On a two-sample test of the variance analysis

A two-sample test for a linear hypthesis about mean values of $r$ normal populations $\mu_i,\sigma$ is constructed. The power of the test depends on $\Sigma(\mu_i-\overline{\mu})^2$ and is independent of $\sigma$. Two asymptotic methods are proposed for determining the sample size with given probabilities of the errors of the first and the second kind.