If you are doing it for a research paper then put some work into it.
A quick google search and didn't find much on the subject so it's going to take some work.
I started with Colorado and pulled up their hunting regulations and they had 218 mountain goat licenses for 2011 with 27 being archery and 191 being rifle.
You'll need to do the same for Montana, Wyoming, Idaho Washington, and Utah. Maybe Oregon and too.
For 2007 there were 692 mountain goat hunters in Alaska according to their statistics I found.
https://secure.wildlife.alaska.gov/index.cfm?adfg=goat.harvest
If you just want a rough guess, let's say there are 1,000 tags issued in the lower 48, 1,000 hunters in Alaska. That's probably a little high, but should be fairly close.
I couldn't find anything on harvest #'s in British Columbia, but they have an estimated goat population of 36,000 - 63,000. They have a low sustainable harvest, but maybe 5,000 goats might be possible.
I would think Alberta has some goats as well.
Add that all up and you probably get around 10,000 mountain goat hunters per year. I think that sounds pretty reasonable.
Depending on sources, there are as many at 45 million hunters in the US alone. Those are folks that have hunted anytime in their life. If you want just the people who have hunted in the last year you are looking at around 15 million in the US.
10,000 mountain goat hunters out of 15 million total hunters is .0667%. That's 1 hunter out of 1,500 hunters that would go on a mountain goat hunt.
That's probably a conservative number, i.e. it's probably a smaller % in reality.