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Statistics Additional

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TABLE OF CONTENTS

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Chapter 1: Representing Data
Section 1.1 1.1.1 Visualizing Information
1.1.2 Histograms and Stem-and-Leaf Plots
1.1.3 Types of Data and Variables
Section 1.2 1.2.1 Choosing Mean or Median
1.2.2 Variance and Standard Deviation
1.2.3 Sample Variance and Sample Standard Deviation
1.2.4 Investigating Data Representations
Section 1.3 1.3.1 Percentiles
1.3.2 Z-Scores
1.3.3 Linear Transformations

Chapter 2: Two-Variable Quantitative Data
Section 2.1 2.1.1 Scatterplots and Association
2.1.2 Line of Best Fit
2.1.3 Residuals
2.1.4 The Least Squares Regression Line
2.1.5 Using Technology to Find the LSRL
Section 2.2 2.2.1 The Correlation Coefficient
2.2.2 Behavior of Correlation and the LSRL
2.2.3 Residual Plots
2.2.4 Association is Not Causation
2.2.5 Interpreting Correlation in Context

Chapter 3: Multivariable Categorical Data
Section 3.1 3.1.1 Probabilities and Two-Way Frequency Tables
3.1.2 Association and Conditional Relative Frequency Tables
3.1.3 Probability Notation
3.1.4 Relative Frequency Tables and Conditional Probabilities
3.1.5 Analyzing False Positives
Section 3.2 3.2.1 Probability Trees
3.2.2 Problem Solving with Categorical Data
3.2.3 Simulations of Probability

Chapter 4: Studies and Experiments
Section 4.1 4.1.1 Survey Design I
4.1.2 Samples and the Role of Randomness
4.1.3 Sampling When Random is Not Possible
4.1.4 Observational Studies and Experiments
4.1.5 Survey Design II (optional)
Section 4.2 4.2.1 Cause and Effect with Experiments
4.2.2 Experimental Design I
4.2.3 Experimental Design II
4.2.4 Experimental Design III

Chapter 5: Density Functions and Normal Distributions
Section 5.1 5.1.1 Relative Frequency Histograms and Random Variables
5.1.2 Introduction to Density Functions
5.1.3 The Normal Probability Density Function
Section 5.2 5.2.1 The Inverse Normal Function
5.2.2 The Standard Normal Distribution and Z-Scores
5.2.3 Additional Practice Problems

Chapter 6: Discrete Probability Distributions
Section 6.1 6.1.1 Mean and Variance of a Discrete Random Variable
6.1.2 Linear Combinations of Independent Random Variables
6.1.3 Exploring the Variability of XX
Section 6.2 6.2.1 Introducing the Binomial Setting
6.2.2 Binomial Probability Density Function
6.2.3 Exploring Binomial pdf and cdf
6.2.4 Shape, Center, and Spread of the Binomial Distribution
6.2.5 Normal Approximation to the Binomial Distribution
Section 6.3 6.3.1 Introduction to the Geometric Distribution
6.3.2 Binomial and Geometric Practice

Chapter 7: Variability in Categorical Sampling
Section 7.1 7.1.1 Introduction to Sampling Distributions
7.1.2 Simulating Sampling Distributions of Sample Proportions
7.1.3 Formulas for the Sampling Distributions of Sample Proportions
Section 7.2 7.2.1 Confidence Interval for a Population Proportion
7.2.2 Confidence Levels for Confidence Intervals
7.2.3 Changing the Margin of Error in Confidence Intervals
7.2.4 Evaluating Claims with Confidence Intervals

Chapter 8: Drawing Conclusions with Categorical Data
Section 8.1 8.1.1 Introduction to Hypothesis Testing
8.1.2 Hypothesis Tests for Proportions
8.1.3 Alternative Hypotheses and Two-Tailed Tests
Section 8.2 8.2.1 Types of Errors in Hypothesis Testing
8.2.2 Power of a Test
Section 8.3 8.3.1 The Difference Between Two Proportions
8.3.2 Two-Sample Proportion Hypothesis Tests
8.3.3 More Proportion Inference

Chapter 9: Chi-Squared Inference Procedures
Section 9.1 9.1.1 Introduction to the Chi-Squared Distribution
9.1.2 Chi-Squared Goodness of Fit
9.1.3 More Applications of Chi-Squared Goodness of Fit
Section 9.2 9.2.1 Chi-Squared Test for Independence
9.2.2 Chi-Squared Test for Homogeneity of Proportions
9.2.3 Practicing and Recognizing Chi-Squared Inference Procedures

Chapter 10: Drawing Conclusions With Quantitative Data
Section 10.1 10.1.1 Quantitative Sampling Distributions
10.1.2 More Sampling Distributions
Section 10.2 10.2.1 The Central Limit Theorem
10.2.2 Using the Normal Distribution with Means
Section 10.3 10.3.1 Introducing the t-Distribution
10.3.2 Calculating Confidence Intervals for μ
10.3.3 z-Tests and t-Tests for Population Means

Chapter 11: Comparing Means and Identifying Tests
Section 11.1 11.1.1 Paired and Independent Data from Surveys and Experiments
11.1.2 Paired Inference Procedures
11.1.3 Tests for the Difference of Two Means
11.1.4 Two-Sample Mean Inference with Experiments and Two-Sample Confidence Intervals
Section 11.2 11.2.1 Inference in Different Situations
11.2.2 Identifying and Implementing an Appropriate Test

Chapter 12: Inference for Regression
Section 12.1 12.1.1 Sampling Distribution of the Slope of the Regression Line
12.1.2 Inference for the Slope of the Regression Line
Section 12.2 12.2.1 Transforming Data to Achieve Linearity
12.2.2 Using Logarithms to Achieve Linearity

Chapter 13: ANOVA and Beyond!
Section 13.1 13.1.1 Modeling With the Chi-Squared Distribution
13.1.2 Introducing the F-Distribution
Section 13.2 13.2.1 One-Way ANOVA
Section 13.3 13.3.1 Sign Test: Introduction to Nonparametric Inference
13.3.2 Mood’s Median Test

 
 

RESOURCE PAGES

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Chapter 1: Representing Data
Chapter 2: Two-Variable Quantitative Data
Chapter 3: Multivariable Categorical Data
Chapter 4: Studies and Experiments
Chapter 5: Density Functions and Normal Distributions

Chapter 6: Discrete Probability Distributions
Chapter 7: Variability in Categorical Sampling

Chapter 8: Drawing Conclusions with Categorical Data

Chapter 9: Chi-Squared Inference Procedures

Chapter 10: Drawing Conclusions with Quantitative Data
Chapter 11: Comparing Means and Identifying Tests

Chapter 12: Inference for Regression
Chapter 13: ANOVA and Beyond!


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