Bridging British Education Virtual Academy

1. Course Basic Information 1. 课程基本信息

Course Name: Matt Alice Lesson 课程名称： Matt Alice 课程

Topic: Hypothesis Testing (One-tail and Two-tail Tests) 主题： 假设检验（单尾和双尾检验）

Date: Date not specified 日期： 日期未指定

Student: Alice 学生： Alice

Teaching Focus 教学重点

Reviewing and practicing the step-by-step process of hypothesis testing using binomial distributions, focusing on identifying the test statistic, hypotheses, calculating probabilities, and forming context-specific conclusions for both one-tail and two-tail tests.

回顾并练习使用二项分布进行假设检验的逐步过程，重点关注识别检验统计量、假设、计算概率以及为单尾和双尾检验形成特定情境的结论。

Teaching Objectives 教学目标

Solidify understanding of the components of a hypothesis test (Test Statistic, H0, H1). 巩固对假设检验组成部分（检验统计量、H0、H1）的理解。
Accurately set up one-tail and two-tail hypotheses based on contextual clues. 根据情境线索准确设置单尾和双尾假设。
Correctly calculate the required probability using the binomial distribution (Binomial PD/CD functions). 使用二项分布（Binomial PD/CD 函数）正确计算所需的概率。
Formulate a contextual conclusion by comparing the calculated probability with the significance level. 通过将计算出的概率与显著性水平进行比较，形成情境化的结论。

2. Course Content Overview 2. 课程内容概览

Main Teaching Activities and Time Allocation 主要教学活动和时间分配

Review Test Statistic and Hypotheses (Example 1): Discussed the definition of the test statistic (number of successes) and set up H0 and H1 for a one-tail test, identifying clues like 'overestimating' to determine direction (p < 0.4).

检验统计量与假设回顾（例1）： 讨论了检验统计量的定义（成功次数）并设置了单尾检验的H0和H1，通过‘过高估计’等线索确定方向（p < 0.4）。

Hypothesis Rejection Condition and Binomial Setup: Explained the condition for rejecting H0 (p-value < significance level) and set up the binomial distribution parameters (n=20, p=0.4), determining the region of extremity (X ≤ 2).

假设拒绝条件与二项分布设置： 解释了拒绝H0的条件（p值 < 显著性水平），并设置了二项分布参数（n=20, p=0.4），确定了极端区域（X ≤ 2）。

Practice One-Tail Test (Example 5): Worked through a complete one-tail test problem (drug improvement). Student correctly identified X, P, H0, H1 (p > 0.4), calculated P(X ≥ 11), compared with 5%, and concluded appropriately.

单尾检验练习（例5）： 完成了一个完整的单尾检验问题（新药改进）。学生正确识别了X, P, H0, H1（p > 0.4），计算了P(X ≥ 11)，与5%比较，并得出恰当结论。

Introduction to Two-Tail Tests (Example 10 & Theory): Introduced two-tail tests where H1 uses '≠' and the significance level must be halved (e.g., 5% becomes 2.5% for comparison). Practiced setting up a two-tail test (Example 10) and calculating the probability of the observed value or more extreme.

双尾检验介绍（例10与理论）： 介绍了使用'≠'的双尾检验，以及显著性水平必须减半（例如，5%变为2.5%进行比较）。练习设置了一个双尾检验（例10）并计算了观察值或更极端值的概率。

Language Knowledge and Skills 语言知识与技能

Vocabulary:
Test statistic, Null hypothesis (H0), Alternative hypothesis (H1), Significance level (α), One-tail test, Two-tail test, Success, Expected value, Critical region, Overestimate, Insufficient evidence.

词汇：
检验统计量, 零假设 (H0), 备择假设 (H1), 显著性水平 (α), 单尾检验, 双尾检验, 成功, 期望值, 临界区域, 过高估计, 证据不足.

Concepts:
Binomial Distribution Application in Hypothesis Testing, Directionality in H1, Halving significance level for two-tail tests, Conclusion contextualization.

概念：
二项分布在假设检验中的应用, H1 中的方向性, 双尾检验显著性水平减半, 结论语境化.

Skills Practiced:
Interpreting contextual clues to define H1 direction, setting up binomial distributions under H0 assumption, using calculator functions (Binomial PD/CD), writing formal statistical conclusions.

练习技能：
解读情境线索以定义H1方向, 在H0假设下设置二项分布, 使用计算器功能（Binomial PD/CD）, 书写正式的统计结论。

Teaching Resources and Materials 教学资源与材料

Worked examples from textbook exercises (focus on contextual problems). 教科书习题中的范例（重点关注情境题）。

3. Student Performance Assessment (Alice) 3. 学生表现评估 (Alice)

Participation and Activeness 参与度和积极性

Very high engagement, actively recalling previous concepts and participating in setting up steps for new examples. 参与度非常高，积极回忆先前概念并参与设置新例题的步骤。

Language Comprehension and Mastery 语言理解和掌握

Strong understanding of the overall hypothesis testing framework, particularly how to determine extremity based on the expected value in one-tail tests. 对假设检验的整体框架理解深刻，特别是单尾检验中如何根据期望值确定极端方向。

Language Output Ability 语言输出能力

Oral: 口语：

Fluency in explaining the reasoning behind hypothesis choices and conclusion structure, although occasional hesitation when shifting between 'less than' and 'more extreme'. 解释假设选择和结论结构的推理很流利，但在切换‘小于’和‘更极端’时偶尔有停顿。

Written: 书面：

Student successfully applied learned procedures to set up and solve complex one-tail and two-tail binomial tests.

