  We compare the Chen-Ruan cohomology ring of the weighted projective spaces
$\IP(1,3,4,4)$ and $\IP(1,...,1,n)$ with the cohomology ring of their crepant
resolutions. In both cases, we prove that the Chen-Ruan cohomology ring is
isomorphic to the quantum corrected cohomology ring of the crepant resolution
after suitable evaluation of the quantum parameters. For this, we prove a
formula for the Gromov-Witten invariants of the resolution of a transversal
${\rm A}_3$ singularity.
