We establish global well-posedness and scattering for solutions to the defocusing mass-critical (pseudoconformal) nonlinear Schrödinger equation $iu_t + \Delta u = |u|^{4/n} u$ for large, spherically symmetric, $L^2_x({\mathbb R}^n)$ initial data in dimensions $n\geq 3$ . After using the concentration-compactness reductions in [32] to reduce to eliminating blow-up solutions that are almost periodic modulo scaling, we obtain a frequency-localized Morawetz estimate and exclude a mass evacuation scenario (somewhat analogously to [10], [23], [36]) in order to conclude the argument