The assumption is bite is the only attack the barbarian makes during the turn, and the barbarian has no other natural attacks. I seem to get three different answers on this:
The barbarian adds 0.5x the strength modifier. This is because the rules on Animal Fury state that “If the bite hits, it deals 1d4 points of damage (assuming the barbarian is Medium; 1d3 points of damage if Small) plus half the barbarian’s Strength modifier.”
The barbarian adds 1x the strength modifier. This is because the 19 STR cannibal from the gamemastery guide has its bite damage listed as 1d4+4, which is consistent with this.
The barbarian adds 1.5x the strength modifier. This is because a bite is a primary natural attack, and the natural attack rules state that “If a creature has only one natural attack, it is always made using the creature’s full base attack bonus and adds 1-1/2 times the creature’s Strength bonus on damage rolls.”
So which one is it?