I realise that it is a 'fun' experiment to provoke related intellectual discussion. I was just questioning how confident you were in the accuracy of your data, if all the sources of uncertainties are not accounted for then the issue of 'to what extent is this data useful' may become relevant. Even for this simple hypothesis test I would be skeptical that the test setup is suitable to accept or reject the null hypothesis even to a 10% confidence level. A couple of things, consider mounting a pair of laser pointer on a firm tripod and mark 2 small points a few inches apart on the bat, this should ensure the bat is in the same place each time, also i would imagine a ball bearing to not be a suitable substitution for a cricket ball unless it is quite heavy, Think about what happens to the fibers when the bat strikes the ball outside the experiment, dropping a ball bearing wont replicate this. My thoughts into this involved a bat attached to a speed controlled rotating arm using a light gate to remotely trigger a ball to relase into the path of the bat and using high speed photography to determine the velocity of the ball, It should be possible to ensure, with the correct delay, that the ball strikes the same spot on the bat consistently and that the path of the ball is perpendicular to the face of the bat. It would then be possible to calculate a 'power factor' using some formula involving the MoI of the bat, and the K.E of the ball after the impact, It would also be possible to deduce does the resultant K.E of the ball increase linearly with the MoI of the bat. I.e. the old bat speed vs bat weight discussion.
Another key part of the test, is that any bat maker should be able to submit a bat for non destructive testing, perhaps one from each tree to account for natural variation within willow