Consider the problem of testing the linear hypothesis on regression coefficients in the nested error regression model. The standard F-test statistic based on the ordinary least squares (OLS) estimator has the serious shortcoming that its type I error rates (sizes) are much larger than nominal significance levels, because the covariance matrix of data is not the identity but has the intraclass correlation structure. One of methods for fixing the problem is to consider an F-test statistic based on the generalized least squares (GLS) estimator, and the resulting GLS F-test performs well in controlling the sizes. However, numerical investigations show that the sizes remain still slightly larger than nominal levels. In this paper, we derive two test procedures: One is an exact test based on the within analysis of variance, and the other is a testing procedure based on the asymptotic correction of the GLS method. It is numerically shown that both procedures are superior to the GLS F-test in controlling the sizes and that the latter test is more powerful than the exact test.