tangentially related, for those of us teaching stats, last evening I
enjoyed Rosencrantz and Guildenstern Are Dead (live stage presentation at
U of Utah). It starts with the main characters flipping coins and
noticing they come up heads time after time after time... about the 5th
head in a row, the audience begins to titter acknowleging it is out of
line with expectation. I think the movie version starts similarly and may
serve as a nice introduction to hypothesis testing.
Paul
Bob Parks wrote on 3/30/00 7:44 AM:
>Consider the following problem (which has a real world
>problem behind it)
>
>You have 100 coins, each of which has a different
>probability of heads (assume that you know that
>probability or worse can estimate it).
>
>Each coin is labeled. You ask one person (or machine
>if you will) to flip each coin a different number of times,
>and you record the number of heads.
>
>Assume that the (known/estimated) probability of heads
>is between .01 and .20, and the number of flips for
>each coin is between 4 and 40.
>
>The question is how to test that the person/machine
>doing the flipping is flipping 'randomly/fairly'. That is,
>the person/machine might not flip 'randomly/fairly/...'
>and you want to test that hypothesis.
>
>One can easily state the null hypothesis as
>
> p_hat_i = p_know_i for i=1 to 100
>
>where p_hat_i is the observed # heads / # flips for each i.
>
>Since each coin has a different probability of heads,
>you can not directly aggregate.
>
>Since the expected number of heads is low, asymptotics for
>chi-squares will not apply (each coin has substantial
>probability of obtaining 0 heads so empirically you obtain
>lots of cells with 0,1,2 etc.).
>
>Given that, I have failed to come up with a statistic to test it.
>
>TIA for any pointers to help.
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