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The aim of this study is to construct simple methods of a multivariate ono-sidod test and a multivariate two-sided test when the covariance matrix is unknown. First we assume that the mean vector has a specified direction as Tang, Gnecco and Geller (1989) considered. Then we set up two kinds of composite hypotheses and derive the likelihood ratio test statistic for our composite hypotheses. However the explicit formula of distribution of this statistic docs not exist. Thus we use the conditional distribution considered by Wang and McDermott (1998) to determine the critical value independently of the unknown covariance matrix. Finally we compare our methods with the method of Wang and McDermott (1998) in terms of a numerical example regarding the power of the test.
