  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.
