For the last eight or so years, I have been a judge at the California State Science fair. At this level, the projects must have won the county or city level (not quite the same for all of them, but it is usually their second or third fair presenting their projects).
There is a a Senior division (for anyone in high school) and a Junior division for everyone younger.
Let me tell you, even though it is usually the kids second or third career fairs, all of the Junior level kids that I have judge have only a very basic idea of the science that they are doing. They are usually very unprepared to talk about their methods or accurately understand the scientific method and what they are measuring. Granted, it is usually the first time talking to a "scientist" with industry or academic experience (rather than elementary school teachers), but usually the conclusions that they draw are rather unlikely. The experiments are never setup properly, they do not measure anything really, they get their ideas off of the internet or out of a "science experiments for science fairs" book (and usually tweak it to win their way to the state level).
This may be different with a professor for a father, but I am skeptical that any child ,even at the high school level, can come up with independent ideas for applicable science experiments.