I personally wouldn't allow it to be honest. But if there is plenty of adult supervision and he/she is a responsable teenager then I would consider it.
I would only let him if 1. you know the parents and trust them with the life of your child (they're going to be functioning as his parents essentially), 2. you trust your son to behave himself, 3. there is some use for the trip (make him visit museums, prospective universities, etc), 4. he stays in consistent contact with you (phone, e-mail, blog, text messaging, whatever). 15 sounds young but in 2 or 3 years, he'll be going off to college or out into the real world so this experience would help him with that transition.
Well, if you think your son is a responsible person, why not?
I spent 1 month in the US when I was 14 and had a great time. I wasn't in a family but in a student group from Europe and we lived in a college, so with a very little adult supervision. Everything was just ok!