On left-orderability and cyclic branched coverings

In a recent paper Y. Hu has given a sufficient condition for the fundamental group of the r-th cyclic branched covering of S^3 along a prime knot to be left-orderable in terms of representations of the knot group. Applying her criterion to a large class of two-bridge knots, we determine a range of the integer r>1 for which the r-th cyclic branched covering of S^3 along the knot is left-orderable.