A city ordinance requires that a smoke detector be installed in all residential housing. There is concern
Question:
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 the proportion of all residences that have a detector.
A random sample of 25 residences will be selected. If the sample strongly suggests that p .80 (fewer than 80%
have detectors), as opposed to p .80, the program will be implemented. Let x 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?
Step by Step Answer:
Statistics The Exploration And Analysis Of Data
ISBN: 9781133171744
007th Edition
Authors: Roxy Peck, Ay L Devore