Beginning Statistics plus Integrated Review, 3rd Edition

1.R.1 Problem Solving with Whole Numbers

• Examples
• Example 1: Application: Adding Whole Numbers
• Example 2: Application: Multiplying Whole Numbers
• Example 3: Application: Dividing Whole Numbers
• Example 4: Application: Calculating Loan Amounts
• Example 5: Application: Balancing a Checking Account
• Example 6: Application: Finding the Area of Rectangles
• Example 7: Calculating an Average
• Example 8: Application: Calculating an Average
• Example 9: Application: Calculating an Average
• Example 10: Application: Calculating an Average

1.R.2 Introduction to Decimal Numbers

• Examples
• Example 1: Reading and Writing Decimal Numbers
• Example 2: Reading and Writing Decimal Numbers
• Example 3: Reading and Writing Decimal Numbers
• Example 4: Comparing Decimal Numbers
• Example 5: Comparing Decimal Numbers
• Example 6: Comparing Decimal Numbers
• Example 7: Rounding Decimal Numbers
• Example 8: Rounding Decimal Numbers

1.R.3 Estimating and Order of Operations with Decimal Numbers

• Examples
• Example 1: Estimating Sums of Decimal Numbers
• Example 3: Estimating Products of Decimal Numbers
• Example 4: Estimating Quotients of Decimal Numbers
• Example 5: Application: Estimating with Decimal Numbers
• Example 6: Using the Order of Operations with Decimal Numbers
• Example 7: Using the Order of Operations with Decimal Numbers

1.R.4 Decimals and Percents

• Examples
• Example 1: Changing Fractions with Denominators of $100$ to Percents
• Example 2: Changing Decimal Numbers to Percents
• Example 3: Changing Percents to Decimal Numbers

1.1 Getting Started

• Examples
• Example 1.1.1: Identifying Population and Sample
• Example 1.1.3: Identifying Descriptive and Inferential Statistics

1.2 Data Classification

• Examples
• Example 1.2.1: Classifying Data as Qualitative or Quantitative
• Example 1.2.2: Classifying Data as Continuous or Discrete
• Example 1.2.3: Understanding the Nominal Level of Measurement
• Example 1.2.5: Classifying Data by the Level of Measurement

1.3 The Process of a Statistical Study

• Examples
• Example 1.3.1: Identifying Population and Variables
• Example 1.3.2: Identifying Observational Studies and Experiments
• Example 1.3.4: Classifying Studies as Cross-Sectional or Longitudinal
• Example 1.3.5: Classifying Studies as Meta-Analysis or Case Study
• Example 1.3.6: Identifying Parts of an Experiment

1.4 How to Critique a Published Study

• Examples
• Example 1.4.1: Considering the Variables

2.R.1 Introduction to Fractions and Mixed Numbers

• Examples
• Example 1: Understanding Fractions
• Example 2: Understanding Fractions
• Example 3: Understanding Proper Fractions
• Example 4: Understanding Improper Fractions
• Example 5: Evaluating Fractions Involving 0
• Example 6: Graphing Proper Fractions
• Example 7: Graphing Improper Fractions
• Example 8: Identifying Types of Fractions and Mixed Numbers
• Example 9: Application: Understanding Mixed Numbers
• Example 10: Application: Understanding Mixed Numbers
• Example 11: Graphing Mixed Numbers
• Example 12: Changing Mixed Numbers to Improper Fractions
• Example 14: Changing Improper Fractions to Mixed Numbers
• Example 15: Changing Improper Fractions to Mixed Numbers

2.R.2 Decimal Numbers and Fractions

• Examples
• Example 1: Changing Decimal Numbers to Fractions
• Example 2: Changing Decimal Numbers to Fractions
• Example 3: Changing Decimal Numbers to Fractions
• Example 4: Changing Fractions to Decimal Numbers
• Example 5: Changing Fractions to Decimal Numbers
• Example 6: Changing Fractions to Decimal Numbers
• Example 7: Changing Fractions to Decimal Numbers
• Example 8: Simplifying Expressions with Decimals and Fractions
• Example 9: Comparing Decimal Numbers and Fractions
• Example 10: Application: Decimal and Fraction Expressions

