In 2005, hurricanes Katrina and Rita flooded 80% of New Orleans with water more than 20 feet deep in some places. About federal aid for victims, CNN wrote, "investigators estimated that 16 percent of the FEMA's (Federal Emergency Management Agency's) disaster relief payments were made to people who submitted invalid registrations, to the tune of about $1billion. Because the figures were calculated using a statistical sample, however, the agency said the amount could range from $600 million to as much as $1.4 billion. Why did the agency use a statistical sample and what was the standard error the investigators computed?