A New Confidence Interval for the Mean of a Bounded Random Variable

Abstract

We present a new method for constructing a confidence interval for the mean of a bounded random variable from samples of the random variable. We conjecture that the confidence interval has guaranteed coverage, i.e., that it contains the mean with high probability for all distributions on a bounded interval, for all samples sizes, and for all confidence levels. This new method provides confidence intervals that are competitive with those produced using Student's t-statistic, but does not rely on normality assumptions. In particular, its only requirement is that the distribution be bounded on a known finite interval.