Summary: An unbalanced one-way random effects model is considered for assessing the proportion of workers whose mean exposure exceeds the occupational exposure limit (OEL) based on exposure measurements of the workers. Hypothesis testing for the relevant parameters of interest is proposed when the exposure data are unbalanced. The method is based on generalized inference. A simulation study is performed to compare it with that of K. Krishnamoorthy and H. Guo [J. Stat. Plann. Inference 128, No. 1, 219–229 (2005; Zbl 1058.62103)]. Simulation results suggest that the proposed method appears to be better, especially in very unbalanced designs.