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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 hypothesistesting... 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 2pound bag. So you have to get your students to spread out over town and buy bags of m & 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 /  Plymouth State College   Plymouth, New Hampshire 03264 USA  *  Rural Route 1, Box 10 /  Ashland, NH 032179702  ) (603) 9689914 (home) L_____/ hayden@oz.plymouth.edu fax (603) 5352943 (work)



