Significant Public Policy Cases of the Roberts Court: Hypothesis Testing in A-Level Maths | 罗伯茨法院重大公共政策案例：A-Level数学中的假设检验

📚 Significant Public Policy Cases of the Roberts Court: Hypothesis Testing in A-Level Maths | 罗伯茨法院重大公共政策案例：A-Level数学中的假设检验

The Roberts Court has decided landmark cases on campaign finance, voting rights, health care, and civil rights. These cases are usually studied in politics or law, but they also raise quantitative questions that can be framed using A-Level Edexcel statistics: Is an observed difference in voter turnout statistically significant? Does an independent-expenditure change lead to a real policy effect? This article uses the Court’s public policy cases as motivating scenarios to revise hypothesis testing, binomial and normal distributions, correlation, conditional probability, and confidence intervals.

罗伯茨法院在竞选资金、投票权、医疗保健和民权等领域作出过里程碑式判决。这些案件通常在政治或法律课程中学习，但它们也提出可以用 A-Level Edexcel 统计学处理的定量问题：观察到的选民投票率差异是否具有统计显著性？独立支出的变化是否导致了真实的政策效应？本文以该法院的公共政策案例为情境，复习假设检验、二项分布与正态分布、相关、条件概率和置信区间。

1. The Roberts Court as a Source of Statistical Questions | 罗伯茨法院作为统计问题的来源

Cases such as Citizens United v. FEC (2010) and Shelby County v. Holder (2013) force judges, lawyers, and researchers to compare data before and after a legal change. For example, after Citizens United removed restrictions on corporate independent expenditure, analysts asked whether the average independent spending in federal elections rose significantly. In A-Level terms, this becomes a hypothesis test of a population mean or proportion. Similarly, after Shelby County struck down the coverage formula of the Voting Rights Act, researchers compared rates of polling-place closures in previously covered counties with those in non-covered counties. A two-sample binomial test or a normal approximation can be used to decide whether the difference is unlikely to have occurred by chance.

诸如 Citizens United v. FEC（2010）和 Shelby County v. Holder（2013）等案件迫使法官、律师和研究者比较法律变化前后的数据。例如，在 Citizens United 取消了对企业独立支出的限制之后，分析人士会问联邦选举中的平均独立支出是否显著上升。用 A-Level 的术语来说，这就变成了对总体均值或比例的假设检验。类似地，在 Shelby County 废除了《投票权法》覆盖公式之后，研究者比较了原先被覆盖县与非覆盖县的投票站关闭率。可以使用双样本二项检验或正态近似来判断该差异是否不太可能仅由偶然造成。

2. Hypothesis Testing: Null and Alternative Hypotheses | 假设检验：原假设与备择假设

Every A-Level hypothesis test begins with two competing statements. The null hypothesis H₀ is the default position: nothing has changed, or any observed difference is due to sampling variation. The

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