r/learnmath•
ACfusion

probability confidence interval?

It's been a long time since I've been in school so my terminology might not be correct. I'm looking for a 95% confidence interval of the true probability of success given a number of sampled successes. I got this formula: {x-z/2sqrt((x(1-x)/n), x+z/2sqrt((x(1-x)/n)}

where x is the observed ratio of success, n is the total number of samples, z=1.96 for 95% confidence. When I plug in 7 successes out of 8 samples, however, I get an upper limit of 1.104... which isn't logically sound. Should I cut the upper limit at 1? Perhaps, I'm applying the formula incorrectly or ignoring certain assumptions? Is there a better formula?

Posted Mar 24, 2012, 10:14 PM UTC

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