Motivated by the observation of confinement effects for the poly(ethylene oxide) (PEO) component in the dynamically asymmetric blend with poly(vinyl acetate) (PVAc), 80% PVAc/20% PEO (Macromolecules, 2006, 39, 3007), we have investigated the dynamics of the PVAc component in this blend. Quasielastic neutron scattering techniquesin particular, backscatteringhave allowed selectively studying the self-motions of PVAc hydrogens in a mixture with deuterated PEO. Moreover, we have extended the temperature/frequency range investigated with complementary broad-band dielectric spectroscopy experiments. The influence of blending on the dynamical behavior of PVAc (the component with higher value of the glass transition temperature T-g) in the alpha-relaxation regime can be explained by the Lodge and McLeish model based on the concept of self-concentration. This means, the high-T-g component behaves in a "standard" way upon blending, contrary to the low-T-g diluted component PEO. We find that the crossover temperature T-c where the dynamics of PEO changes qualitatively from glass-forming polymer-like (T > T-c) to confined (T <= T-c), coincides with the merging temperature of the alpha- and beta-processes of PVAc in the blend, T-M. This provides a framework to explain the origin of the confinement for the low-T-g component in this blend. Above T-M, the diffusive motions involved in the structural relaxation of PVAc constitute the overwhelming dynamics. In such a mobile environment, PEO segments are able to fully relax at different length scales. Below T-M, the time scales in which the sublinear regime of the alpha-process develops become slower than the local beta-process. Therefore, PEO chains find a surrounding local mobility which facilitates their own motions at short length scales, but the intermolecular correlations do not decay fast enough to accommodate PEO's large length scale dynamics.