In the three-factor nested variance component model with equal numbers in the cells given by $y_{ijkm} = mu + A_i + B_{ij} + C_{ijk} + varepsilon_{ijkm}$, the exact confidence intervals of the variance component of $sigma^2_A, sigma^2_B, sigma^2_C, sigma^2_{varepsilon}, sigma^2_A/sigma^2_{varepsilon}, sigma^2_B/sigma^2_{varepsilon}, sigma^2_C/sigma^2_{varepsilon}, sigma^2_A/sigma^2_C, sigma^2_B/sigma^2_C$ and $sigma^2_A/sigma^2_B$ are not found out yet. In this paper approximate lower and upper confidence intervals are presented.