No, not necessarily.
Rankings are correlated highly with admissions standards and entrance statistics simply because the rankings methodology is determined in large part by admissions standards and entrance statistics, or by factors that are heavily correlated with them. That’s because the people who make rankings believe (or at least, they know their customers believe) that these inputs are important factors that determine a university’s prestige or quality or worth.
These statistics can be partially indicative a program’s quality - at the very least, you know what kinds of classmates you’ll be surrounded by and what the intellectual environment might be like at the school writ large. But there are a variety of reasons why admissions standards, the admissions rate and better statistics may not perfectly overlap.
One great example is Lawrence University, a small liberal arts college in Wisconsin. Lawrence has a 70-80% acceptance rate, which on face makes it sound like an almost-open access college. But the middle 50% of Lawrence’s accepted students score between the mid 600s and mid 700s on the SAT sections and were largely in the top 10% of their high school graduating class, with an average GPA of around 3.6-3.7. By all accounts, students at Lawrence get a high quality education as well.
With all that said, I wouldn’t put too much stock into rankings (they’re done oddly in some places) and rather investigate the quality of the education beyond that. I think you are going on the basis of UNCC being ranked in the ‘national universities’ list while UNCW and App State are ranked in the ‘regional universities’ list. But that’s not a measure of quality; U.S. News seems to have labeled universities national simply on the basis of doctoral programs:
*Like National Universities, Regional Universities offer a full range of undergraduate programs and provide graduate education at the master’s level. However, they differ by offering few, if any, doctoral programs. Of the 653 Regional Universities, 257 are public, 385 are private and 11 are for-profit.
The 334 Regional Colleges, including 118 public institutions, 198 private schools and 18 for-profits, focus on undergraduate education but grant less than 50 percent of their degrees in liberal arts disciplines. The Regional Colleges category includes some institutions where only a small number of the degrees awarded are at the bachelor’s level.*
So UNCC is in national universities because it has more doctoral programs than UNCW or App State, but that doesn’t mean it’s better. I would argue that UNCW and App State are both better universities for undergrad experience than UNCC.