a. Explanation Given info: The number of success is, x = 35 , the sample size of a simple random sample from a population is, n = 50 and 99% level. Calculation: Condition: By rule of thumb, the confidence interval for the one-proportion plus-four z- interval procedure should be 90% or greater The sample size should be 10 or more. Here the confidence level is 99%, that is, greater than 90% and the sample size is 50 which is greater than 10. Therefore both the conditions are satisfied, hence the One–Proportion Plus-Four z -interval Procedure is appropriate to use. The plus-four z -interval is obtained by adding the two success and two failures, the sample proportion is, p ˜ = ( x + 2 ) ( n + 4 ) . Substitute x as 35 and n as 50 in the formula, p ˜ = ( 35 + 2 ) ( 50 + 4 ) = 37 54 = 0.685 Thus, the value of p ˜ is 0.685. For confidence level 99%, α = 0.01 . The 99% confidence interval for One-proportion Plus-Four z -interval Procedure is, p ˜ ± z α 2 ⋅ p ˜ ( 1 − p ˜ ) / ( n + 4 ) Substitute, p ˜ as 0.685 α as 0.01 and n as 50 in the formula, p ˜ ± z α 2 ⋅ p ˜ ( 1 − p ˜ ) / ( n + 4 ) = 0 b. To determine If the confidence interval in part (a) is appropriate, compareit with the confidence interval found in exercise 12.27.

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Author: Neil A. Weiss

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Chapter 12.1, Problem 71E

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Use one-proportion plus-four z-interval procedure to obtain the confidence interval.

To determine

If the confidence interval in part (a) is appropriate, compareit with the confidence interval found in exercise 12.27.

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Chapter 12.1, Problem 70E

Chapter 12.1, Problem 72E

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Chapter 12 Solutions

Introductory Statistics (10th Edition)

Ch. 12.1 - Why is statistical inference generally used to...Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Regarding a sample proportion: a. What is it? b....Ch. 12.1 - Regarding the phrase number of successes: a. For...Ch. 12.1 - For what is the phrase number of failures an...Ch. 12.1 - Explain the relationships among the sample...Ch. 12.1 - Prob. 9E Ch. 12.1 - Repeat parts (b)(e) of Exercise 12.9 for samples...Ch. 12.1 - Prob. 11E

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Use one-proportion plus-four z -interval procedure to obtain the confidence interval.

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Use one-proportion plus-four z-interval procedure to obtain the confidence interval.

If the confidence interval in part (a) is appropriate, compareit with the confidence interval found in exercise 12.27.

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Chapter 12 Solutions