On Logarithmic Approximations for the One-Sided Binomial Confidence Interval

A one-sided binomial confidence interval occurs when all trials are successful or unsuccessful. This research considers the case when all trials are successful, and derives logarithmic approximations for the variable lower-bound under two common significance levels. We then establish ranges on the sample size for which the absolute differences between the approximations and the exact lower-bound are less than the chosen level.