Answer: An example of an extravagant hypothesis could be the idea that aliens have been visiting Earth for centuries and have been responsible for many of the technological advancements made by human civilization. This hypothesis suggests that aliens have been secretly interacting with humans, providing them with knowledge and technology, and influencing the course of human history. This idea is considered extravagant because it goes beyond the current scientific understanding of the universe and the capabilities of extraterrestrial life, and lacks concrete evidence to support it. It would require a large amount of additional evidence and research to be considered a valid scientific theory.