Stud wall that doesn't connect to ceiling?
There are lots of ways to do this.  I wanted my pony wall very stiff, so I ran a 2-inch pipe from the top plate to some blocking at the bottom of the joists below the subfloor.  You might get away with screwing the bottom plate to the josts and using a bracket designed for preventing the studs from prying away from the bottom plate.  Also, you might consider a 2x6 wall instead of 2x4.

Here is a nice rundown of the options.