The certified flight instructor's (CFI's) inadequate preflight planning/preparation of a test altitude that would afford an on airport landing in the event of engine power loss. Additional causes were the CFI not flying a traffic pattern that would allow for an on airport landing should an engine power loss occur, the partial fuel system obstruction, and the inadequate maintenance by the mechanic. Contributing factors were the improperly serviced fuel selector and the low altitude at the time of engine power loss.