Answer:
Beta decay involves changing an up quark into a down quark (Beta+) or a down quark into an up quark (Beta-). This causes a neutron to change into a proton (Beta-) and emit a W- boson which decays into a beta particle (electron and electron antineutrino), or, with extra energy, it causes a proton to change into a neutron (Beta+) which emits a beta particle (positron and electron neutrino).
Quarks are involved because protons and neutrons are comprised of quarks in sets of three, two up quarks and one down quark to form a proton, and two down quarks and one up quark to form a neutron.