A new interpretation of the rule of thumb for the Bernoulli parameter

Interval estimation of a Bernoulli parameter p is a very fundamental and important problem in quality control area. The standard Wald confidence interval (CI) is in nearly universal use, especially in constructing control charts. Moreover, the rule of thumb “” for the standard Wald CI is introduced in most probability textbooks, despite its unsatisfactory performance with the sample size n. The constant 5 is named as the rule-of-thumb threshold for the Bernoulli parameter. This paper offers a new interpretation for the general rule of thumb “,” where the positive real value k is named as the general rule-of-thumb threshold for the Bernoulli parameter. One of our analytical results shows that “” is a necessary condition, while “” is a sufficient condition, to ensure “ and ,” respectively, where and . Moreover, this papers shows when the rule of thumb guarantees good coverage probability of the Wald interval.