学生成功应用所学程序来设置和解决复杂的一尾和双尾二项式检验问题。

Student's Strengths 学生的优势

Quickly grasps the structure of the hypothesis test and the marking scheme logic. 能快速掌握假设检验的结构和评分方案的逻辑。
Accurately identifies the 'success' definition for the test statistic (X). 能准确识别检验统计量(X)的‘成功’定义。
Understands the need to halve the significance level in two-tail tests. 理解在双尾检验中需要将显著性水平减半。

Areas for Improvement 需要改进的方面

Ensuring the conclusion strictly adheres to the context using the language provided in the question, especially when rejecting H0. 确保结论严格遵循问题的上下文语言，特别是在拒绝H0时。
Rigorously including the observed sample value (x) in the 'more extreme' range (e.g., P(X ≤ x) instead of P(X < x) when necessary). 严格确保观察到的样本值(x)包含在‘更极端’的范围内（例如，在需要时使用 P(X ≤ x) 而不是 P(X < x)）。

4. Teaching Reflection 4. 教学反思

Effectiveness of Teaching Methods 教学方法的有效性

The teacher effectively guided the student through complex contextual problems by breaking them down into manageable steps (Model -> Setup -> Calculation -> Conclusion). 教师通过将复杂的情境问题分解为可管理的步骤（模型 -> 设置 -> 计算 -> 结论）有效地引导了学生。
Strong clarification provided on the subtle differences between one-tail and two-tail tests, particularly regarding the alternative hypothesis and significance level adjustment. 对单尾和双尾检验之间的细微差别提供了清晰的解释，特别是关于备择假设和显著性水平的调整。

Teaching Pace and Time Management 教学节奏和时间管理

The pace was fast but manageable, covering both one-tail and two-tail procedures in depth due to the student's solid foundational knowledge. 由于学生扎实的基础知识，课程节奏快但可控，深入涵盖了单尾和双尾过程。

Classroom Interaction and Atmosphere 课堂互动和氛围

Interactive, analytical, and focused, with the teacher ensuring the student understood the 'why' behind the mathematical steps, especially the logical shift in conclusions.

互动、分析性强且专注，教师确保学生理解数学步骤背后的‘原因’，特别是结论中的逻辑转变。

Achievement of Teaching Objectives 教学目标的达成

All primary objectives relating to hypothesis setup, calculation, and conclusion formation were met through guided practice. 所有与假设设置、计算和结论形成相关的首要目标都通过指导练习得以实现。

5. Subsequent Teaching Suggestions 5. 后续教学建议

Teaching Strengths 教学优势

Identified Strengths: 识别的优势：

Excellent use of contextual examples to illustrate abstract statistical concepts. 出色地利用情境范例来说明抽象的统计概念。
Detailed breakdown of the four key marks in an exam-style conclusion. 详细分解了考试风格结论中的四个关键分数点。

Effective Methods: 有效方法：

Systematically comparing the observed sample result against the expected value to determine the tail/direction of testing. 系统地将观察到的样本结果与期望值进行比较，以确定检验的尾部/方向。
Explicitly contrasting one-tail vs. two-tail tests in terms of H1 and α adjustment. 明确对比单尾与双尾检验在H1和α调整方面的差异。

Positive Feedback: 正面反馈：

The student demonstrated high retention of the overall testing procedure after intense review. 学生在密集的复习后，对整体检验程序表现出很高的掌握度。

Next Teaching Focus 下一步教学重点

Formal introduction to Critical Regions as an alternative method for hypothesis testing, specifically how to find and use them for both one-tail and two-tail tests. 正式介绍临界区域作为假设检验的替代方法，特别是如何为单尾和双尾检验找到并使用它们。

Specific Suggestions for Student's Needs 针对学生需求的具体建议

Hypothesis & Conclusion Structure: 假设与结论结构：

Always write out the full context for the conclusion. E.g., 'There is sufficient evidence to reject H0, suggesting the new drug *is* better than the standard treatment (p > 0.4).' 始终写出结论的完整语境。例如：‘有充分证据拒绝H0，表明新药*确实*优于标准治疗（p > 0.4）。’
When setting H1 for one-tail tests, explicitly state *why* you chose '>' or '<' based on the wording (e.g., 'improvement' means '>'). 在设置单尾检验的H1时，明确说明选择‘>’还是‘<’是基于问题的措辞（例如，‘改进’意味着‘>’）。

Calculation Precision: 计算精确性：

In binomial probability calculations, be extremely careful to include the observed value (x) in the region of extremity (e.g., use P(X ≤ 11) or P(X ≥ 11) as required). 在二项分布概率计算中，务必将观察值(x)包含在极端区域内（例如，根据要求使用 P(X ≤ 11) 或 P(X ≥ 11)）。

Recommended Supplementary Learning Resources or Homework 推荐的补充学习资源或家庭作业

Review the structural differences between one-tail (H1: ≠) and two-tail (H1: =/≠) tests, paying close attention to the significance level adjustment for two-tail tests. 复习单尾检验（H1: ≠）和双尾检验（H1: =/≠）之间的结构差异，密切关注双尾检验的显著性水平调整。