方差成比例时2个正态总体均值的假设检验

Hypothesis Test of the Means of Two Normal Populations with Proportional Variances

在方差未知但相等,或方差未知且大样本的情况下,2个正态总体均值的假设检验已经给出了解决方法;但是在方差不等且小样本的情况下,2个正态总体均值的假设检验少有研究。针对这一问题,给出了理论证明的处理方法,并设计了实现流程和用于实现的MATLAB程序,最后,以实际案例给出了实现的具体方法。与大样本情况下的方法对比,该方法所需样本数量较小。

For two normal populations with unknown but equal variances or unknown variances but with large sample size, hypothesis test of the means has given a solution. But there is short of research for unequal variances with small sample size. To address the problem, the processing method of theoretical proof is put forward, and the realizing process and MATLAB program for realization are designed. Finally an actual case is used to illustrate the feasibility of the method. Compared with the situation of large sample, this method needs less samples.