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# Sometimes experiments involving success or ISBN: 9781305251809 122

## Solution for problem 56 Chapter 9.4

Probability and Statistics for Engineering and the Sciences | 9th Edition

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Problem 56

Sometimes experiments involving success or failureresponses are run in a paired or before/after manner.Suppose that before a major policy speech by a politicalcandidate, n individuals are selected and asked whether(S) or not (F) they favor the candidate. Then after thespeech the same n people are asked the same question.The responses can be entered in a table as follows:S FS x1 x2F x3 x4AfterBeforewhere x1 1 x2 1 x3 1 x4 5 n. Let p1, p2, p3, and p4denote the four cell probabilities, so that p1 5 P(S beforeand S after), and so on. We wish to test the hypothesis thatthe true proportion of supporters (S) after the speech hasnot increased against the alternative that it has increased.a. State the two hypotheses of interest in terms of p1, p2,p3, and p4.b. Construct an estimator for the after/before differencein success probabilities.c. When n is large, it can be shown that the rv (Xi 2 Xj)ynhas approximately a normal distribution with variancegiven by [pi 1 pj 2 (pi 2 pj)2]yn. Use this to constructa test statistic with approximately a standard normaldistribution when H0 is true (the result is calledMcNemars test).d. If x1 5 350, x2 5 150, x3 5 200, and x4 5 300,what do you conclude?

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STAT 2004 WEEK 9 BERNOULLI DISTRIBUTION  In a Bernoulli distribution, an outcome has two possibilities: success or failure. o Success- What we were interested in happened. o Success is represented by a 1, while failure is represented by a 0.  Probability of success is represented by a p.  For a Bernoulli random...

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##### ISBN: 9781305251809

The answer to “Sometimes experiments involving success or failureresponses are run in a paired or before/after manner.Suppose that before a major policy speech by a politicalcandidate, n individuals are selected and asked whether(S) or not (F) they favor the candidate. Then after thespeech the same n people are asked the same question.The responses can be entered in a table as follows:S FS x1 x2F x3 x4AfterBeforewhere x1 1 x2 1 x3 1 x4 5 n. Let p1, p2, p3, and p4denote the four cell probabilities, so that p1 5 P(S beforeand S after), and so on. We wish to test the hypothesis thatthe true proportion of supporters (S) after the speech hasnot increased against the alternative that it has increased.a. State the two hypotheses of interest in terms of p1, p2,p3, and p4.b. Construct an estimator for the after/before differencein success probabilities.c. When n is large, it can be shown that the rv (Xi 2 Xj)ynhas approximately a normal distribution with variancegiven by [pi 1 pj 2 (pi 2 pj)2]yn. Use this to constructa test statistic with approximately a standard normaldistribution when H0 is true (the result is calledMcNemars test).d. If x1 5 350, x2 5 150, x3 5 200, and x4 5 300,what do you conclude?” is broken down into a number of easy to follow steps, and 204 words. Probability and Statistics for Engineering and the Sciences was written by and is associated to the ISBN: 9781305251809. This textbook survival guide was created for the textbook: Probability and Statistics for Engineering and the Sciences, edition: 9. Since the solution to 56 from 9.4 chapter was answered, more than 224 students have viewed the full step-by-step answer. This full solution covers the following key subjects: . This expansive textbook survival guide covers 88 chapters, and 2432 solutions. The full step-by-step solution to problem: 56 from chapter: 9.4 was answered by , our top Statistics solution expert on 11/08/17, 04:06AM.

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