How do I frame a 2" (1.5") thick wall?
An easy way to complete a wall like you describe is to build it flat on the floor. That way you can screw or nail the studs to the plates through the plates.  I recommend installing a separate plate on the floor or across the upper joists first. Floor usually works best.  Then simply measure the shortest dimension from the floor plate  you just installed to the joists and build your wall to that measurement less 1/4 inch.  Now you can stand it up usually without the angle getting hung up on existing ceiling and walk it into place. If you don't use the extra separate plate, it is almost impossible to stand it up into place. Attach it to which ever plate (top or bottom) you installed first, then shim it to keep it stable and plumb it as you nail it to the bottom plate or the joists. When you build the wall on the ground, lay out your 16 inch centers etc. Flush up the second plate to the one you just marked and transfer the marks to other plate with a square. Now you know where to place the studs between the plates. This method is the most common practice for building non-load bearing walls in an existing structure and works with any size lumber you want to use.