Question

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

Answer 1

Answer:

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.