The integral Chow rings of the stacks of hyperelliptic Weierstrass points

We compute the integral Chow rings of the stacks ${\mathcal{H}}_{g,n}^w$ parametrizing hyperelliptic curves with $n$ marked Weierstrass points. We prove that the integral Chow rings of each of these stacks is generated as an algebra by any of the $\mathrm{\Psi }$-classes and that all relations live in degree one.