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Summary This paper presents an application of the multivariate beta distribution to the problem of testing whether a given sample of multivariate observations could have come from a multivariate normal population with an unknown mean vector and dispersion matrix. By using a series of transformations and the principle of randomization it is shown that the above problem can be reduced to that of testing for univariate normality. No attempt is made to investigate the power of this test; but some brief thoughts are expressed in the concluding section.
B. Wagle (Sun,) studied this question.