The two-factor nested variance component model with equal numbers in the cells are given by $y_{ijk};=;{mu};+;A_i;+;B_{ij};+;C_{ijk}$ and the confidence intervals for the ratio of variance components, ${sigma}^{2}_{A}/{sigma}^{2}_{B}$ are obtained in various forms by many authors. This article shows the probability ranges of these confidence intervals on ${sigma}^{2}_{A}/{sigma}^{2}_{B}$ proved by the mathematical computation.