Quantum mechanics deals with things on the atomic and subatomic level. Statistical mechanics deals with large systems, on the order of 10^23 particles. So those are currently mutually exclusive areas of physics. That is not to say that one day that issue will be rectified, but as of current there is no overlap.
AnswerI disagree. Statistical mechanics explains the connection between the very small and the not-so-small things. It explains large-scale properties, such as energy, temperature, pressure, current, etc. in terms of the movements of particles at an atomic scale. Statistical mechanics was first formulated in the 19th century, before quantum mechanics, and was built on classical mechanics; however, it has also been done for quantum mechanics.