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Module: Foundation Mathematics I (ITE3705 / GCNU310A)

單元：基礎數學一（ITE3705 / GCNU310A）

Tutorial Worksheet: Statistical Surveys & Sampling Techniques

課堂導修工作紙：統計調查與抽樣技術

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Section 1: Data Sources (Primary vs. Secondary Data)

第 1 節：數據來源（一手數據對比二手數據）

Question 1.1: Local Transit Fare Concession Analysis

題目 1.1：本地交通票價優惠分析

An IVE Business student is investigating the impact of the Hong Kong Public Transport Fare Subsidy Scheme on monthly travel expenses.

一名 IVE 工商管理系學生正在調查香港「公共交通費用補貼計劃」對市民每月交通開支的影響。

1. Identify whether each of the following scenarios gathers Primary Data or Secondary Data:
2. 判斷以下各個情境所收集的是 一手數據（Primary Data） 還是 二手數據（Secondary Data）：
   • (a) The student extracts monthly total subsidy payout figures directly from the Hong Kong Transport Department website.
   • (a) 該學生直接從香港運輸署網站下載每月補貼發放的總金額數據。
   • (b) The student stands at the concourse of Kwun Tong MTR Station and asks 40 commuters to show their recent Octopus monthly transit rebate balances.
   • (b) 該學生站在港鐵觀塘站大堂，邀請 40 名通勤乘客展示其八達通最近的每月交通補貼領取紀錄。
3. State one advantage and one disadvantage of using the dataset obtained in (a) to assess local student travel expenses.
4. 指出使用在 (a) 中獲得的數據集來評估本地學生交通開支的一項優點及一項缺點。

Question 1.2: Fantasy RPG Drop-Rate Audit

題目 1.2：奇幻 RPG 抽卡掉落率審核

A mobile gaming guild investigates whether an in-game limited weapon banner complies with the declared 2.0% ultra-rare drop rate.

一個手機遊戲公會正在調查遊戲內限定武器卡池的極稀有道具實際掉落率，是否符合官方宣稱的 2.0%。

1. Classify the following as Primary Data or Secondary Data:
2. 將下列各項分類為 一手數據 或 二手數據 ：
   • (a) The guild master downloads a spreadsheet containing 50,000 public pull logs aggregated by an overseas player forum.
   • (a) 公會會長下載由海外玩家討論區匯總、包含 50,000 次公開抽卡紀錄的試算表。
   • (b) 20 guild members each record and combine their own next 100 consecutive summoning pulls on the live server.
   • (b) 20 名公會成員各自在正式伺服器上實測並記錄接下來連續 100 次的召喚結果，並將數據合併。
3. State one major limitation of relying exclusively on source (a).
4. 指出完全依賴來源 (a) 的一項主要局限。

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Section 2 & 3: Data Collection Methods

第 2 及 3 節：數據收集方法

Question 2.1: Method Matching

題目 2.1：方法配對

Match each scenario with the most appropriate collection method:

將各個情境與最合適的數據收集方法進行配對：

• I. Direct Observation
• I. 直接觀察法
• II. Personal Interview
• II. 個人面談訪問
• III. Telephone Interview
• III. 電話訪問
• IV. Experiment
• IV. 實驗法
• V. Questionnaire
• V. 問卷調查

Item / 項目	Scenario / 調查情境	Recommended Method / 建議方法
(a)	Determining the battery lifespan of three different smartphone brands running a heavy mobile game continuously. 測定三個不同品牌的智能手機在持續運行高負載手機遊戲時的電池續航時間。
(b)	Counting the number of passengers boarding public light buses (green minibuses) at Mong Kok between 08:00 and 09:00. 點算早上 08:00 至 09:00 期間在旺角登上公共小型巴士（綠色專線小巴）的乘客人數。
(c)	Gathering opinions on campus catering pricing from 400 IVE students across different campuses within 3 days on a low budget. 在有限預算下於 3 天內向來自不同分校的 400 名 IVE 學生收集對飯堂餐飲定價的意見。
(d)	Investigating emotional attachment and reasons behind spending over HK$10,000 on virtual anime merchandise among hardcore collectors[cite: 4, 6]. 深入探討核心收藏家花費超過 HK$10,000 購買虛擬動漫周邊背後的情感寄託與深層原因。

Question 2.2: Method Trade-Offs

題目 2.2：方法的權衡比較

An IVE Computing student wants to evaluate the usability of a newly developed campus indoor navigation mobile app.

