  We investigate parameter dependence of the calculated $\beta$-decay
properties, as well as low-lying states for the neutron-rich Zr isotopes within
the neutron-proton interacting boson model (IBM-2) and interacting
boson-fermion-fermion model (IBFFM-2). It is shown that the calculated
$\log_{10}ft$ values for the transitions of the $0^+_1$ ground states of the
parent even-even nuclei $^{96-102}$Zr into the $1^+_1$ states of the daughter
odd-odd nuclei $^{96-102}$Nb consistently exhibit a strong dependence on those
parameters associated with the quadrupole-quadrupole boson interaction, and
with the residual interaction between an unpaired neutron and an unpaired
proton in the IBFFM-2 Hamiltonian for the odd-odd Nb nuclei. By the reduction
in magnitude of the quadrupole-quadrupole interaction strength by approximately
a factor of 2, the calculated $\log_{10}ft$ values for the
Zr$(0^+_1)\to$Nb$(1^+_1)$ transitions increase and agree with the experimental
values. This points to a significant improvement over the previous study
performed in the same mass region, that consists of the mapping from a
relativistic energy density functional calculation onto the IBM-2 Hamiltonian.
