Conjugated base of a stronger acid is weak.
The corresponding acids of the given conjugated bases are as (in order of acidity)
$C _{2} H _{5} OH < CH _{3} COOH < HF < HNO _{3}$
$\therefore $ The order of basicity is
$C _{2} H _{5} O ^{-} > CH _{3} COO > F ^{-} > NO _{3}^{-}$
Thus, $NO _{3}^{-}$is the weakest base among the given.