Confidence limits of chance

I am looking to determine the confidence interval of chance for a three class problem.

I know i need to use binomial test, but am not sure that all my values are correct.

Number of samples per class = 60 per class.

I want the value for alpha = 0.05 (so the 95% CI)

I believe it would be from 22.7%-46%....

Could anyone confirm this?
Last edited:
I don't want to know the limits with respect 95% CI. It shouldn't need number of sucesses. Essentially the CI should tell you the number of success minumum required give 60 samples total that would mean it couldn't have happened by chance.

For example,
technically for a 3-class problem chance is 33%. But that is only true with infinite samples. Given 60 samples, what accuracy is required to be 95% sure that the result was not chance.

So, is 34% as a result of chance.... yes very likely, is 80% a result of chance... very unlikely......

At what percent does the switch over happen....? Given alpha = 0.05.

It is essentially a reverse binomial problem.