Long duration gamma-ray bursts are a rare subclass of stripped-envelope core-collapse supernovae that launch collimated relativistic outflows (jets). All gamma-ray-burst-associated supernovae are spectroscopically of Type Ic with broad lines, but the fraction of broad-lined Type Ic supernovae harboring low-luminosity gamma-ray-burst remains largely unconstrained. Some supernovae should be accompanied by off-axis $\gamma$-ray burst jets that remain invisible initially, but then emerge as strong radio sources (as the jets decelerate). However, this critical prediction of the jet model for gamma-ray bursts has yet to be verified observationally. Here, we present K. G. Jansky Very Large Array observations of 15 broad-lined supernovae of Type Ic discovered by the Palomar Transient Factory in an untargeted manner. Most of the supernovae in our sample exclude radio emission observationally similar to that of the radio-loud, relativistic SN\,1998bw. We constrain the fraction of 1998bw-like broad-lined Type Ic supernovae to be
Comment: 20 pages, 10 figures; accepted for publication in ApJ. This version addresses Referee's comments