On Fri, Nov 10, 2006 at 03:55:26AM +0100, Segher Boessenkool wrote:
> > p = probability of success = .997 (897 / 900)
> > q = probability of failure = .003 (1.0 - .997)
> > n = number of trials       = 2323
> > X = number of successes    = 2323
> >
> >Applying these to the binomial probability formula, we get:
> >
> > P(2323) = 2323! / ((2323 - 2323)! * 2323!) * .997**2323 * .003** 
> >(2323-2323)
> >         = .0009307922
> >
> >So we conclude that the probability that our trials with this patch
> >applied achieved exactly 2323 successes because of chance alone is . 
> >0009.
> 
> Not prematurely rounding p to a useless precision gives you
> 
>       p**2323 ~ 0.000428

Sure.  I just rounded early because most online tools that people would
use to verify the calculation cannot deal with the higher precion.

> even.  And that just calculates the chance that 2323 tries all
> succeed given that the chance for one to succeed is 897/900; it
> doesn't compare two hypotheses at all.

What?  The null hypothesis is that this patch has no effect.  Since the
probability of observing 2323/2323 successes is .000428, we reject the
null hypothesis under a 95% confidence interval.  No?


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