In case
pip install -U numpy
doesn't work (even with sudo), you may want to make sure you're using the right version of numpy. I had the same "numpy.core.multiarray failed to import" issue, but it was because I had 1.6 installed for the version of Python I was using, even though I kept installing 1.8 and assumed it was installing in the right directory.
I found the bad numpy version by using the following command in my Mac terminal:
python -c "import numpy;print numpy.version;print numpy.file";
This command gave me the version and location of numpy that I was using (turned out it was 1.6.2). I went to this location and manually replaced it with the numpy folder for 1.8, which resolved my "numpy.core.multiarray failed to import" issue. Hopefully someone finds this useful!