A city requires that smoke detectors be installed in all houses. There is concern that too many houses are still without detectors, so a costly inspection program is being considered. Let p be the proportion of all houses that have a detector. A random sample of 25 houses 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 ≤ 17. (Round your answers to three decimal places.)