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An ordinance requiring that a smoke detector be installed

Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye ISBN: 9780321629111 32

Solution for problem 59E Chapter 3

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 59E

An ordinance requiring that a smoke detector be installed in all previously constructed houses has been in effect in a particular city for 1 year. The fire department is concerned that many houses remain without detectors. Let p = the true proportion of such houses having detectors, and suppose that a random sample of 25 homes is inspected. If the sample strongly indicates that fewer than 80% of all houses have a detector, the fire department will campaign for a mandatory inspection program. Because of the costliness of the program, the department prefers not to call for such inspections unless sample evidence strongly argues for their necessity. Let ?X ?denote the number of homes with detectors among the 25 sampled. Consider rejecting the claim that p ? .8 if x ? 15. a.? ?What is the probability that the claim is rejected when the actual value of ?p ?is .8? b.? ?What is the probability of not rejecting the claim when p = .7? when p = .6? c. ?How do the “error probabilities” of parts (a) and (b) change if the value 15 in the decision rule is replaced by 14?

Step-by-Step Solution:

Solution : Step 1: It is given that the fire department conducted a survey find how many previously constructed houses have the smoke detector., if p=the true proportion of such houses having detectors, and suppose that a random sample of 25 homes is inspected. And the sample shows that fewer than 80% of the hoses have the fire detector. The department claims that there is not to do inspections unless sample evidence strongly argues for their necessity. If X denote the number of homes with detectors among the 25 sampled. They rejecting the claim that p .8 if x 15.

Step 2 of 2

Chapter 3, Problem 59E is Solved
Textbook: Probability and Statistics for Engineers and the Scientists
Edition: 9
Author: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye
ISBN: 9780321629111

The full step-by-step solution to problem: 59E from chapter: 3 was answered by , our top Statistics solution expert on 05/06/17, 06:21PM. Probability and Statistics for Engineers and the Scientists was written by and is associated to the ISBN: 9780321629111. Since the solution to 59E from 3 chapter was answered, more than 420 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Probability and Statistics for Engineers and the Scientists, edition: 9. The answer to “An ordinance requiring that a smoke detector be installed in all previously constructed houses has been in effect in a particular city for 1 year. The fire department is concerned that many houses remain without detectors. Let p = the true proportion of such houses having detectors, and suppose that a random sample of 25 homes is inspected. If the sample strongly indicates that fewer than 80% of all houses have a detector, the fire department will campaign for a mandatory inspection program. Because of the costliness of the program, the department prefers not to call for such inspections unless sample evidence strongly argues for their necessity. Let ?X ?denote the number of homes with detectors among the 25 sampled. Consider rejecting the claim that p ? .8 if x ? 15. a.? ?What is the probability that the claim is rejected when the actual value of ?p ?is .8? b.? ?What is the probability of not rejecting the claim when p = .7? when p = .6? c. ?How do the “error probabilities” of parts (a) and (b) change if the value 15 in the decision rule is replaced by 14?” is broken down into a number of easy to follow steps, and 192 words. This full solution covers the following key subjects: houses, claim, detectors, sample, Department. This expansive textbook survival guide covers 18 chapters, and 1582 solutions.

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An ordinance requiring that a smoke detector be installed

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