Beginning Statistics, 3rd Edition

2.1 Frequency Distributions

2.2 Graphical Displays of Data

• Examples
• Example 2.2.1: Creating a Pie Chart
• Example 2.2.2: Creating a Bar Graph
• Example 2.2.3: Creating a Pareto Chart
• Example 2.2.4: Creating a Side-by-Side Bar Graph
• Example 2.2.5: Creating a Stacked Bar Graph
• Example 2.2.9: Creating and Interpreting a Stem-and-Leaf Plot

2.3 Analyzing Graphs

• Examples
• Example 2.3.2: Shapes of Graphs

3.1 Measures of Center

• Examples
• Example 3.1.1: Calculating the Sample Mean
• Example 3.1.2: Using the Mean to Find a Data Value
• Example 3.1.3: Calculating a Weighted Mean
• Example 3.1.4: Calculating a Weighted Mean
• Example 3.1.5: Finding the Median
• 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

4.1 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

• Examples
• Example 4.4.1: Calculating Factorial Expressions
• Example 4.4.2: Calculating Numbers of Combinations and Permutations
• Example 4.4.3: Calculating the Number of Permutations
• Example 4.4.4: Calculating the Number of Combinations

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

5.1 Discrete Random Variables

• Examples
• Example 5.1.1: Creating a Discrete Probability Distribution
• Example 5.1.2: Calculating Expected Values

5.2 Binomial Distribution

• Examples
• Example 5.2.1: Finding the Mean and Standard Deviation of a Binomial Distribution
• Example 5.2.2: Calculating a Binomial Probability Using the Formula
• Example 5.2.3: Finding a Binomial Probability Using a Table
• Example 5.2.4: Calculating a Binomial Probability, $P\left(X=x\right)$
• 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
• Example 5.3.3: Calculating a Poisson Probability, $P\left(X=x\right)$
• Example 5.3.4: Calculating a Poisson Probability, $P\left(X=x\right)$

5.4 Hypergeometric Distribution

• Examples
• Example 5.4.1: Finding the Mean and Variance of a Hypergeometric Distribution
• Example 5.4.2: Calculating a Hypergeometric Probability, $P\left(X=x\right)$
• Example 5.4.3: Calculating a Hypergeometric Probability, $P\left(X=x\right)$

6.1 Introduction to the Normal Distribution

• Examples
• Example 6.1.1: Identifying Properties of Normal Curves
• Example 6.1.2: Determining if a Distribution is Normal

6.2 The Standard Normal Distribution

• Examples
• Example 6.2.1: Calculating and Graphing z-values
• Example 6.2.2: Finding Area to the Left of a Positive z-value Using a Cumulative Normal Table
• Example 6.2.3: Finding Area to the Left of a Negative z-value Using a Table
• Example 6.2.4: Finding Area to the Right of a Positive z-value Using a Cumulative Normal Table
• Example 6.2.5: Finding Area to the Right of a Negative z-value Using a Table

6.3 Finding Probability Using a Normal Distribution

• Examples
• Example 6.3.1: Finding the Probability that a Normally Distributed Random Variable Will Be Less Than a Given Value
• Example 6.3.2: Finding the Probability that a Normal Distributed Random Variable Will Be Greater Than a Given Value
• Example 6.3.3: Finding the Probability that a Normally Distributed Random Variable Will Be between Two Given Values Or in the Tails Defined by Two Given Values

6.4 Finding Values of a Normally Distributed Random Variable

• