One student's floor-covering is in a state (8)
I believe the answer is:
illinois
'a state' is the definition.
(Illinois is an example)
'one student's floor-covering is' is the wordplay.
'one' becomes 'i' (Roman numeral).
'student' becomes 'l' (as in L-plates for learner drivers).
'floor covering' becomes 'lino' (short for linoleum).
'i'+'l'+'lino'+'is'='ILLINOIS'
'in' is the link.
(Other definitions for illinois that I've seen before include "USstate (Chicago)" , "US state by L. Michigan" , "Chicago's state" , "US state and river" , "State to west of Indiana" .)