My first thought is whether the mic is working. Does it need a battery to be inserted? If you are confident that you have set up the mic fully (battery etc, look at the handbook) then try the mic with another camera (a friend's camera? )and see if it works on that camera. Or indeed, as noted by Spacemissing, your mic might need powering by the camera, and you camera does not have that facility in its mic socket.
It is just possible that, although the socket on the camera is the right size for the plug on the mic, the electrical wiring arrangements within the socket in the camera are different from those in the mic plug, and thus connection is not made. At one time Panasonic camcorders had a different wiring arrangement, so I have come across that problem some years ago.
All in all, it might be better to return the mic and get your money back, then to go to a good camera retailer with the camera in your hand and ask for a mic that works with your camera. Then at least you will know that the system works as you leave the retailer, because you will have tested it in the shop.