正态总体均值的枢轴量及区间估计的教学

Teaching of the pivot quantity and interval estimation of the expectation of normal distribution

枢轴量及区间估计是数理统计教学中的难点.基于枢轴量选择不唯一的特点,探讨枢轴量选择的步进式教学方法,由浅入深讨论了单个样本构造枢轴量、两样本构造枢轴量、样本均值构造枢轴量、样本中位数构造枢轴量等方法,分析不同枢轴量对应区间估计结果,对比了精度的差异性,辅以数值模拟和可视化方法,使学生对枢轴量和区间估计的思想有更深入的理解.

Pivot quantity and interval estimation are difficult topics in the teaching of mathematical statistics.Based on the non-uniqueness of pivot quantity selection,a stepwise teaching method for pivot quantity selection is explored.This method discusses the construction of pivot quantity based on a single sample,two samples,sample means,sample medians,etc,from shallow to deep.Interval estimation results corresponding to different pivotal quantities are analyzed,and the differences in their accuracy are compared by using of numerical simulation and visualization method,so that students can have a deeper understanding of the ideas behind pivot quantity and interval estimation.