The chapter focuses on inferences on the mean of n independent binary responses. For most applied problems the exact one-sided p-values and the exact central confidence interval (also called the Clopper–Pearson interval) are appropriate. Less common exact confidence intervals (by Sterne or Blaker) may have smaller width at the cost of giving up the centrality (equal error bounds on both sides of the interval). We also discuss mid-p tests and confidence intervals that do not have guaranteed coverage, but instead have coverage that is approximately the nominal level “on average.” Asymptotic methods are briefly described. We discuss three different ways of determining sample size for a one sample study with binary responses: pick the sample size that (1) gives appropriate power to reject the null hypothesis for a particular alternative, (2) gives appropriate power to observe at least one event, or (3) bounds the expected 95% confidence interval width.