2.R.3 Comparisons and Order of Operations with Fractions

• Examples
• Example 1: Comparing Fractions
• Example 2: Comparing Fractions
• Example 3: Comparing Fractions
• Example 4: Using the Order of Operations with Fractions
• Example 5: Using the Order of Operations with Fractions
• Example 6: Using the Order of Operations with Fractions
• Example 8: Finding the Average

2.R.4 Fractions and Percents

• Examples
• Example 1: Changing Fractions to Percents
• Example 2: Changing Fractions to Percents
• Example 3: Changing Mixed Numbers to Percents
• Example 5: Changing Fractions to Percents
• Example 5: Application: Changing Fractions to Percents
• Example 7: Changing Percents to Fractions
• Example 8: Changing Percents to Mixed Numbers

2.R.5 Reading Graphs

• Examples
• Example 1: Reading a Bar Graph
• Example 2: Reading a Circle Graph
• Example 3: Reading a Line Graph
• Example 4: Reading a Histogram

2.R.6 Constructing Graphs from Databases

• Examples
• Example 1: Constructing a Bar Graph
• Example 2: Constructing a Circle Graph

2.R.7 The Real Number Line and Absolute Value

• Examples
• Example 1: Finding the Opposite of an Integer
• Example 2: Graphing Integers on a Number Line
• Example 3: Identifying Types of Numbers
• Example 4: Graphing Sets of Numbers
• Example 5: Graphing Sets of Numbers
• Example 6: Verifying Inequalities
• Example 7: Finding Absolute Values
• Example 8: Verifying Absolute Value Inequalities
• Example 9: Solving Absolute Value Equations
• Example 10: Solving Absolute Value Equations
• Example 11: Application: Solving Absolute Value Equations

2.1 Frequency Distributions

2.2 Graphical Displays of Data

• Examples
• Example 2.2.3: Creating a Pareto Chart
• Example 2.2.9: Creating and Interpreting a Stem-and-Leaf Plot

2.3 Analyzing Graphs

• Examples
• Example 2.3.2: Shapes of Graphs

3.R.1 Addition with Real Numbers

• Examples
• Example 1: Adding Real Numbers with Like Signs
• Example 2: Adding Real Numbers with Unlike Signs
• Example 3: Adding More Than Two Real Numbers
• Example 4: Adding Three or More Real Numbers

3.R.2 Subtraction with Real Numbers

• Examples
• Example 1: Finding Additive Inverses
• Example 2: Subtracting Real Numbers
• Example 3: Application: Calculating Change in Value
• Example 4: Application: Calculating Change in Value
• Example 5: Application: Calculating Net Change
• Example 6: Application: Calculating Net Change

3.R.3 Multiplication and Division with Real Numbers

• Examples
• Example 1: Multiplying Positive and Negative Real Numbers
• Example 2: Multiplying Two Negative Real Numbers
• Example 3: Multiplication by $0$
• Example 4: Dividing Real Numbers
• Example 5: Dividing Fractions and Decimals
• Example 6: Application: Calculating an Average
• Example 7: Application: Calculating an Average
• Example 8: Application: Calculating an Average

3.R.4 Rules for Exponents

• Examples
• Example 1: Using the Product Rule for Exponents
• Example 2: Using the Product Rule for Exponents
• Example 3: Evaluating the Exponent 0
• Example 4: Using the Quotient Rule for Exponents
• Example 5: Dividing Terms with Coefficients
• Example 6: Negative Exponents
• Example 7: Combining Rules for Exponents

3.R.5 Simplifying and Evaluating Algebraic Expressions

• Examples
• Example 1: Identifying Like Terms
• Example 2: Combining Like Terms
• Example 3: Evaluating Algebraic Expressions
• Example 4: Simplifying and Evaluating Algebraic Expressions
• Example 5: Simplifying and Evaluating Algebraic Expressions
• Example 6: Simplifying and Evaluating Algebraic Expressions

