Summary: In an unbalanced and heteroscedastic one-way random effects model of analysis of variance, a confidence interval on the among group variance component is proposed, based on a Satterthwaite-Patnaik moment matching approach. Using a concavity argument and a fixed-point iteration, several refinements of the derived basic confidence interval are obtained. By way of simulations, the confidence coefficients and lengths of these confidence intervals are compared. The refined versions of the initial confidence interval give acceptable empirical confidence coefficients and lengths.