一名 IVE 資訊科技系學生希望評估一款新開發的校園室內導航手機應用程式的可用性。

1. Explain why conducting an Experiment in a network laboratory might be preferable to distributing an online Questionnaire for measuring screen loading latency.
2. 解釋為何在網絡實驗室進行實驗法，比起派發網上問卷調查更適合用作量度畫面加載延遲時間。
3. Give two disadvantages of using a Personal Interview to collect data from 500 busy commuters outside an MTR station during peak morning hours.
4. 列出在早上繁忙時間於港鐵站外，以個人面談訪問向 500 名忙碌的上班族收集數據的兩項缺點。

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Section 4: Questionnaire Design & Evaluation

第 4 節：問卷設計與評估

Question 3.1: Identifying Design Flaws

題目 3.1：識別設計缺陷

Evaluate the following draft survey questions intended for IVE students. Identify the primary flaw in each and write an improved version:

評估以下擬定給 IVE 學生填寫的問卷草案題目。指出每題的主要缺陷，並寫出改良後的版本：

• Question A:
• 題目 A：“How much money did you spend on dining at local Hong Kong cafes (Cha Chaan Tengs) and MTR travel over the last 90 days?”「在過去 90 天內，你在本地茶餐廳用餐和搭乘港鐵的總花費是多少？」
• Flaw:
• 缺陷：
• Improved Version:
• 改良版本：
• Question B:
• 題目 B：“Don’t you agree that multiplayer online battle games are far more entertaining than single-player role-playing games?”「難道你不同意多人線上戰鬥競技遊戲遠比單人角色扮演遊戲好玩嗎？」
• Flaw:
• 缺陷：
• Improved Version:
• 改良版本：

Question 3.2: Eliminating Ambiguity and Technical Jargon

題目 3.2：消除模稜兩可與專業術語

• Question C:
• 題目 C：“Do you play mobile games often?”「你經常玩手機遊戲嗎？」
  • Yes / 是
  • No / 否
• Flaw:
• 缺陷：
• Improved Version:
• 改良版本：
• Question D:
• 題目 D：“Please state your main character’s current base AoE DPS stat without gear buffs.”「請寫出你的主力角色在未加裝備 Buff 下的目前基礎 AoE DPS 數值。」
• Flaw:
• 缺陷：
• Improved Version:
• 改良版本：

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Section 5: Target Population and Sample Identification

第 5 節：目標總體與樣本識別

Question 4.1: Chai Wan Campus Canteen Study

題目 4.1：柴灣分校學生飯堂研究

The IVE Campus Facility Office plans to assess student satisfaction regarding dining area seating capacity at the Chai Wan campus. They randomly select and survey 250 students entering the campus library.

IVE 校園設施組計劃評估柴灣分校學生對飯堂座位容量的滿意度。他們隨機抽選並訪問了 250 名正進入校園圖書館的學生。

1. Define the Target Population of this study.
2. 定義本研究的目標總體（Target Population）。
3. Identify the Sample.
4. 指出其樣本（Sample）。
5. Explain why surveying only students entering the library may introduce bias to the sample.
6. 解釋為何僅調查進入圖書館的學生可能會給樣本帶來偏差。

Question 4.2: Mobile Gaming Server Maintenance

題目 4.2：手機遊戲伺服器維護

A game publisher monitors daily active users (DAU) across its Asia-Pacific realm. Out of 80,000 registered accounts, the technical team tracks the ping values of 1,200 randomly selected active accounts during a weekend tournament.

