According to the Rule of Three, when we have a sample size n with xequals0 successes, we have 95% confidence that the true population proportion has an upper bound of StartFraction 3 Over n EndFraction. 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

0 < p < 0.075

Step-by-step explanation:

Solution:-

According to the rule of three, when we have a sample size = n.

and x = 0 successes (The lowest possible value of true population proportion). Then we are 95% confident that the upper bound of the true population proportion is given by:

3 / n

If n = 40 couples use a method of gender selection and each couple has a baby girl, the the possibility of successes is zero. This calls on for the use of Rule of three to determine the upper bound for the true population of couple having a baby girl.

- The 95 % upper bound for true population proportion of all the babies born are girl is determined by:

p = 3 / n = 3 / 40

p ≈ 0.075

- The number of successes were = 0, hence the lower bound for the population proportion is 0 and the upper bound was calculated above. Hence,

0 < p < 0.075

- The range of true population proportion.