## Table of Contents

Introduction 1

Connecting Statistics to the Common Core State Standards for Mathematics (CCSSM) 1

Why You Need This Book 2

How to Use This Book 3

Hundreds of Practice Questions Online! 3

Chapter 1 Overview 5

Types of Statistics 5

Descriptive statistics 6

Inferential statistics 6

Numerical statistics 6

Pictorial statistics 6

Statistical Variables 7

Making an Inference 7

Making Predictions 8

Comparing Results 9

Probability 9

Common Statistics Mistakes 10

Chapter 2 Interpreting Graphic Displays 13

Bar Charts 14

Pie Charts 15

Dot Plots 16

Ogives 16

Frequency Histograms 18

Relative frequency histograms 19

Frequency polygons 20

Frequency distributions 21

Stem-and-Leaf Plots 23

Box Plots (Box-and-Whisker Plots) 24

Scatter Plots 25

Chapter 3 Measures of Central Tendency and Variability 31

Measures of Central Tendency 32

Mean 32

Median 32

Midrange 33

Mode 33

Notation and formulas 33

Mean for grouped data 33

Median for grouped data 35

Symmetric distribution 36

Skewed curves 36

Measures of Variability 37

Range 38

Deviation and variance 38

Standard deviation 39

Notation 39

Empirical rule: The normal curve 39

Shortcut formulas 40

Sensitivity to outliers 41

Percentile 42

Quartiles and interquartile range 42

Measurement Scales 43

Chapter 4 Probability 45

Classic Theory 46

Relative Frequency Theory 47

Probability of Simple Events 47

Independent Events 48

Dependent Events 48

Probability of Joint Occurrences 49

Multiplication rule 49

Addition rule 50

Outcomes That Are Not Mutually Exclusive 51

Double-Counting 51

Conditional Probability 53

Bayes' Theorem 54

Probability Distributions 55

Discrete versus continuous variables 56

Total of probabilities of discrete variables 56

The Binomial 56

Binomial experiments 56

Binomial table 57

Mean and standard deviation 57

Chapter 5 Random Sampling 61

Populations, Samples, Parameters, and Statistics 62

Sampling Distributions 64

Random and Systematic Error 65

Central Limit Theorem 66

Properties of the Normal Curve 67

Normal Approximation to the Binomial 70

Chapter 6 Principles of Hypothesis Testing 75

Stating a Hypothesis 76

The Test Statistic 77

One- and Two-Tailed Tests 79

Type I and II Errors 81

Statistical Significance 82

Point Estimates and Confidence Intervals 84

Estimating a Difference Score 85

Univariate Tests: An Overview 87

Chapter 7 Univariate Inferential Tests 91

One-Sample z-test 92

Confidence interval for population mean using z 94

Choosing a sample size 94

One-Sample t-test 95

Confidence interval for population mean using t 98

Two-Sample z-test for Comparing Two Means 99

Two-Sample t-test for Comparing Two Means 100

Confidence interval for comparing two means 101

Pooled variance method 102

Paired Difference t-test 104

Test for a Single Population Proportion 106

Confidence interval for a single population proportion 107

Choosing a sample size 107

Test for Comparing two Proportions 108

Confidence interval for comparing two proportions 110

Chapter 8 Bivariate Relationships 113

Correlation 113

Finding the significance of r 118

The coefficient of determination 120

Simple Linear Regression 120

Confidence interval for the slope 123

Confidence interval for prediction 125

Assumptions and cautions 126

Causation and correlation 127

Chi-Square (X_{2}) 128

Review Questions 133

Glossary 143

Appendix A Common Mistakes 151

Appendix B Formulas and Tables 153

Notation Symbols 153

Formulas 154

Descriptive statistics 154

Probability 154

Probability distributions 155

Normal distribution 155

Confidence intervals (one population) 155

Test statistics 156

Pearson correlation 156

Table B-1 Binomial Probabilities, P(x) for n < 20 157

Table B-2 Standard Normal Probabilities 170

Table B-3 The t-distribution Critical Values 174

Table B-4 The Chi-Square Distribution: X_{2} Critical Values 176

Index 179