Confidence Intervals for Proportions, n<30

[WWGD]

Hi All,
I am having trouble finding a good ref. for finding confidence intervals for population proportions
for small sample sizes; n<30. I have seen suggestions to use simulations, t-distributions, etc. .
Any ref. , please?
Thanks.

 

[andrewkirk]

No refs I'm afraid, but what about using the binomial distribution?

To get a $\alpha$-quantile one-sided upper-tail confidence interval for the proportion of a population with property X when we have observed k data with the property in a sample of n, we could solve for $p$ the equation:

$$B^p_n(k-1)=1-\alpha$$

where $B^p_n$ is the cdf of a binomial distribution with parameters $p,n$.

Then, if the population proportion with property X is $p$, the probability of observing $k$ or more data with the property in a sample of size $n$ is $\alpha$.

This is just trying to follow the same logic that I think I recall is used to set conf interval limits for larger samples, where a normal approximation can be used for the distribution of the proportion in the sample.

 

[WWGD]

Thanks,this works, I was thinking something along this lines but the person who asked me just wanted refs.