设计简答题问题

题目（简答题，统计推断） 背景与目标：评估学生对单样本均值的参数估计与假设检验的掌握，包括模型设定、统计量计算、结论解释与前提假设识别。

题干 某制造过程产出重量近似独立同分布。为评估该过程的平均重量μ，随机抽取 n = 35 个样本，得到样本均值 x̄ = 102.4 与样本标准差 s = 4.2。管理方宣称过程均值为 μ0 = 100。

请回答：

1. 在合理前提下，构造 μ 的95%置信区间，并给出数值结果与区间的情境化解释。
2. 以显著性水平 α = 0.05，检验 H0: μ = 100 与 H1: μ ≠ 100。报告检验统计量、p 值（或临界值判断）及结论。
3. 简述上述推断所依赖的关键统计前提，并说明若存在明显偏离（如强烈偏态或离群）对结论的潜在影响。

作答限制：写出主要公式与关键中间量（如标准误、t 分位数），数值可四舍五入至小数点后两位。

参考答案要点与评分细则（总分10分）

• 构念对齐：单样本 t 推断（未知总体方差），含估计与检验的解释性应用。

A. 95%置信区间（3分）

• 方法选择（1分）：识别采用单样本 t 区间，x̄ ± t0.975, df=34 × s/√n。
• 计算（1分）：SE = s/√n = 4.2/√35 ≈ 0.71；t0.975,34 ≈ 2.03；误差界 ≈ 2.03 × 0.71 ≈ 1.44。
• 区间与解释（1分）：CI ≈ (102.4 − 1.44, 102.4 + 1.44) = (100.96, 103.84)；解释为：在重复抽样的95%情形下，构造的区间将覆盖μ；本次区间不包含100，提示均值高于宣称值的证据。

B. 假设检验（3分）

• 设定与统计量（1分）：H0: μ = 100；H1: μ ≠ 100；t = (x̄ − μ0)/(s/√n) = (102.4 − 100)/0.71 ≈ 3.38，df = 34。
• p 值/临界值与结论（2分）：两侧 p 值 ≈ 0.002（允许 p < 0.01 的近似表述）；或 |t| > t0.975,34 ≈ 2.03，故在 α = 0.05 拒绝 H0；结论：数据表明该过程均值显著高于100。

C. 前提与稳健性（2分）

• 关键前提（1分）：独立同分布；样本来自近似正态总体或样本量足够大以依赖 t 程序的稳健性/中心极限定理；无严重离群与强烈偏态。
• 影响（1分）：强离群或重尾可夸大/缩小标准误并扭曲 t 分布近似，导致第一类/第二类错误率偏离标称水平；系统性依赖或非随机抽样会破坏结论的可推广性。

D. 表达与解释准确性（2分）

• 将置信区间与p值的含义表述为长期频率/反事实重复抽样框架，避免将“95%概率地包含μ”误解为针对固定 μ 的概率陈述（1分）。
• 论断与数据一致、无过度外推（1分）。

部分给分与容差

• t 分位数取 2.03 的近似可接受；SE 与边际误差的数值误差在±0.02 内不扣分。
• 仅给出正确区间或正确检验结论之一，可按相应小项计分。
• 若采用 z 程序但结论方向一致，且说明理由，可酌情给 0.5–1.0 分，但不得满分（因未知σ时 t 程序更合适）。

认知层次与难度

• 认知层次：应用—分析（计算+假设识别+情境化解释）。
• 难度：中等；预计作答时间 8–10 分钟。

测量学合理性说明（简述）

• 效度：题目直接取样本均值推断的核心证据（t 区间与双侧检验），与“统计推断”学习目标高度对齐；同时要求阐明前提与影响，减少“只会算不懂用”的构念无关方差（AERA, APA, & NCME, 2014；Wasserman, 2004）。
• 评分信度：采用分析型评分量表、明确数值容差与要点列举，可提升评分一致性（Brookhart, 2018；Lane, Raymond, & Haladyna, 2016）。
• 解释恰当性：同时要求报告区间与检验并进行情境化解释，有助于抑制对单一 p 值的过度依赖与误读（Wasserstein & Lazar, 2016）。

参考文献（APA 第七版）

• American Educational Research Association, American Psychological Association, & National Council on Measurement in Education. (2014). Standards for Educational and Psychological Testing. American Educational Research Association.
• Brookhart, S. M. (2018). How to create and use rubrics for formative assessment and grading. ASCD.
• Casella, G., & Berger, R. L. (2002). Statistical inference (2nd ed.). Duxbury.
• Lane, S., Raymond, M. R., & Haladyna, T. M. (Eds.). (2016). Handbook of test development (2nd ed.). Routledge.
• Wasserman, L. (2004). All of statistics: A concise course in statistical inference. Springer.
• Wasserstein, R. L., & Lazar, N. A. (2016). The ASA’s statement on p-values: Context, process, and purpose. The American Statistician, 70(2), 129–133.

