Smith (1976,J. R. Statist. Soc., A,139, 183–204) has argued that survey statisticians should attempt to model finite population structures in the same way that statisticians in other disciplines have to provide models of finite or infinite populations. Following this argument, we suggest in this paper that an obvious model for a stratified population when auxiliary information regarding variate values is available, is the one way analysis of covariance model with unequal variances and we consider the problem of estimating the finite population mean. Finally a possible extension of this result is discussed.