In this paper, we consider two new q-Sturm-Liouville problems and prove that their polynomial solutions are finitely orthogonal with respect to two weight functions which correspond to Fisher and T-student distributions as q → 1. Then, we obtain the general properties of these polynomial solutions, such as orthogonality relations, three term recurrence relations, q-difference equations and basic hypergeometric representations, where all results in the continuous case are recovered as q → 1.