Confidence intervals are obtained by a procedure first given in
Clopper and Pearson (1934). This guarantees that the confidence
level is at least (1-\(\alpha\)).
Details can be found in the publication listed below.
References
Clopper, C. J. & Pearson, E. S. The use of confidence or
fiducial limits illustrated in the case of the binomial. Biometrika 1934.