of tan M&Ms
would be close to normal. Suppose they mix them so badly that
virtually every bag contian only one color. Then the sampling
distribution of the proportion of tan ones has spikes at 0% and 100%
and virtually nothing around the population proportion of tan M&Ms.
It will not have the variance or shape that sampling theory predict
(and use as the basis for inference).

To see how bad the problem is, open many bags of M&Ms and compare the
empirical and theoretical variance of the sampling distribution of the
proportion of each color. (I did it many years ago.)

_
| | Robert W. Hayden
| | Department of Mathematics
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