Thanks for the info Brian, and yes I've got the same results as you did.

I've been playing with different variations and settings.

This is what I tried.

Particle Emitter -> Basic -> Shape -> Objects

Advanced -> Replicated Objects -> Replicator

I also added a sphere to the Replicator.

Oh and also created a converted replicator, which changed
the behaviour of the particles bouncing everywhere but still sinking problem.

Same thing the replicated Spheres are sinking.

Another description of what I'm trying to achieve is to create the effect of droping a bucket of tennis balls onto a floor.  The balls simply bounce around everywhere and eventually rest/stop moving.