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Answer: Of n1 randomly selected male smokers, X1 smoked

Probability and Statistics for Engineering and the Sciences (with Student Suite Online) | 7th Edition | ISBN: 9780495382171 | Authors: Jay L. Devore ISBN: 9780495382171 196

Solution for problem 6.11 Chapter 6

Probability and Statistics for Engineering and the Sciences (with Student Suite Online) | 7th Edition

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Probability and Statistics for Engineering and the Sciences (with Student Suite Online) | 7th Edition | ISBN: 9780495382171 | Authors: Jay L. Devore

Probability and Statistics for Engineering and the Sciences (with Student Suite Online) | 7th Edition

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Problem 6.11

Of n1 randomly selected male smokers, X1 smoked filter cigarettes, whereas of n2 randomly selected female smokers, X2 smoked filter cigarettes. Let p1 and p2 denote the probabilities that a randomly selected male and female, respectively, smoke filter cigarettes. a. Show that (X1/n1) (X2/n2) is an unbiased estimator for p1 p2. [Hint: E(Xi ) nipi for i 1, 2.] b. What is the standard error of the estimator in part (a)? c. How would you use the observed values x1 and x2 to estimate the standard error of your estimator? d. If n1 n2 200, x1 127, and x2 176, use the estimator of part (a) to obtain an estimate of p1 p2. e. Use the result of part (c) and the data of part (d) to estimate the standard error of the estimator.

Step-by-Step Solution:
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Chapter 6, Problem 6.11 is Solved
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Textbook: Probability and Statistics for Engineering and the Sciences (with Student Suite Online)
Edition: 7
Author: Jay L. Devore
ISBN: 9780495382171

This full solution covers the following key subjects: . This expansive textbook survival guide covers 23 chapters, and 1318 solutions. The full step-by-step solution to problem: 6.11 from chapter: 6 was answered by , our top Statistics solution expert on 01/02/18, 08:17PM. Since the solution to 6.11 from 6 chapter was answered, more than 305 students have viewed the full step-by-step answer. Probability and Statistics for Engineering and the Sciences (with Student Suite Online) was written by and is associated to the ISBN: 9780495382171. This textbook survival guide was created for the textbook: Probability and Statistics for Engineering and the Sciences (with Student Suite Online), edition: 7. The answer to “Of n1 randomly selected male smokers, X1 smoked filter cigarettes, whereas of n2 randomly selected female smokers, X2 smoked filter cigarettes. Let p1 and p2 denote the probabilities that a randomly selected male and female, respectively, smoke filter cigarettes. a. Show that (X1/n1) (X2/n2) is an unbiased estimator for p1 p2. [Hint: E(Xi ) nipi for i 1, 2.] b. What is the standard error of the estimator in part (a)? c. How would you use the observed values x1 and x2 to estimate the standard error of your estimator? d. If n1 n2 200, x1 127, and x2 176, use the estimator of part (a) to obtain an estimate of p1 p2. e. Use the result of part (c) and the data of part (d) to estimate the standard error of the estimator.” is broken down into a number of easy to follow steps, and 134 words.

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Answer: Of n1 randomly selected male smokers, X1 smoked