3.R.6 Evaluating Radicals

• Examples
• Example 1: Evaluating Square Roots
• Example 2: Evaluating Square Roots
• Example 3: Estimating Square Roots
• Example 4: Evaluating Cube Roots

3.1 Measures of Center

• Examples
• Example 3.1.4: Calculating a Weighted Mean
• Example 3.1.9: Determining Mean, Median, and Mode from a Graph

3.2 Measures of Dispersion

• Examples
• Example 3.2.1: Calculating the Range
• Example 3.2.4: Interpreting Standard Deviations
• Example 3.2.8: Standard Deviation of Grouped Data
• Example 3.2.9: Standard Deviation of Grouped Data

3.3 Measures of Relative Position

• Examples
• Example 3.3.1: Finding Data Values Given the Percentiles
• Example 3.3.2: Finding the Percentile of a Given Data Value
• Example 3.3.5: Writing the Five-Number Summary of a Given Data Set
• Example 3.3.10: Comparing Standard Scores

4.R.1 Multiplication with Fractions

• Examples
• Example 1: Multiplying Fractions
• Example 2: Multiplying Fractions
• Example 3: Application: Multiplying Fractions
• Example 4: Recognizing the Properties of Multiplication
• Example 5: Reducing Fractions to Lowest Terms
• Example 6: Reducing Fractions to Lowest Terms
• Example 8: Application: Reducing Fractions to Lowest Terms
• Example 9: Multiplying and Reducing Using Prime Factors
• Example 10: Multiplying and Reducing Using Prime Factors
• Example 11: Multiplying and Reducing Using Prime Factors
• Example 13: Application: Multiplying and Reducing Fractions
• Example 14: Multiplying and Reducing Using the Division Method
• Example 15: Multiplying and Reducing Using the Division Method
• Example 16: Multiplying and Reducing Using the Division Method
• Example 17: Multiplying and Reducing Using the Division Method

4.R.2 Division with Fractions

• Examples
• Example 1: Finding Reciprocals
• Example 2: Finding Reciprocals
• Example 3: Dividing Fractions
• Example 4: Dividing Fractions
• Example 5: Dividing and Reducing Fractions
• Example 6: Dividing and Reducing Fractions
• Example 9: Finding a Missing Number
• Example 10: Application: Dividing Fractions
• Example 11: Application: Multiplying and Dividing Fractions

4.R.3 Least Common Multiple (LCM)

• Examples
• Example 1: Finding the Least Common Multiple (LCM)
• Example 2: Finding the Least Common Multiple (LCM)
• Example 4: Finding the Least Common Multiple (LCM)
• Example 5: Finding the Least Common Multiple (LCM)
• Example 6: Finding the Least Common Multiple (LCM)
• Example 7: Finding the Least Common Multiple (LCM)
• Example 9: Application: Finding the LCM
• Example 10: Finding Equivalent Fractions
• Example 11: Finding Equivalent Fractions

4.R.4 Addition and Subtraction with Fractions

• Examples
• Example 1: Adding Fractions with the Same Denominator
• Example 2: Finding the Least Common Denominator (LCD)
• Example 3: Adding Fractions with Different Denominators
• Example 4: Adding Fractions with Different Denominators
• Example 5: Adding Three Fractions with Different Denominators
• Example 6: Application: Adding Fractions
• Example 7: Application: Adding Fractions
• Example 8: Subtracting Fractions with the Same Denominator
• Example 9: Subtracting Fractions with Different Denominators
• Example 10: Subtracting Fractions with Different Denominators
• Example 11: Subtracting Fractions with Different Denominators
• Example 12: Application: Subtracting Fractions with Different Denominators

4.R.5 Union and Intersection of Sets

4.1 Introduction to Probability

• Examples
• Example 4.1.1: Identifying Outcomes in a Sample Space or Event
• Example 4.1.2: Using a Pattern to List All Outcomes in a Sample Space
• Example 4.1.5: Calculating Classical Probability
• Example 4.1.8: Calculating Classical Probability

4.2 Addition Rules for Probability

• Examples
• Example 4.2.2: Using the Complement Rule for Probability
• Example 4.2.3: Using the Complement Rule for Probability
• Example 4.2.4: Using the Addition Rule for Probability
• Example 4.2.5: Using the Addition Rule for Probability
• Example 4.2.6: Using the Addition Rule for Probability

