The National Association of Fire Fighters says that 45 percent of homes now have smoke detectors, whereas only 30 percent of homes had them 10 years ago. This makes early detection of house fires no more likely, however, because over half of the domestic smoke detectors are either without batteries or else inoperative for some other reason. In order for the conclusion above to be properly drawn, which one of the following assumptions would have to be made? ['The proportion of domestic smoke detectors that are inoperative has increased in the past ten years.', 'Fifteen percent of domestic smoke detectors were installed less than 10 years ago.', 'Not all of the smoke detectors in homes are battery operated.', 'Unlike automatic water sprinklers, a properly functioning smoke detector cannot by itself increase fire safety in a home.']