某遊戲發行商正在監控其亞太區伺服器的每日活躍用戶（DAU）。在 80,000 個註冊帳號中，技術團隊於週末錦標賽期間隨機抽選並追蹤了 1,200 個活躍帳號的網絡延遲（Ping 值）。

1. State the population size ($N$N) and sample size ($n$n).
2. 指出總體大小（$N$N）及樣本大小（$n$n）。
3. State the sampling unit.
4. 指出其抽樣單位（Sampling Unit）。

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Section 6: Probability Sampling Methods

第 6 節：概率抽樣方法

======================= RANDOM NUMBER TABLE / 隨機數字表 =======================
Row 1:  0  8  4  1  2  9  8  5  3  1  4  0  7  6  2  0  9  3  1  5
Row 2:  2  4  9  2  1  7  8  6  1  0  1  6  6  3  5  9  8  6  8  9
Row 3:  7  7  6  4  0  9  7  6  3  6  3  7  3  9  7  9  3  3  7  9
Row 4:  1  2  0  5  4  8  2  0  1  1  9  4  5  2  0  3  6  1  7  4
=============================================================================

Question 5.1: Simple Random Sampling (SRS)

題目 5.1：簡單隨機抽樣

An IVE Esports Club consists of $N=36$N=36 tournament contenders numbered sequentially from $01$01 to $36$36. The coach must select a sample of $n=4$n=4 players to test a new low-latency fiber network connection.

某 IVE 電競學會共有 $N=36$N=36 名參賽選手，編號由 $01$01 至 $36$36。教練需要抽取 $n=4$n=4 名選手組成樣本，以測試全新的低延遲光纖網絡連接。

1. Using the random number table above, start at Row 1, Column 1 and read 2-digit numbers horizontally from left to right.
2. 使用上方的隨機數字表，從第 1 行、第 1 列開始，由左至右橫向讀取兩位數字。
3. List the first 8 two-digit numbers encountered.
4. 列出最初讀取到的 8 個兩位數字。
5. Identify which players are selected (ignoring out-of-range values and duplicates) until all 4 players are chosen.
6. 依序指出被選中的選手（忽略超出範圍及重複的數值），直至選滿 4 位選手為止。

Question 5.2: Systematic Sampling

題目 5.2：系統抽樣

A retail electronics shop in the Wan Chai Computer Centre serves $N=480$N=480 customers during a weekend promotion. The manager wants to audit service quality by sampling $n=16$n=16 customers using systematic sampling.

灣仔電腦城的一家電腦周邊專賣店在週末促銷期間共接待了 $N=480$N=480 名顧客。經理希望透過系統抽樣抽選 $n=16$n=16 名顧客進行服務質素審查。

1. Determine the sampling interval $k$k:
2. 計算抽樣間距 $k$k：

$$k=\lfloor \frac{N}{n}\rfloor$$k=⌊nN​⌋

2. If the first customer selected is Customer 09, list the next 4 customer numbers to be included in the sample.
3. 若抽中的第一位顧客為 09 號，列出接下來入選樣本的 4 位顧客編號。
4. Explain one potential risk of systematic sampling if store sales announcements occur at regular time intervals.
5. 若店舖每隔固定時間進行一次特價廣播，解釋系統抽樣可能面臨的 一項潛在風險。

Question 5.3: Stratified Random Sampling

題目 5.3：分層隨機抽樣

The Vocational Training Council plans to establish a student advisory committee across three departments at an IVE campus. The breakdown of student enrollment is shown below:

職業訓練局計劃在某 IVE 分校的三個學系中成立學生諮詢委員會，各系學生人數分佈如下：

Department / 學系	Number of Students / 學生人數
Information Technology (IT) / 資訊科技系	900
Engineering (ENG) / 工程系	600
Health & Life Sciences (HLS) / 健康及生命科學系	500
Total (NN) / 總計 (NN)	2,000

A representative sample of $n=40$n=40 students is to be selected using proportional stratified sampling.

