Table of Contents
Introduction 1
What You'll Find 1
How This Workbook Is Organized 1
Part 1 The Questions 2
Part 2 The Answers 3
Beyond the Book 3
What you'll find online 3
How to register 4
Where to Go for Additional Help 4
Part 1 The Questions 5
Chapter 1 Basic Vocabulary 7
The Problems You'll Work On 7
What to Watch Out For 7
Picking Out the Population, Sample, Parameter, and Statistic 8
Distinguishing Quantitative and Categorical Variables 8
Getting a Handle on Bias, Variables, and the Mean 9
Understanding Different Statistics and Data Analysis Terms 9
Using Statistical Techniques 10
Working with the Standard Deviation 10
Chapter 2 Descriptive Statistics 11
The Problems You'll Work On 11
What to Watch Out For 11
Understanding the Mean and the Median 12
Surveying Standard Deviation and Variance 13
Employing the Empirical Rule 15
Measuring Relative Standing with Percentiles 16
Delving into Data Sets and Descriptive Statistics 17
Chapter 3 Graphing 21
The Problems You'll Work On 21
What to Watch Out For 21
Interpreting Pie Charts 22
Considering Three-Dimensional Pie Charts 22
Interpreting Bar Charts 23
Introducing Other Graphs 24
Interpreting Histograms 24
Digging Deeper into Histograms 25
Comparing Histograms 26
Describing the Center of a Distribution 27
Interpreting Box Plots 27
Comparing Two Box Plots 28
Comparing Three Box Plots 29
Interpreting Time Charts 30
Getting More Practice with Histograms 31
Chapter 4 Random Variables and the Binomial Distribution 33
The Problems You'll Work On 33
What to Watch Out For 33
Comparing Discrete and Continuous Random Variables 34
Understanding the Probability Distribution of a Random Variable 35
Determining the Mean of a Discrete Random Variable 35
Digging Deeper into the Mean of a Discrete Random Variable 35
Working with the Variance of a Discrete Random Variable 36
Putting Together the Mean, Variance, and Standard Deviation of a Random Variable 36
Digging Deeper into the Mean, Variance, and Standard Deviation of a Random Variable 37
Introducing Binomial Random Variables 37
Figuring Out the Mean, Variance, and Standard Deviation of a Binomial Random Variable 38
Finding Binomial Probabilities with a Formula 38
Digging Deeper into Binomial Probabilities Using a Formula 39
Finding Binomial Probabilities with the Binomial Table 39
Digging Deeper into Binomial Probabilities Using the Binomial Table 40
Using the Normal Approximation to the Binomial 40
Digging Deeper into the Normal Approximation to the Binomial 41
Getting More Practice with Binomial Variables 41
Chapter 5 The Normal Distribution 43
The Problems You'll Work On 43
What to Watch Out For 43
Defining and Describing the Normal Distribution 44
Working with z-Scores and Values of X 45
Digging Deeper into z-Scores and Values of X 45
Writing Probability Notations 46
Introducing the Z-Table 47
Finding Probabilities for a Normal Distribution 47
Digging Deeper into z-Scores and Probabilities 47
Figuring Out Percentiles for a Normal Distribution 48
Digging Deeper into Percentiles for a Normal Distribution 49
Getting More Practice with Percentiles 49
Chapter 6 The t-Distribution 51
The Problems You'll Work On 51
What to Watch Out For 51
Understanding the t-Distribution and Comparing It to the Z-Distribution 52
Using the t-Table 53
Using the t-Distribution to Calculate Confidence Intervals 55
Chapter 7 Sampling Distributions and the Central Limit Theorem 57
The Problems You'll Work On 57
What to Watch Out For 57
Introducing the Basics of Sampling Distributions 58
Checking Out Random Variables and Sample Means 59
Examining Standard Error 59
Surveying Notation and Symbols 60
Understanding What Affects Standard Error 61
Digging Deeper into Standard Error 61
Connecting Sample Means and Sampling Distributions 62
Digging Deeper into Sampling Distributions of Sample Means 64
Looking at the Central Limit Theorem 65
Getting More Practice with Sample Mean Calculations 66
Finding Probabilities for Sample Means 66
Digging Deeper into Probabilities for Sample Means 67
Adding Proportions to the Mix 68
Figuring Out the Standard Error of the Sample Proportion 68
Using the Central Limit Theorem for Proportions 68
Matching z-Scores to Sample Proportions 69
Finding Approximate Probabilities 69
Getting More Practice with Probabilities 69
Digging Deeper into Approximate Probabilities 70
Chapter 8 Finding Room for a Margin of Error 71
The Problems You'll Work On 71
What to Watch Out For 71
Defining and Calculating Margin of Error 72
Using the Formula for Margin of Error When Estimating a Population Mean 72
Finding Appropriate z*-Values for Given Confidence Levels 73
Connecting Margin of Error to Sample Size 73
Getting More Practice with the Formula for Margin of Error 73
Linking Margin of Error and Population Proportion 74
Chapter 9 Confidence Intervals: Basics for Single Population Means and Proportions 75
The Problems You'll Work On 75
What to Watch Out For 75
Introducing Confidence Intervals 76
Checking Out Components of Confidence Intervals 77
Interpreting Confidence Intervals 79
Spotting Misleading Confidence intervals 80
Calculating a Confidence Interval for a Population Mean 83
