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If I live in North Dakota and I apply to schools (Oregon, Syracuse, etc.) which have few to no North Dakotan students, does it help my chances of acceptance, or really have no effect on the decision process whatsoever?

It won't get you in anywhere that your numbers won't if you aren't an ethnic minority, but to a certain extent you add diversity to their class and represent an underrepresented area of the US, and they would appreciate being able to claim that extra state amongst their class and graduates.

In other words, it will certainly help you a bit, but you still need to have the numbers to get in.