Short-answer item (customer complaint handling)

Assessment objective: Evaluate the examinee’s ability to design a timely, principled, and feasible response to a customer complaint that aligns with recognized standards and justice-based service recovery.

Prompt: You are the customer service supervisor at a mid-sized e-commerce firm. A five-year loyal customer reports receiving a defective product, waited 25 minutes on hold before the call dropped, and has posted a negative public review threatening to switch suppliers. Replacement stock is limited; policy allows refund or replacement within 30 days; carrier damage is suspected. Within the next 24 hours, what actions will you take to address the complaint and stabilize the relationship? In 180–220 words, explicitly address: (a) acknowledgement/apology and ownership; (b) information gathering and documentation; (c) remedy selection under operational constraints and its rationale; (d) communication channel(s) and message content; and (e) follow-up and prevention. Briefly justify your choices using distributive, procedural, and interactional justice.

Scoring rubric (analytic; 10 points total)

• Acknowledgement/apology and ownership (2): Provides an immediate, sincere apology; accepts organizational responsibility; specifies timely outreach within 24 hours. Partial credit if apology lacks ownership or timeliness.
• Information gathering and documentation (2): Verifies order/defect facts; records the complaint and actions in a case log; captures root-cause hypothesis; aligns with a documented complaints process (e.g., ISO 10002). Partial if ad hoc or lacks documentation.
• Remedy selection and rationale (3): Chooses a feasible remedy (e.g., expedited replacement/backorder with clear timeline, refund, goodwill credit) that fits policy and loss incurred; explicitly justifies via distributive and procedural justice under stock constraints and addresses the public review. Partial if remedy is generic or ignores constraints/justice rationale.
• Communication strategy (2): Selects channel(s) (e.g., phone for immediacy plus written confirmation); specifies respectful, transparent messaging, offers choice, and explains steps; ties to interactional justice. Partial if “contact customer” is stated without content/channel rationale.
• Follow-up and prevention (1): Commits to confirm satisfaction, invite revision of the public review without pressure, and trigger internal corrective action (e.g., carrier QA, queue-time audit). Partial if follow-up is mentioned but lacks prevention.

Validity and reliability notes (for assessors): The item targets applied decision-making and justification using established complaint-handling standards (ISO 10002:2018) and the three justice dimensions shown to predict post-complaint satisfaction and loyalty (Tax, Brown, & Chandrashekaran, 1998; Colquitt, 2001). An analytic rubric supports inter-rater reliability and construct coverage (Jonsson & Svingby, 2007) and aligns evidence with the intended inference about competency (Messick, 1995). The constrained word limit promotes focus and comparability.

References (APA 7th)

• Colquitt, J. A. (2001). On the dimensionality of organizational justice: A construct validation of a measure. Journal of Applied Psychology, 86(3), 386–400. https://doi.org/10.1037/0021-9010.86.3.386
• International Organization for Standardization. (2018). ISO 10002:2018 Quality management—Customer satisfaction—Guidelines for complaints handling. ISO.
• Jonsson, A., & Svingby, G. (2007). The use of scoring rubrics: Reliability, validity and educational consequences. Educational Research Review, 2(2), 130–144. https://doi.org/10.1016/j.edurev.2007.05.002
• Messick, S. (1995). Validity of psychological assessment: Validation of inferences from persons’ responses and performances as scientific inquiry. American Psychologist, 50(9), 741–749. https://doi.org/10.1037/0003-066X.50.9.741
• Tax, S. S., Brown, S. W., & Chandrashekaran, M. (1998). Customer evaluations of service complaint experiences: Implications for relationship marketing. Journal of Marketing, 62(2), 60–76. https://doi.org/10.2307/1252161
• Davidow, M. (2003). Organizational responses to customer complaints: What works and what doesn’t. Journal of Service Research, 5(3), 225–250. https://doi.org/10.1177/1094670502238917