Determining the Needed Sample Size 86
Introducing a Population Proportion 87
Connecting a Population Proportion to a Survey 88
Calculating a Confidence Interval for a Population Proportion 88
Digging Deeper into Population Proportions 89
Getting More Practice with Population Proportions 90
Chapter 10 Confidence Intervals for Two Population Means and Proportions 91
The Problems You'll Work On 91
What to Watch Out For 91
Working with Confidence Intervals and Population Proportions 92
Digging Deeper into Confidence intervals and Population Proportions 92
Working with Confidence Intervals and Population Means 93
Making Calculations When Population Standard Deviations Are Known 93
Digging Deeper into Calculations When Population Standard Deviations Are Known 94
Working with Unknown Population Standard Deviations and Small Sample Sizes 95
Digging Deeper into Unknown Population Standard Deviations and Small Sample Sizes 96
Chapter 11 Claims, Tests, and Conclusions 97
The Problems You'll Work On 97
What to Watch Out For 97
Knowing When to Use a Hypothesis Test 98
Setting Up Null and Alternative Hypotheses 98
Finding the Test Statistic and the p-Value 100
Making Decisions Based on Alpha Levels and Test Statistics 101
Making Conclusions 101
Understanding Type I and Type II Errors 103
Chapter 12 Hypothesis Testing Basics for a Single Population Mean: z- and t-Tests 105
The Problems You'll Work On 105
What to Watch Out For 105
Knowing What You Need to Run a z-Test 106
Determining Null and Alternative Hypotheses 106
Introducing p-Values 107
Calculating the z-Test Statistic 107
Finding p-Values by Doing a Test of One Population Mean 108
Drawing Conclusions about Hypotheses 108
Digging Deeper into p-Values 109
Digging Deeper into Conclusions about Hypotheses 109
Digging Deeper into Null and Alternative Hypotheses 110
Knowing When to Use a t-Test 111
Connecting Hypotheses to t-Tests 111
Calculating Test Statistics 112
Working with Critical Values of t 112
Linking p-Values and t-Tests 113
Drawing Conclusions from t-Tests 114
Performing a t-Test for a Single Population Mean 115
Drawing More Conclusions from t-Tests 115
Chapter 13 Hypothesis Tests for One Proportion, Two Proportions, or Two Population Means 117
The Problems You'll Work On 117
What to Watch Out For 118
Testing One Population Proportion 118
Comparing Two independent Population Means 120
Digging Deeper into Two Independent Population Means 121
Getting More Practice with Two Independent Population Means 121
Using the Paired t-Test 122
Digging Deeper into the Paired t-Test 123
Comparing Two Population Proportions 124
Digging Deeper into Two Population Proportions 124
Chapter 14 Surveys 127
The Problems You'll Work On 127
What to Watch Out For 127
Planning and Designing Surveys 128
Selecting Samples and Conducting Surveys 128
Chapter 15 Correlation 131
The Problems You'll Work On 131
What to Watch Out For 131
Interpreting Scatter Plots 132
Creating Scatter Plots 132
Understanding What Correlations Indicate 133
Digging Deeper into Scatter Plots 133
Digging Deeper into What Correlations Indicate 134
Calculating Correlations 134
Noting How Correlations Can Change 135
Looking at the Properties of Correlations 135
Digging Deeper into How Correlations Can Change 136
Making Conclusions about Correlations 136
Getting More Practice with Scatter Plots and Correlation Changes 136
Making More Conclusions about Correlations 137
Chapter 16 Simple Linear Regression 139
The Problems You'll Work On 139
What to Watch Out For 139
Introducing the Regression Line 140
Knowing the Conditioner Regression 140
Examining the Equation for Calculating the Least-Squares Regression Line 140
Finding the Slope and y-Intercept of a Regression Line 141
Seeing How Variables Can Change in a Regression Line 141
Finding a Regression Line 141
Digging Deeper into Finding a Regression Line 142
Connecting to Correlation and Linear Relationships 144
Determining Whether Variables Are Candidates for a Linear Regression Analysis 144
Digging Deeper into Correlations and Linear Relationships 145
Describing Linear Relationships 145
Getting More Practice with Finding a Regression Line 146
Making Predictions 147
Figuring Out Expected Values and Differences 148
Digging Deeper into Expected Values and Differences 149
Digging Deeper into Predictions 150
Getting More Practice with Expected Values and Differences 151
Chapter 17 Two-Way Tables and Independence 153
The Problems You'll Work On 153
What to Watch Out For 153
Introducing Variables and Two-Way Tables 154
Reading a Two-Way Table 154
Interpreting a Two-Way Table by Using Percentages 156
Interpreting a Two-Way Table by Using Counts 156
Connecting Conditional Probabilities to Two-Way Tables 157
Investigating Independent Variables 158
Calculating Marginal Probability and More 159
Adding Joint Probability to the Mix 160
Digging Deeper into Conditional and Marginal Probabilities 161
Figuring Out the Number of Cells in a Two-Way Table 162
Including Conditional Probability 162
Digging into Research Designs 163
Digging Deeper into Two-Way Tables 163
Part 2 The Answers 165
Chapter 18 Answers 167
Appendix: Tables for Reference 463
Index 475
