In this paper we propose a method to test $ extit{H}$:$ ho_i$=$gamma_i$ for 1$leq$$ extit{i}$$leq$$ell$ against $ extit{K}$:$ ho_i$$ eq$$gamma_i$ for some ｉin k-variance component random or mixed linear model where $ ho$i denotes the ratio of the i-th variance component to the error variance and $ell$$leq$K. The test which we call Rao-Wald test is exact and does not depend upon nuisance parameters. From a numerical study of the power performance of the test of the interaction effect for the case of a two-way random model Rao-Wald test was seen to be quite comparable to the locally best invariant (LBI) test when the nuisance parameters of the LBI test are assumed known. When the nuisance parameters of the LBI test are replaced by maximum likelihood estimators Rao-Wald test outperformed the LBI test.