两个正态总体均值与方差同时检验问题的研究

The Researches on Coinstantaneous Testing the Hypothesis about Means and Variances on Two Normal Population

假设Xij(j=1,…,n;i=1,2)是取自相互独立的正态总体N(μi,δi2)(i=1,2)的简单随机样本。令:H0:μ1=μ2,δ12=δ22;H1:μ1≤μ2,δ12≥δ22。在几个定理的基础上,讨论两个正态总体的均值与方差同时假设检验问题:H0vsH1-H0。重点放在大样本的假设检验上,最后给出此问题的检验函数,从而解决了该检验问题。

Suppose xij(j =1,…, n ; i = 1 ,2) are simple samples and be from complete independent normal population N(μi,δi2) ( i =1, 2) , suppose H0:μ1=μ2,δ12 = δ22;H1:μ1≤μ2,δ12≥δ22 base on a few theorems, we discuss testing the hypothesis about means and variances on two normal population: H0 vs H1 -H0, and the important point is the large samples in the paper. The testing function is given and the test problem is finished in the end.