We consider inferences in a one-way ANOVA model with equicorrelation error structures. Hypotheses of the equality of the means are discussed. A generalized F-test has been proposed by in the literature to compare the means of all populations. However, they did not discuss the performance of that test. We propose two methods, a generalized pivotal quantities-based method and a parametric bootstrap method, to test the hypotheses of equality of the means. We compare the empirical performance of the proposed tests with the generalized F-test. It can be seen from the simulation results that the generalized F-test does not perform well in terms of Type I error rate, and the proposed tests perform much better. We also provide corresponding simultaneous confidence intervals for all pair-wise differences of the means, whose coverage probabilities are close to the confidence level.