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 < 0.80 (less than 80% have detectors), as opposed to p ≥ 0.80, 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 = 0.8 and implement the program if x ≤ 15. (Round your answers to three decimal places.) a.)What is the probability that the program is implemented when p = 0.80? b.)What is the probability that the program is not implemented if p = 0.60?
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 < 0.80 (less than 80% have detectors), as opposed to p ≥ 0.80, 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 = 0.8 and implement the program if x ≤ 15. (Round your answers to three decimal places.)
a.)What is the probability that the program is implemented when p = 0.80?
b.)What is the probability that the program is not implemented if p = 0.60?
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