Hypothesis Testing In The Normal Population

This article discusses the generalized confidence interval problem in the non-equilibrium het-eroscedasticity model and the equality test of the covariance matrix of two independent multivariate normal states.The first chapter is the introduction part,one-way classification model,the corresponding hypothesis testing problem,and the research present situation of relevant test question of one-way classification model are introduced,and the research situation of two independent multivariate normal population covariance matrix equality test are also introduced simply.In the second chapter,the question of generalized confidence interval problem in the non-equilibrium heteroscedasticity model is studied.In this chapter the question of simultaneous generalized confidence regions of means estimation of multiple normal populations which means and variances are all dilferent is discussed.With the definition of Scheffe and Bonferroni intervals,the paper gives the relevant generalized test variable and generalized pivotal quantity and acquires the simultaneous generalized confidence regions of population means and through the date simulation and compared with the methods given in literature[l].and the method given in this paper good feasible.The third chapter studies the problems of covariance matrix equality test of two independent multivariate normal population which have the different sample size and sample mean.In this paper,we will first transfer the mltivariate problems of equality of covariance matrix into one-dimensional problems,then using the likelihood ratio test,and combining the properties of Wishart distribution and multiple Beta distribution.by solving the eigenvalues of the covariance matrix to test equality of covariance matrix of multivariate normal population.