  The longitudes of perihelia and orbital poles of the solar system's dozen or
so most remote detected objects are clustered in a manner inconsistent with
that of a random sample of uniformly distributed orbits. While small number
statistics and observational biases may explain these features, the statistical
significance of the clustering has led to the recent development of the "Planet
Nine hypothesis." In the proposed scenario, orbits in the distant solar system
are shepherded via secular perturbations from an undetected massive planet on
an eccentric orbit. However, the precession of perihelia and nodes in the outer
Kuiper Belt and inner Oort Cloud are also affected by the the giant planets,
passing stars, and the galactic tide. We perform a large suite of numerical
simulations designed to study the orbital alignment of Extreme Trans-Neptunian
Objects (ETNOs) and Inner Oort Cloud Objects (IOCOs). In our various
integrations that include Planet Nine, we consistently find that >60% of ETNOs
and IOCOs that are detectable after 4 Gyr are also anti-aligned in perihelia
with the distant massive perturber. However, when we randomly select 17 objects
from this sample of remaining orbits, there is significant scatter in the
degree of longitude of perihelion and orbital pole clustering that might be
observed. Furthermore, we argue that, in the absence of Planet Nine, 17
randomly drawn orbits should still exhibit some clustering even if the
underlying distribution is uniform. Thus, we find that still more ETNO and IOCO
detections are required to confidently infer the presence of Planet Nine.
