Hypothesis Testing | 假设检验

📚 Hypothesis Testing | 假设检验

Hypothesis testing is a core topic in Edexcel A Level Mathematics. It gives a formal framework for using sample data to judge whether a claim about a binomial probability p is supported by evidence.

假设检验是 Edexcel A-Level 数学的核心主题。它提供了一个正式框架，用于根据样本数据判断关于二项概率 p 的论断是否得到证据支持。

This article covers null and alternative hypotheses, significance levels, one-tailed and two-tailed tests, critical regions, p-values, and worked examples with the binomial distribution.

本文涵盖原假设与备择假设、显著性水平、单尾与双尾检验、临界区域、p 值，以及基于二项分布的例题。

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

Hypothesis testing is a formal statistical method for deciding whether there is enough evidence in a sample to reject a stated belief about a population parameter, such as the probability p in a binomial model.

假设检验是一种正式的统计方法，用于判断样本中是否有足够证据来拒绝关于总体参数的某个既定论断，例如二项模型中的概率 p。

In Edexcel A Level Mathematics, hypothesis testing is introduced through the binomial distribution, where you test claims about the probability of success p using observed counts from n independent trials.

在 Edexcel A-Level 数学中，假设检验通过二项分布引入，即利用 n 次独立试验中的观测次数来检验关于成功概率 p 的命题。

2. Null and Alternative Hypotheses | 原假设与备择假设

The null hypothesis, written H₀, is the default position or status quo. It usually takes the form H₀: p = p₀, where p₀ is a claimed probability. The alternative hypothesis, written H₁, is what you are trying to prove and takes one of three forms: p > p₀, p < p₀, or p ≠ p₀.

原假设记为 H₀，是默认立场或现状，通常写作 H₀: p = p₀，其中 p₀ 是声称的概率。备择假设记为

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