So I installed Ubuntu 15.4 on a different partition just like I used to do with Windows 7. I'm using GRUB 2 to choose the OS and I can boot into the two operating systems just fine.
When I try to shut down or hibernate from Windows, however, the computer doesn't shut down or hibernate. If I want to shut down the computer I have to restart and then hit the power button at the boot sequence. This is, of course, not optimal. I think that this might be a hybrid boot issue but I am not sure.