未知总体方差和数学期望条件下的假设检验

Hypothetic Test under the Condition of the Unknown Total Variance and Expentancy

在未知总体方差和数学期望的条件下 ,如何检验假设H0:μ=μ0,一直是统计学研究中未能解决的问题。对此 ,作者提出了一种有效的解决方法 ,它的重大理论和实践意义在于 :(1)不需要已知某种标准信息 (如μ) ,就能对样本平均数是否与总体平均数相一致进行检验 ;(2)能够为抽样推断提供先行信息 ,并据此作出是否抽样推断的判断 ,消除了抽样推断时所隐含的“样本信息结构必须与总体信息结构相近或相同”的前提条件 ,为抽样推断提供了可靠的理论基础。因此从一定意义上说 ,本文的方法实是假设检验理论的一种最新发展。

This paper proposes a feasible method of deducing H0:μ=μ0 with total variance and expectan-cy unknown as it is a controversial issue in statistics. The method lays stress on theory and practice just for the following reasons : one could test the consistence between sample and total means without some stan-dard information ; the other is to make sampling deduce or not on theoretical verification without assuming sample structure similarly to the total. It makes a great progress in hypothesis theory.