4.3 Multiplication Rules for Probability

• Examples
• Example 4.3.7: Using the Fundamental Counting Principle
• Example 4.3.8: Using the Fundamental Counting Principle (Without Replacement)
• Example 4.3.9: Using the Fundamental Counting Principle to Calculate Probability

4.4 Combinations and Permutations

4.5 Combining Probability and Counting Techniques

• Examples
• Example 4.5.1: Calculating Probability Using Combinations
• Example 4.5.2: Calculating Probability Using Permutations
• Example 4.5.3: Using Numbers of Combinations with the Fundamental Counting Principle
• Example 4.5.4: Using Numbers of Combinations with the Fundamental Counting Principle

5.R.1 Order of Operations with Real Numbers

• Examples
• Example 1: Using the Order of Operations with Real Numbers
• Example 2: Using the Order of Operations with Real Numbers
• Example 3: Using the Order of Operations with Real Numbers
• Example 4: Using the Order of Operations with Real Numbers
• Example 6: Using the Order of Operations with Real Numbers
• Example 7: Using the Order of Operations with Real Numbers

5.R.2 Solving Linear Inequalities in One Variable

• Examples
• Example 1: Graphing Intervals
• Example 2: Graphing Intervals
• Example 3: Graphing Intervals
• Example 4: Graphing Intervals
• Example 5: Solving an Inequality and Graphing the Solution Set
• Example 6: Solving an Inequality and Graphing the Solution Set
• Example 7: Solving an Inequality and Graphing the Solution Set
• Example 8: Solving an Inequality and Graphing the Solution Set
• Example 9: Solving Linear Inequalities
• Example 10: Solving Linear Inequalities
• Example 11: Solving Linear Inequalities
• Example 13: Application: Using Inequalities

5.R.3 Compound Inequalities

5.1 Discrete Random Variables

5.2 Binomial Distribution

• Examples
• Example 5.2.5: Calculating Binomial Probabilities, $P\left(X\le x\right)$

5.3 Poisson Distribution

• Examples
• Example 5.3.1: Calculating a Poisson Probability Using the Formula
• Example 5.3.2: Finding a Poisson Probability Using a Table

5.4 Hypergeometric Distribution

6.R.1 Area

• Examples
• Example 1: Calculating the Area of a Triangle Using a Formula
• Example 2: Calculating the Area of a Trapezoid Using a Formula
• Example 3: Calculating the Area of a Composite Figure
• Example 4: Calculating Area
• Example 5: Calculating Area
• Example 6: Application: Calculating Perimeter and Area

6.R.2 Solving Linear Equations: ax + b = c

• Examples
• Example 1: Solving Linear Equations of the Form ax + b = c
• Example 2: Solving Linear Equations of the Form ax + b = c
• Example 3: Solving Linear Equations Involving Decimals
• Example 4: Solving Linear Equations Involving Decimals
• Example 5: Solving Linear Equations Involving Fractions
• Example 6: Solving Linear Equations Involving Fractions

6.R.3 Working with Formulas

• Examples
• Example 1: Application: Evaluating Formulas
• Example 2: Evaluating Formulas
• Example 3: Application: Evaluating Formulas
• Example 4: Evaluating Formulas
• Example 5: Solving for Different Variables
• Example 6: Solving for Different Variables
• Example 7: Solving for Different Variables
• Example 8: Solving for Different Variables

6.1 Introduction to the Normal Distribution

6.2 The Standard Normal Distribution

6.3 Finding Probability Using a Normal Distribution

6.4 Finding Values of a Normally Distributed Random Variable

6.5 Approximating a Binomial Distribution Using a Normal Distribution

• Examples
• Example 6.5.1: Using the Continuity Correction Factor with a Normal Distribution to Approximate a Binomial Probability

7.1 Sampling Distributions and the Central Limit Theorem

• Examples
• Example 7.1.3: Applying the Central Limit Theorem

7.2 Central Limit Theorem with Means

• Examples
• Example 7.2.3: Finding the Probability that a Sample Mean Will Differ from the Population Mean by Less Than a Given Amount

