The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » Courses » ap-stat

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: M&M's -Reply
Replies: 2   Last Post: Sep 18, 1996 12:03 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Timothy Brown

Posts: 42
Registered: 12/6/04
M&M's -Reply
Posted: Sep 18, 1996 8:59 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Thanks for clarifying why I have been getting more and more
uncomfortable about this M&M's thing. I had pretty much come to the
conclusion that it was a terrible fit the the Chi-Square G.O.F.
model, since you aren't sampling individual candies, but bags of

Do you (does anybody?) have any other ideas for a hands-on
application of Chi-Square?


Bob Hayden's Message Text:

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.)

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.