"What do you study at university?"
Translation:Was studierst du?
studieren = to study at university / to be a university student. It can also mean to carefully examine
Ich studiere Chinesisch = I study Chinese as a degree
Ich studiere. = I am a university student
Ich studiere die Zeitung = I am thoroughly reading the newspaper
If you want to use study in the non-university conext, use "lernen"
You will encounter many people that say Ich studiere but they do not study at a university, they study at a Fachhochschule. So I would not agree entirely with you.