Does your undergraduate institution matter when applying for graduate programs?

Their EE program is ranked kind of low, 31st overall, and I was kind of wanting to get out of state. I also prefer the class sizes at Purdue to UF, at UF it seems like I would be lost in the mass. Is it just the cost bit that I should be considering? I haven’t heard back from Purdue with whether or not I will be getting any scholarships.