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Coping with No Success According to the Rule of Three,

Chapter 7, Problem 42BB

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QUESTION:

Problem 42BB

Coping with No Success 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 Jovanovic 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?

Questions & Answers

QUESTION:

Problem 42BB

Coping with No Success 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 Jovanovic 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?

ANSWER:

Solution 42BB

a)

Assume that there are ‘n’ trials and no successes in an experiment.

That is, Number of trials

Number of successes,

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