A nine-year-old girl and a seven-year-old boy ask their parents to let them stay awake an hour later ...

ANSWER:
Baumrind proposed three socialization styles: permissive, authoritarian, and authoritative. Permissive parents often give their children complete freedom and are lenient about using discipline. If these parents are permissive, they will probably agree to their children's request and might not need to have a discussion about it. Authoritarian parents value obedience. If these parents are authoritarian, they may deny their children's request because they see themselves as the rule makers and their children as the rule followers. They may not discuss or explain their decisions. Authoritative parents would probably sit down with their children and discuss the situation. They may ask the children to explain their reasons for requesting a later bedtime, while pointing out practical considerations, such as school. They may give their children the opportunity to help make the decision, thus encouraging the children to be independent while still setting limits.