Hypothesis Testing with the Normal Distribution | 正态分布假设检验

📚 Hypothesis Testing with the Normal Distribution | 正态分布假设检验

In Edexcel A-Level Mathematics, hypothesis testing with the normal distribution extends earlier ideas of binomial hypothesis testing to continuous data. It is used when we wish to test a population mean μ under the assumption that the sample data are normally distributed or the sample size is large enough for the Central Limit Theorem to apply.

在 Edexcel A-Level 数学中，正态分布假设检验将二项分布假设检验的思想推广到连续数据。当样本数据服从正态分布，或样本量足够大使得中心极限定理适用时，我们用它来检验总体均值 μ。

1. What is a Hypothesis Test? | 什么是假设检验？

A hypothesis test is a formal procedure for deciding whether a statement about a population parameter is supported by sample data. It begins with two competing hypotheses: the null hypothesis H₀ and the alternative hypothesis H₁.

假设检验是一种正式程序，用于判断关于总体参数的陈述是否得到样本数据的支持。它从两个对立的假设开始：原假设 H₀ 和备择假设 H₁。

The null hypothesis represents the default or established claim, usually that the parameter equals a specific value. The alternative hypothesis represents the new claim or the change we are testing for.

原假设代表默认的或已有的声明，通常表示参数等于某个特定值。备择假设代表我们要检验的新声明或变化。

We use sample data to decide whether there is enough evidence to reject H₀. A test never proves H₀ or H₁

Published by TutorHao | A-Level Mathematics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）