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 (X2) 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: X2 Critical Values 176
Index 179