Statistics: 1001 Practice Problems For Dummies (+ Free Online Practice)

by Unknown

• ISBN13: 9781119883593
• ISBN10: 1119883598
• Edition: 1st
• Format: Paperback
• Copyright: 2022-05-24
• Publisher: For Dummies

Summary

Become more likely to succeed—gain stats mastery with Dummies

Statistics: 1001 Practice Problems For Dummies gives you 1,001 opportunities to practice solving problems from all the major topics covered in Statistics classes—in the book and online! Get extra help with tricky subjects, solidify what you’ve already learned, and get in-depth walk-throughs for every problem with this useful book. These practice problems and detailed answer explanations will help you gain a valuable working knowledge of statistics, no matter what your skill level. Thanks to Dummies, you have a resource to help you put key stats concepts into practice.

• Work through practice problems on all Statistics topics covered in school classes
• Read through detailed explanations of the answers to build your understanding
• Access practice questions online to study anywhere, any time
• Improve your grade and up your study game with practice, practice, practice

The material presented in Statistics: 1001 Practice Problems For Dummies is an excellent resource for students, as well as parents and tutors looking to help supplement Statistics instruction.

Statistics: 1001 Practice Problems For Dummies (9781119883593) was previously published as 1,001 Statistics Practice Problems For Dummies (9781118776049). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product.

Author Biography

The Experts at Dummies are smart, friendly people who make learning easy by taking a not-so-serious approach to serious stuff.

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 Conditions for 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