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統計學導論

Introductory Statistics

《Introductory Statistics》是開放授權的統計學教科書，共 13 章，從抽樣、機率與機率分配，談到信賴區間、假設檢定與迴歸。以下為 ReadPilot 翻譯的中文章節大綱。

第 1 章抽樣與資料Sampling and Data

  1. 1.1統計學、機率與關鍵術語的定義Definitions of Statistics, Probability, and Key Terms
  2. 1.2資料、抽樣，以及資料與抽樣的變異Data, Sampling, and Variation in Data and Sampling
  3. 1.3次數、次數分配表與衡量尺度Frequency, Frequency Tables, and Levels of Measurement
  4. 1.4實驗設計與倫理Experimental Design and Ethics
  5. 1.5資料蒐集實驗Data Collection Experiment
  6. 1.6抽樣實驗Sampling Experiment

第 2 章敘述統計Descriptive Statistics

  1. 2.1莖葉圖、折線圖與長條圖Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs
  2. 2.2直方圖、次數多邊圖與時間序列圖Histograms, Frequency Polygons, and Time Series Graphs
  3. 2.3資料位置的衡量Measures of the Location of the Data
  4. 2.4盒狀圖Box Plots
  5. 2.5資料中心的衡量Measures of the Center of the Data
  6. 2.6偏態與平均數、中位數、眾數Skewness and the Mean, Median, and Mode
  7. 2.7資料離散程度的衡量Measures of the Spread of the Data
  8. 2.8敘述統計Descriptive Statistics

第 3 章機率主題Probability Topics

  1. 3.1基本術語Terminology
  2. 3.2獨立事件與互斥事件Independent and Mutually Exclusive Events
  3. 3.3機率的兩個基本法則Two Basic Rules of Probability
  4. 3.4列聯表Contingency Tables
  5. 3.5樹狀圖與文氏圖Tree and Venn Diagrams
  6. 3.6機率主題Probability Topics

第 4 章離散型隨機變數Discrete Random Variables

  1. 4.1離散型隨機變數的機率分配函數（PDF）Probability Distribution Function (PDF) for a Discrete Random Variable
  2. 4.2平均數（期望值）與標準差Mean or Expected Value and Standard Deviation
  3. 4.3二項分配Binomial Distribution
  4. 4.4幾何分配Geometric Distribution
  5. 4.5超幾何分配Hypergeometric Distribution
  6. 4.6卜瓦松分配Poisson Distribution
  7. 4.7離散分配（撲克牌實驗）Discrete Distribution (Playing Card Experiment)
  8. 4.8離散分配（幸運骰子實驗）Discrete Distribution (Lucky Dice Experiment)

第 5 章連續型隨機變數Continuous Random Variables

  1. 5.1連續型機率函數Continuous Probability Functions
  2. 5.2均勻分配The Uniform Distribution
  3. 5.3指數分配The Exponential Distribution
  4. 5.4連續分配Continuous Distribution

第 6 章常態分配The Normal Distribution

  1. 6.1標準常態分配The Standard Normal Distribution
  2. 6.2常態分配的應用Using the Normal Distribution
  3. 6.3常態分配（單圈時間）Normal Distribution (Lap Times)
  4. 6.4常態分配（小指長度）Normal Distribution (Pinkie Length)

第 7 章中央極限定理The Central Limit Theorem

  1. 7.1樣本平均數的中央極限定理The Central Limit Theorem for Sample Means (Averages)
  2. 7.2總和的中央極限定理The Central Limit Theorem for Sums
  3. 7.3中央極限定理的應用Using the Central Limit Theorem
  4. 7.4中央極限定理（口袋零錢）Central Limit Theorem (Pocket Change)
  5. 7.5中央極限定理（餅乾食譜）Central Limit Theorem (Cookie Recipes)

第 8 章信賴區間Confidence Intervals

  1. 8.1以常態分配推估單一母體平均數A Single Population Mean using the Normal Distribution
  2. 8.2以學生 t 分配推估單一母體平均數A Single Population Mean using the Student t Distribution
  3. 8.3母體比例A Population Proportion
  4. 8.4信賴區間（房屋價格）Confidence Interval (Home Costs)
  5. 8.5信賴區間（出生地）Confidence Interval (Place of Birth)
  6. 8.6信賴區間（女性身高）Confidence Interval (Women's Heights)

第 9 章單一樣本的假設檢定Hypothesis Testing with One Sample

  1. 9.1虛無假設與對立假設Null and Alternative Hypotheses
  2. 9.2結果與第一型、第二型錯誤Outcomes and the Type I and Type II Errors
  3. 9.3假設檢定所需的分配Distribution Needed for Hypothesis Testing
  4. 9.4罕見事件、樣本、決策與結論Rare Events, the Sample, Decision and Conclusion
  5. 9.5補充資訊與完整的假設檢定範例Additional Information and Full Hypothesis Test Examples
  6. 9.6單一平均數與單一比例的假設檢定Hypothesis Testing of a Single Mean and Single Proportion

第 10 章兩個樣本的假設檢定Hypothesis Testing with Two Samples

  1. 10.1標準差未知時的兩個母體平均數Two Population Means with Unknown Standard Deviations
  2. 10.2標準差已知時的兩個母體平均數Two Population Means with Known Standard Deviations
  3. 10.3比較兩個獨立母體比例Comparing Two Independent Population Proportions
  4. 10.4配對樣本Matched or Paired Samples
  5. 10.5兩個平均數與兩個比例的假設檢定Hypothesis Testing for Two Means and Two Proportions

第 11 章卡方分配The Chi-Square Distribution

  1. 11.1卡方分配的特性Facts About the Chi-Square Distribution
  2. 11.2適合度檢定Goodness-of-Fit Test
  3. 11.3獨立性檢定Test of Independence
  4. 11.4同質性檢定Test for Homogeneity
  5. 11.5各種卡方檢定的比較Comparison of the Chi-Square Tests
  6. 11.6單一變異數的檢定Test of a Single Variance
  7. 11.7實驗一：卡方適合度檢定Lab 1: Chi-Square Goodness-of-Fit
  8. 11.8實驗二：卡方獨立性檢定Lab 2: Chi-Square Test of Independence

第 12 章線性迴歸與相關Linear Regression and Correlation

  1. 12.1線性方程式Linear Equations
  2. 12.2散佈圖Scatter Plots
  3. 12.3迴歸方程式The Regression Equation
  4. 12.4相關係數的顯著性檢定Testing the Significance of the Correlation Coefficient
  5. 12.5預測Prediction
  6. 12.6離群值Outliers
  7. 12.7迴歸（離學校的距離）Regression (Distance from School)
  8. 12.8迴歸（教科書費用）Regression (Textbook Cost)
  9. 12.9迴歸（燃油效率）Regression (Fuel Efficiency)

第 13 章F 分配與單因子變異數分析F Distribution and One-Way ANOVA

  1. 13.1單因子變異數分析One-Way ANOVA
  2. 13.2F 分配與 F 比值The F Distribution and the F-Ratio
  3. 13.3F 分配的特性Facts About the F Distribution
  4. 13.4兩個變異數的檢定Test of Two Variances
  5. 13.5實驗：單因子變異數分析Lab: One-Way ANOVA