Re: Statistics Question

"Don McC" <DonMcC@xxxxxxxxxxxx> wrote in
news:Q8SdnXkOcNKAVGrZnZ2dnUVZ_vCdnZ2d@xxxxxxxxxxxx:

"David in NYC" <sorry@xxxxxxxxxxxxxxx> queries:

You are trying to estimate the *discrete* binomial distribution
with the *continuous* normal distribution.

On a continuous distribution, 16 runs from 15.5 to 16.5,
so you want the probability of 16.5 or fewer heads.

z = (20 - 16.5) / SQRT (.5 * .5 * 40) = 1.107; p. = .134

or .5 - (16.5 / 40) / .079 = 1.107; p. = .134 QED

So using 16.5 as the upper limit of 16 on a continuous
distribution yields a much more accurate estimate of the
actual discrete binomial probability.

--
Don

Facts are stubborn things, but statistics are much more pliable.
~ Mark Twain



Awesome, thanks. (Thanks also to Gerry for the point about sample
sizes). Just seeing how to get .134 through the continuous distribution
is a big boon (this has been driving me nuts).

So why do statisticians not always use the binomial distribution when
testing the proportion in a population? I am talking discrete
situations, e.g. testing if 25% of all Americans are smokers. I
understand that at larger sample sizes, the continuous distribution gets
more accurate, but why not just be 100% accurate? Is it because the
binomial distribution gets too calculation-intensive?

Thanks,
Dave
.

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