Introductory Statistics

Introductory Statistics

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ISBN-10

1938168208

ISBN-13

978-1-938168-20-8

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ST-1-000-RS

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Table of Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 1: Sampling and Data . . . . . . . . . . . . . . . . . . . . . . . . . .

1.1 Definitions of Statistics, Probability, and Key Terms . . . . . . . . . . .

1.2 Data, Sampling, and Variation in Data and Sampling . . . . . . . . . .

1.3 Frequency, Frequency Tables, and Levels of Measurement . . . . . . .

1.4 Experimental Design and Ethics . . . . . . . . . . . . . . . . . . . . .

1.5 Data Collection Experiment . . . . . . . . . . . . . . . . . . . . . . .

1.6 Sampling Experiment . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 2: Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . .

2.1 Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs . . .

2.2 Histograms, Frequency Polygons, and Time Series Graphs . . . . . . .

2.3 Measures of the Location of the Data . . . . . . . . . . . . . . . . . .

2.4 Box Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.5 Measures of the Center of the Data . . . . . . . . . . . . . . . . . . .

2.6 Skewness and the Mean, Median, and Mode . . . . . . . . . . . . . .

2.7 Measures of the Spread of the Data . . . . . . . . . . . . . . . . . . .

2.8 Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 3: Probability Topics . . . . . . . . . . . . . . . . . . . . . . . . . .

3.1 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2 Independent and Mutually Exclusive Events . . . . . . . . . . . . . . .

3.3 Two Basic Rules of Probability . . . . . . . . . . . . . . . . . . . . . .

3.4 Contingency Tables . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.5 Tree and Venn Diagrams . . . . . . . . . . . . . . . . . . . . . . . . .

3.6 Probability Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 4: Discrete Random Variables . . . . . . . . . . . . . . . . . . . . .

4.1 Probability Distribution Function (PDF) for a Discrete Random Variable

4.2 Mean or Expected Value and Standard Deviation . . . . . . . . . . . .

4.3 Binomial Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.4 Geometric Distribution . . . . . . . . . . . . . . . . . . . . . . . . . .

4.5 Hypergeometric Distribution . . . . . . . . . . . . . . . . . . . . . . .

4.6 Poisson Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.7 Discrete Distribution (Playing Card Experiment) . . . . . . . . . . . . .

4.8 Discrete Distribution (Lucky Dice Experiment) . . . . . . . . . . . . . .

Chapter 5: Continuous Random Variables . . . . . . . . . . . . . . . . . . .

5.1 Continuous Probability Functions . . . . . . . . . . . . . . . . . . . .

5.2 The Uniform Distribution . . . . . . . . . . . . . . . . . . . . . . . . .

5.3 The Exponential Distribution . . . . . . . . . . . . . . . . . . . . . . .

5.4 Continuous Distribution . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 6: The Normal Distribution . . . . . . . . . . . . . . . . . . . . . . .

6.1 The Standard Normal Distribution . . . . . . . . . . . . . . . . . . . .

6.2 Using the Normal Distribution . . . . . . . . . . . . . . . . . . . . . .

6.3 Normal Distribution (Lap Times) . . . . . . . . . . . . . . . . . . . . .

6.4 Normal Distribution (Pinkie Length) . . . . . . . . . . . . . . . . . . .

Chapter 7: The Central Limit Theorem . . . . . . . . . . . . . . . . . . . . .

7.1 The Central Limit Theorem for Sample Means (Averages) . . . . . . .

7.2 The Central Limit Theorem for Sums . . . . . . . . . . . . . . . . . .

7.3 Using the Central Limit Theorem . . . . . . . . . . . . . . . . . . . . .

7.4 Central Limit Theorem (Pocket Change) . . . . . . . . . . . . . . . . .

7.5 Central Limit Theorem (Cookie Recipes) . . . . . . . . . . . . . . . .

Chapter 8: Confidence Intervals . . . . . . . . . . . . . . . . . . . . . . . . .

8.1 A Single Population Mean using the Normal Distribution . . . . . . . .

8.2 A Single Population Mean using the Student t Distribution . . . . . . .

8.3 A Population Proportion . . . . . . . . . . . . . . . . . . . . . . . . .

8.4 Confidence Interval (Home Costs) . . . . . . . . . . . . . . . . . . . .

8.5 Confidence Interval (Place of Birth) . . . . . . . . . . . . . . . . . . .

8.6 Confidence Interval (Women's Heights) . . . . . . . . . . . . . . . . .

Chapter 9: Hypothesis Testing with One Sample . . . . . . . . . . . . . . . .

9.1 Null and Alternative Hypotheses . . . . . . . . . . . . . . . . . . . . .

9.2 Outcomes and the Type I and Type II Errors . . . . . . . . . . . . . . .

9.3 Distribution Needed for Hypothesis Testing . . . . . . . . . . . . . . .

9.4 Rare Events, the Sample, Decision and Conclusion . . . . . . . . . . .

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