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Acceptance rate means nothing. It's all dependent on 1) the stats of those accepted and 2) how self-selective the applicant pool is. In Chicago's case, the applicant pool is very self-selective: unqualified applicants don't apply (at least, a large number of them don't apply, comparatively). But in the case of, say, Stanford, the applicant pool is amazingly un-self-selective, i.e. a very large number of people who ordinarily wouldn't get in will apply, thus lowering the admit rate. You can't gauge how difficult a school is to get into just by its admit rate; you need to look at its average stats and such. You'll also notice that Chicago's and Stanford's average SAT scores are virtually the same.
And quality of student body is not the only indicator of the quality of an institution, though it is part of it. Of course, 'quality' is an entirely subjective measure. Many define Harvard's student body to be high-quality, whereas some random religious college with much lower (objective) stats considers its own student body to be high-quality since they were chosen based on religious commitment. And the quality of an institution is probably the most hotly contested issue in the college world -- how many rankings do we have now? Each claims to know what 'quality' is, and many people will disagree.
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