Interesting points in the two posts above. What about TV though? You don't have to have travelled to a country to be aware of its make-up and population because there are things about it on telly. Although that said I've also heard it said that US tv, news especially, is very US-centric, not covering much at all to do with other countries. Can't vouch for how true that is, obviously, since I've never seen it.
baglady, re saying you're a quarter Swedish, someone raised an interesting point about that upthread in how Americans identify with their heritage more than others seem to and I meant to touch on that earlier. I'm of Scottish and Irish descent - I'm actually only a technically a quarter English. The biggest part of my makeup - 50 percent - is Scottish, followed closely by Irish. But I would never say 'I'm Scottish' or 'I'm Irish', because I'm not. I'm English. I was born in England, I've lived in England all my life, I speak with an English accent. Whereas an American with my ancestry might say 'I'm Irish', even though they were born in the US, have lived there all their life, speak with an American accent and have probably never even been to Ireland.
I don't think it's a 'how many generations' thing either, because my mother was entirely Scottish in her ancestry and her parents actually were from Scotland. She would still have said she was English through and through, because she was born here and lived here.