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Somewhat. The opportunities available to students affect students’ ability to put together strong graduate applications, and the number and quality of opportunities available to students correlate loosely with conventional notions of prestige. It’s not really the prestige per se that helps, though, it’s the relationships with well-known academics, the availability of outstanding research opportunities, and those sorts of things that are helpful.</p>
<p>You should attend the undergraduate school where you personally will be happy and successful. That particular school is different for different people: some want to be the outstanding student at a state school, and others want to be one of many bright students at a top-tier school. Not everybody would be equally successful in both situations – personally, I feel that I’m in the graduate program I’m in because I went to a top-tier undergrad school, because I really thrived in that environment, while I don’t feel I would have at my state school. Others feel differently.</p>
<p>Ultimately, you can’t know going into undergrad whether you will actually want to go to a top grad program in your field, or whether you’re really good enough to do so. You have to pick the best environment for you at the time – the grad school stuff will work itself out.</p>