Estimation and Test for the Mean in a Model II of the Analysis of Variance

A sample (y₁₁, …, y_in1…, y_a1,…,y_ana) may be given. For y_ij the model II of a hierarchical analysis of variance may be true. For description of precision α and d²(expectation of the square of the half length of the confidence interval) are used. A procedure for determining an optimal (linear cost of sampling) design in theset of designs with given precision is presented. For the test H₀: μ≦ μ₀ against H_A: μ> μ₀ on the same way the optimal design of an experiment is worked out.