I have checked normals and removed doubles but still cannot get the Difference operation on Boolean modifier to work properly. The choker object is hollow, however I expected the modifier would still function using these two meshes. My aim is to cut a hole at the end of the choker. I am able to use the modifier using other basic shapes in a new file. How can I correct this problem? The choker object is hollow to save on material costs when used for 3D printing. 
The simplest definition of Boolean with the Difference operation is that it eliminates the common region that is occupied by 2 geometries.
In your project, You may notice that both the geometries share a common region.
You added the modifier to the Cylinder with Choker as the target object.
Ultimately the some the Cylinder part will get removed as the modifier is for the Cylinder, not for the Choker. But you want a hole in the Choker.So the best solution is to add the Boolean modifier to the Choker, with Difference as the operation, and the target object as the Cylinder.
However there will still be some portion remaining in the bottom.
So you have to apply the modifier and delete it in Edit Mode. But you may have to apply the first 2 modifiers to get the desired result.
Hope this helped!