7.3 Central Limit Theorem with Proportions

8.R.1 Absolute Value Equations

• Examples
• Example 1: Solving Absolute Value Equations
• Example 2: Solving Equations with Two Absolute Value Expressions

8.R.2 Absolute Value Inequalities

• Examples
• Example 1: Solving Absolute Value Inequalities
• Example 2: Solving Absolute Value Inequalities
• Example 3: Solving Absolute Value Inequalities
• Example 4: Solving Absolute Value Inequalities
• Example 5: Solving Absolute Value Inequalities
• Example 6: Solving Absolute Value Inequalities
• Example 7: Solving Absolute Value Inequalities
• Example 8: Solving Absolute Value Inequalities
• Example 9: Solving Absolute Value Inequalities

8.1 Estimating Population Means (Sigma Known)

• Examples
• Example 8.1.1: Finding a Point Estimate for a Population Mean
• Example 8.1.2: Constructing a Confidence Interval with a Given Margin of Error
• Example 8.1.3: Finding the Margin of Error of a Confidence Interval for a Population Mean (σ Known)
• Example 8.1.7: Interpreting a Confidence Interval
• Example 8.1.8: Finding the Minimum Sample Size Needed for a Confidence Interval for a Population Mean

8.2 Student's t-Distribution

• Examples
• Example 8.2.1: Finding the Value of t_α Using a Table
• Example 8.2.2: Finding the Value of t Given the Area to the Left
• Example 8.2.3: Finding the Value of t Given the Area to the Right
• Example 8.2.5: Finding the Value of t Given Area between ${-t}_{\raisebox{1ex}{$\alpha $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$ and $t_{\raisebox{1ex}{$\alpha $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$
• Example 8.2.6: Finding the Critical t-value for a Confidence Interval

8.3 Estimating Population Means (Sigma Unknown)

• Examples
• Example 8.3.1: Finding the Margin of Error of a Confidence Interval for a Population Mean (σ Unknown)

8.4 Estimating Population Proportions

• Examples
• Example 8.4.1: Finding a Point Estimate for a Population Proportion
• Example 8.4.5: Finding the Minimum Sample Size Needed for a Confidence Interval for a Population Proportion
• Example 8.4.6: Finding the Minimum Sample Size, Point Estimate, and Confidence Interval for a Population Proportion

8.5 Estimating Population Variances

• Examples
• Example 8.5.1: Finding Point Estimates for the Population Standard Deviation and Variance
• Example 8.5.2: Constructing a Confidence Interval for a Population Variance
• Example 8.5.3: Constructing a Confidence Interval for a Population Standard Deviation
• Example 8.5.4: Constructing a Confidence Interval for a Population Variance
• Example 8.5.5: Constructing a Confidence Interval for a Population Standard Deviation
• Example 8.5.6: Finding the Minimum Sample Size Needed for a Confidence Interval for a Population Standard Deviation

9.1 Comparing Two Population Means (Sigma Known)

• Examples
• Example 9.1.2: Constructing a Confidence Interval for the Difference between Two Population Means (σ Known, Independent Samples)

9.2 Comparing Two Population Means (Sigma Unknown)

• Examples
• Example 9.2.1: Finding the Margin of Error of a Confidence Interval for the Difference between Two Population Means with Unequal Variances (σ Unknown, Independent Samples)

9.3 Comparing Two Population Means (Sigma Unknown, Dependent Samples)

• Examples
• Example 9.3.1: Calculating Paired Differences
• Example 9.3.2: Finding a Point Estimate for the Mean of the Paired Differences for Two Populations (σ Unknown, Dependent Samples)

9.4 Comparing Two Population Proportions

9.5 Comparing Two Population Variances

10.R.1 Translating English Phrases and Algebraic Expressions

• Examples
• Example 1: Translating English Phrases into Algebraic Expressions
• Example 2: Application: Translating English Phrases
• Example 3: Translating Algebraic Expressions to English Phrases
• Example 4: Translating Equations into Word Problems

