Test of equality of normal means in the absence of independent estimator of variance

Let X_l,…,X_n be normally and independently distributed with means θ_l,…,θ_nand a cornmorl variance. Thus there are n observations and n+i unknwon parameters. A test of the null hypothesis that, the θ_i's are all zero and the alternative that the vector (θ_l,…,θ_n) lies in a convex cone with its vertex a.t the origin is connsidered in this paper. It is shown that under a mild condition the likelihood ratio test is possible. The ordinary one sided t - test belongs to the class of tests considered in this paper. The hypothesis of equality of means against the simple order alternative can be tested in certain cases .