Observations of astronomical objects include vectors that are transverse, perpendicular to the direction from the objects to us. The Hub Test judges how well transverse vectors on the sky align by calculating their mutual alignment angle to each point on the sky. Then the most focused and least focused values constitute two measures of the collective alignment of these transverse vectors. This article deals with statistics. How likely is it that a given alignment angle would occur with randomly directed transverse vectors? We discuss and apply a Library of probability distributions from randomly directed sources that is created elsewhere. The Library here has 294 sets of probability distributions with the number of sources ranging from 9 to 900, 14 values total, and the nominal sample radii ranging from 0.14\[Degree] to 64\[Degree], 21 values total. We apply the Library to the problem of estimating the significance of the values obtained by the two Hub Test correlation measures. For a given experimental sample, the Library can be used either by an interpolation of the data or by substitution in formulas that fit the Library data. An Appendix presents detailed calculations in a self-contained Mathematica notebook.