Setting the Hypotheses | 假设的设定

📚 Setting the Hypotheses | 假设的设定

In hypothesis testing, setting the hypotheses is the first and most important step. A clearly written null hypothesis H₀ and alternative hypothesis H₁ tell you exactly what you are testing, whether the test is one-tailed or two-tailed, and which parameter is under investigation.

在假设检验中，设定假设是第一步，也是最重要的一步。清晰写出原假设 H₀ 和备择假设 H₁，能让你明确正在检验什么、检验是单尾还是双尾，以及所研究的参数是什么。

1. The Role of Hypotheses in a Test | 假设在检验中的作用

Every hypothesis test compares two competing statements about a population parameter. The null hypothesis represents the default or current belief, while the alternative hypothesis represents the claim we want to find evidence for.

每个假设检验都会对总体参数的两个对立陈述进行比较。原假设代表默认或当前的看法，而备择假设代表我们想要寻找证据支持的声明。

Edexcel questions often ask you to ‘test whether…’ or ‘investigate whether…’. Your first line of working should always state H₀ and H₁ using correct notation.

Edexcel 题目常要求你“检验是否……”或“调查是否……”。你的第一行解答应当始终使用正确记号写出 H₀ 和 H₁。

2. Null Hypothesis H₀ | 原假设 H₀

The null hypothesis always contains an equals sign. In many Edexcel mark schemes it is written as H₀: p = k, H₀: μ = k or H₀: λ = k, where k is the assumed value.

原假设总是包含等号。在 Edexcel 评分方案中，通常写成 H₀: p = k、H₀: μ = k 或 H₀: λ = k，其中 k 是假设的取值。

Some textbooks also allow H₀: p ≤ k or H₀: p ≥ k for one-tailed tests, but the cleanest and safest form for exams is to write the equality version.

有些教材也允许在单尾检验中写 H₀: p ≤ k 或 H₀: p ≥ k，但考试中最简洁、最安全的形式是写等式版本。

Do not put a sample statistic such as x̄ or p̂ in the hypotheses. Hypotheses are about population parameters, not sample results.

不要把样本统计量如 x̄ 或 p̂ 放进假设中。假设是关于总体参数的，而不是样本结果。

3. Alternative Hypothesis H₁ | 备择假设 H₁

The alternative hypothesis is the statement you are testing for. It uses a strict inequality: <, > or ≠. It never

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