If your firearm is not capable of shooting a tight group before you get excited, the chances of taking an animal with a firearm that has the capability of shooting a 6-inch group are not worth considering. Even when excited the hunter should pick an exact spot he plans on hitting the animal and then putting the bullet in that exact place. To get the most from your gun's accuracy potential, practice at local ranges that offer shooting at 300 yards or better. It may take a bit of fine tuning to find a bullet weight, design and powder charge that your particular rifle likes. But I have seen few guns that will not shoot this type of accuracy when you do find the right bullet, powder combination.
Every rifle has particular likes and dislike when it comes to ammunition.
If you're interested in shooting at ranges of 300 yards and beyond, and quite often the terrain hunted dictates such shots, make certain your rifle is extremely accurate at 100 yards. Before going to the field to hunt take the time to set up targets at 100 yard intervals and learn exactly where your guns shoots at the different ranges. At the point that your bullet drops below the 1,000 foot pounds of energy level. That exact distance will depend upon the caliber and load. After traveling through airports and rugged roads, check and make sure your gun's crosshairs are still where they need to be.