現採用按比例分層隨機抽樣法，從中抽取一個 $n=40$n=40 名學生的代表性樣本。

1. Calculate the number of students that must be sampled from each department:
2. 計算每個學系應抽取的學生人數：

• (a) Information Technology ($n_{\text{IT}}$nIT​)
• (a) 資訊科技系（$n_{\text{IT}}$nIT​）
• (b) Engineering ($n_{\text{ENG}}$nENG​)
• (b) 工程系（$n_{\text{ENG}}$nENG​）
• (c) Health & Life Sciences ($n_{\text{HLS}}$nHLS​)
• (c) 健康及生命科學系（$n_{\text{HLS}}$nHLS​）

2. Verify that the sum of the stratum samples equals the total sample size $n$n.
3. 驗證各層樣本數之總和是否等於總樣本大小 $n$n。

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Section 7: Non-Probability Sampling Methods

第 7 節：非概率抽樣方法

Question 6.1: Judgement vs. Quota Sampling Scenarios

題目 6.1：判斷抽樣與配額抽樣情境辨析

Identify whether each scenario describes Judgement Sampling or Quota Sampling:

判斷以下各情境屬於判斷抽樣法（Judgement Sampling）還是配額抽樣法（Quota Sampling）：

1. An interviewer stationed at the entrance of a Sha Tin shopping mall is told to collect completed surveys from exactly 20 elderly citizens, 20 working adults, and 20 secondary school students, choosing respondents at their own discretion.
2. 駐守於沙田某商場入口的訪問員接獲指示，需訪問剛好 20 位長者、20 位在職成年人及 20 位中學生，訪問員可自行決定攔截哪些對象。
3. A marketing director personally selects three specific comic book cafes in Mong Kok and Causeway Bay to test customer interest in a new Japanese anime merchandise line, believing these locations attract the most dedicated fans.
4. 市場總監親自挑選了旺角和銅鑼灣三家特定的動漫女僕咖啡廳，以測試顧客對全新日本動漫周邊系列的興趣，因為他相信這些地點能聚集最狂熱的粉絲。

Question 6.2: Method Evaluation

題目 6.2：方法評估

State two key disadvantages of using non-probability sampling methods compared to probability sampling methods when publishing statistical survey findings.

指出在發佈統計調查報告時，非概率抽樣法相比概率抽樣法的兩項主要缺點。

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Comprehensive Practical Task: Campus Transit Survey Design

綜合實踐任務：校園交通調查設計

An IVE student project group wants to investigate the average daily transit cost of students commuting to the Sha Tin campus.

一個 IVE 學生專題小組希望調查到沙田分校上課的學生平均每日交通開支。

The student population ($N=1,200$N=1,200) is divided by transport mode:

該校學生總體（$N=1,200$N=1,200）按主要乘搭的交通方式劃分如下：

• MTR Commuters: $720$720 students
• 乘搭港鐵： $720$720 名學生
• Bus / Minibus Commuters: $360$360 students
• 乘搭巴士／小巴： $360$360 名學生
• Walking / Cycling: $120$120 students
• 步行／騎單車： $120$120 名學生

1. If the group decides to draw a sample of $n=60$n=60 students using Stratified Sampling, calculate the number of students to sample from each transport category.
2. 若該小組決定採用分層抽樣法抽取 $n=60$n=60 名學生作為樣本，計算各交通類別應抽取的學生人數。
3. Draft two closed questions for their survey questionnaire:
4. 為他們的調查問卷擬定兩條封閉式題目：

• One question recording daily travel expenditure in Hong Kong Dollars using clear, non-overlapping numerical categories.
• 一條使用清晰、互不重疊的金額區間記錄每日交通開支（港元）的題目。
• One 5-point rating scale question measuring satisfaction with transit connections to the campus.
• 一條評估對前往分校的交通接駁滿意度的五點量表（Likert Scale）評分題。