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## Problem 9E Chapter 5.10

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition

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Problem 9E

Problem 9E

This exercise is designed to compare the performance of the Agresti-Coull confidence interval for a proportion (expression 5.5 on page 339) with that of the traditional confidence interval (expression 5.8 on page 341). We will use sample sizes of n = 10, n = 17, and n = 40, with p = 0.5.

a. Generate 10,000 observations Xi*, each from a binomial distribution with n = 10 and p = 0.5. For each observation, compute the upper and lower limits for both the Agresti-Coull 95% confidence interval and the traditional one. For each confidence interval, compute its width (upper limit - lower limit). Use the simulated data to estimate the coverage probability and mean width for both the Agresti-Coull and the traditional confidence interval.

b. Repeat part (a), using n = 17.

c. Repeat part (a), using n = 40.

d. The performance of the traditional confidence interval does not improve steadily as the sample size increases; instead it oscillates, so that the coverage probability can be better for a smaller sample than for a larger one. Compare the coverage probabilities for the traditional method for sample sizes of 17 and of 40. Do your results confirm this fact?

e. For which sample sizes does the Agresti-Coull interval have greater coverage probability than does the traditional one? For which sample size are the coverage probabilities nearly equal?

f. Other things being equal, a narrower confidence interval is better than a wider one. Which method produces confidence intervals with the narrower mean width?

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##### ISBN: 9780073401331

This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. This full solution covers the following key subjects: interval, confidence, Traditional, sample, coverage. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. The full step-by-step solution to problem: 9E from chapter: 5.10 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Since the solution to 9E from 5.10 chapter was answered, more than 254 students have viewed the full step-by-step answer. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The answer to “This exercise is designed to compare the performance of the Agresti-Coull confidence interval for a proportion (expression 5.5 on page 339) with that of the traditional confidence interval (expression 5.8 on page 341). We will use sample sizes of n = 10, n = 17, and n = 40, with p = 0.5.a. Generate 10,000 observations Xi*, each from a binomial distribution with n = 10 and p = 0.5. For each observation, compute the upper and lower limits for both the Agresti-Coull 95% confidence interval and the traditional one. For each confidence interval, compute its width (upper limit - lower limit). Use the simulated data to estimate the coverage probability and mean width for both the Agresti-Coull and the traditional confidence interval.________________b. Repeat part (a), using n = 17.________________c. Repeat part (a), using n = 40.________________d. The performance of the traditional confidence interval does not improve steadily as the sample size increases; instead it oscillates, so that the coverage probability can be better for a smaller sample than for a larger one. Compare the coverage probabilities for the traditional method for sample sizes of 17 and of 40. Do your results confirm this fact?________________e. For which sample sizes does the Agresti-Coull interval have greater coverage probability than does the traditional one? For which sample size are the coverage probabilities nearly equal?________________f. Other things being equal, a narrower confidence interval is better than a wider one. Which method produces confidence intervals with the narrower mean width?” is broken down into a number of easy to follow steps, and 246 words.

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Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 5.10 - Problem 9e

Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 5.10 - Problem 9e