Poor sophomores majoring in public administration all applied for student loans. All the students who applied for student loans have already paid their tuition fees.

Therefore, poor sophomores majoring in public administration in universities have all paid tuition fees.

B:

All the poor sophomores majoring in public administration in this university have paid tuition fees, but some poor sophomores may have paid tuition fees as tutors.

Therefore, among the students who are tutors in this university, there may be poor sophomores majoring in public administration.

C:

Some students majoring in business in this university work as tutors after school, but some of them have not paid their tuition fees.

So some people in this university are not registered. They may be students majoring in business administration.

d:

All poor sophomores majoring in public administration have applied for student loans. All the students who applied for student loans paid their tuition fees. However, not all poor students majoring in public administration have applied for student loans, so not all students majoring in public administration have paid tuition fees. Students can only register if they pay tuition.

Therefore, not all the poor students majoring in public administration in this university have successfully signed up.

According to the above discussion, choose D.