In any case, "inability to dismiss H0" for this situation does not infer guiltlessness, but rather simply that the confirmation was inadequate to convict. So the jury does not really acknowledge H0 but rather neglects to dismiss H0. While one cannot "demonstrate" an worthless theory, one can test that it is so near being suitable with a power test, which tests for type II blunders. Philosophy In this thesis, named "Iterative Methods for Solving Systems of Linear Equations: Hy-perpower, Conjugate Gradient and Monte Carlo Methods" and submitted to the University of Manchester by Lukas Steiblys for the degree of Master.