10.R.2 Applications: Scientific Notation

• Examples
• Example 1: Writing Decimals in Scientific Notation
• Example 2: Using Scientific Notation while Simplifying
• Example 3: Application: Scientific Notation

10.1 Fundamentals of Hypothesis Testing

10.2 Hypothesis Testing for Population Means (Sigma Known)

10.3 Hypothesis Testing for Population Means (Sigma Unknown)

• Examples
• Example 10.3.1: Finding the Critical t-value for a Right-Tailed Hypothesis Test

10.4 Hypothesis Testing for Population Proportions

10.5 Hypothesis Testing for Population Variances

10.6 Chi-Square Test for Goodness of Fit

10.7 Chi-Square Test for Association

11.1 Hypothesis Testing: Two Population Means (Sigma Known, Independent Samples)

11.2 Hypothesis Testing: Two Population Means (Sigma Unknown, Independent Samples)

11.3 Hypothesis Testing: Two Population Means (Sigma Unknown, Dependent Samples)

11.4 Hypothesis Testing: Two Population Proportions

11.5 Hypothesis Testing: Two Population Variances

11.6 ANOVA (Analysis of Variance)

12.R.1 The Cartesian Coordinate System

• Examples
• Example 1: Plotting Ordered Pairs
• Example 2: Plotting Ordered Pairs
• Example 3: Finding Ordered Pairs
• Example 4: Finding Ordered Pairs
• Example 6: Locating Points on the Graph of a Line

12.R.2 Graphing Linear Equations in Two Variables

• Examples
• Example 1: Graphing a Linear Equation in Two Variables
• Example 2: Graphing a Linear Equation in Two Variables
• Example 3: Graphing a Linear Equation in Two Variables
• Example 4: Using Intercepts to Graph Linear Equations
• Example 5: Using Intercepts to Graph Linear Equations
• Example 7: Graphing Horizontal Lines
• Example 8: Graphing Vertical Lines

12.R.3 Slope-Intercept Form

• Examples
• Example 1: Finding the Slope of a Line
• Example 2: Finding the Slope of a Line
• Example 3: Finding the Slope of a Horizontal Line
• Example 4: Finding the Slope of a Vertical Line
• Example 5: Using Slope and the y‑Intercept to Graph a Line
• Example 6: Using Slope and the y-Intercept to Graph a Line
• Example 7: Finding Equations Given the Slope and the y‑Intercept

12.1 Scatter Plots and Correlation

12.2 Linear Regression

• Examples
• Example 12.2.2: Making Predictions Using a Least-Squares Regression Line

12.3 Regression Analysis

• Examples
• Example 12.3.2: Calculating the Sum of Squared Errors

12.4 Multiple Regression

A.1 Constructing Samples

• Examples
• Example 1: Example A.1.1: Construct a Sample
• Example 2: Example A.1.2: Construct a Sample
• Example 3: Example A.1.3: Construct a Bimodal Sample
• Example 4: Example A.1.4: Adding a Sample Value
• Example 5: Example A.1.5: Adding a Sample Value
• Example 6: Example A.1.6: Adding a Sample Value
• Example 7: Example A.1.7: Construct a Sample

A.2 Games of Chance

• Examples
• Example 1: Example A.2.1: Expected Value
• Example 2: Example A.2.2: Expected Value
• Example 3: Example A.2.3: Expected Value

A.3 Name That Distribution

A.4 Type II Errors

A.5 Direct Mail

A.6 Statistical Process Control

• Examples
• Example 1: Example A.6.1
• Example 2: Example A.6.2
• Example 3: Example A.6.3
• Example 4: Example A.6.4: Mean Charts Using s
• Example 5: Example A.6.5: p-Charts
• Example 6: Example A.6.6: c-Charts

A.7 Choosing the Correct Statistic for Estimating a Population Mean

• Examples
• Example 1: Example A.7.1: Best Point Estimate
• Example 2: Example A.7.2: Confidence Intervals
• Example 3: Example A.7.3: Determining the Appropriate Method
• Example 4: Example A.7.4: Determining the Appropriate Method