A city ordinance requires that a smoke detector be
Chapter 0, Problem 7.59(choose chapter or problem)
A city ordinance requires that a smoke detector be installed in all residential housing. There is concern that too many residences are still without detectors, so a costly inspection program is being contemplated. Let p be the proportion of all residences that have a detector. A random sample of 25 residences is selected. If the sample strongly suggests that p .80 (less than 80% have detectors), as opposed to p .80, the program will be implemented. Let x be the number of residences among the 25 that have a detector, and consider the following decision rule: Reject the claim that p .8 and implement the program if x 15. a. What is the probability that the program is implemented when p .80? b. What is the probability that the program is not implemented if p .70? if p .60? c. How do the error probabilities of Parts (a) and (b) change if the value 15 in the decision rule is changed to 14?
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