📚 IGCSE AQA Maths: Hypothesis Testing Exam Tips | IGCSE AQA 数学：假设检验 考点精讲
Hypothesis testing is a key topic in IGCSE AQA Mathematics (Higher Tier), bridging probability theory and statistical inference. It empowers you to critically evaluate claims about a population proportion using sample data. In the exam, you must master setting up hypotheses, working with binomial probabilities, and interpreting results in context under a given significance level. This revision guide distils every essential point for top marks.
假设检验是 IGCSE AQA 数学（高阶段）的核心专题，它将概率理论与统计推断联系起来。这让你能够根据样本数据，批判性地评估关于总体比例的声明。考试中，你必须掌握设定假设、运用二项概率、以及在给定显著性水平下结合背景解释结果。本复习指南提炼了拿满分所需的每个要点。
1. What Is Hypothesis Testing? | 什么是假设检验？
Hypothesis testing is a formal procedure that helps us decide whether to reject a stated claim (the null hypothesis) based on sample evidence. Rather than proving a claim true, we look for sufficient evidence to contradict it. The process uses probability to measure how extreme the observed data would be if the null hypothesis were true.
假设检验是一个规范化的流程，帮助我们在样本证据的基础上决定是否拒绝原假设。它不是证明某个说法正确，而是寻找足够的证据来反驳它。这一过程利用概率度量：如果原假设为真，得到所观测数据的极端程度有多大。
In an IGCSE setting, we always test a single population proportion p. The sample follows a binomial distribution. You will be given a sample size n, a claimed proportion p₀, and a significance level α. Your task: determine whether the sample result falls inside the critical region, leading you to reject the null hypothesis.
在 IGCSE 情境下，我们始终检验单个总体比例 p。样本服从二项分布。题目会给定样本容量 n、声明的比例 p₀ 以及显著性水平 α。你的任务是判断样本结果是否落入临界区域，从而拒绝原假设。
2. Stating the Null and Alternative Hypotheses | 陈述原假设与备择假设
₀. The alternative hypothesis H₁ (or Hₐ) challenges this, indicating the direction we suspect the true proportion might deviate: either greater than, less than, or simply different from p₀.
原假设 H₀ 是无效应或没有差异的陈述；通常假设声称的总体比例成立，写作 H₀: p = p₀。备择假设 H₁（或 Hₐ）对此提出质疑，指出我们猜测的真实比例可能偏离的方向：大于、小于或不同于 p₀。
Exactly phrasing the hypotheses is critical. For a test where you suspect an increase, use H₁: p > p₀ (upper‑tail). If you suspect a decrease, use H₁: p < p₀ (lower‑tail). When the direction is not specified, use a two‑tailed alternative H₁: p ≠ p₀. The hypotheses always refer to the population, not the sample.
准确表述假设至关重要。若怀疑增加，用 H₁: p > p₀（上尾）。若怀疑降低，用 H₁: p < p₀（下尾）。若未指明方向，则采用双尾备择假设 H₁: p ≠ p₀。注意，假设针对的是总体，而非样本。
3. Significance Levels (α) | 显著性水平 (α)
he null hypothesis when it is actually true (a Type I error). Common values at IGCSE are 5% (α = 0.05) or 1% = 0.01). The exam question will state α; you must use it to determine the critical region.
显著性水平 α 是原假设实际为真却被拒绝的概率（即第一
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