People are now beginning to check their DNA. I imagine if people had ancestors here for a century or two, there is a chance of having a little Native American blood. I am not recommending any particular DNA site but listed a few so you can check the info to see if this is what you want and want to pay for.
National Geographic is having a study determing where our ancestors originated.
For females, it tests only the maternal side
For males, it's just the paternal side.
the ancestors they were researching were in England, Ireland, Scotland, Germany, Norway, Russia and the USA.
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Haplogroup J is found at highest frequencies in Middle Eastern and north African populations where it most likely evolved. This marker has been carried by Middle Eastern traders into Europe, central Asia, India, and Pakistan
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They need to write a book called DNA for Dummies.
As I find more on the subject, I'll pass it on.
Karen