According to the Rule of Three, when we have a sample size n with x = 0 successes, we have 95% confidence that the true population proportion has an upper bound of 3>n. (See “A Look at the Rule of Three,” by Jovanovich and Levy, American Statistician, Vol. 51, No. 2.)
a. If n independent trials result in no successes, why can’t we find confidence interval limits by using the methods described in this section?
b. If 40 couples use a method of gender selection and each couple has a baby girl, what is the 95% upper bound for p, the proportion of all babies who are boys?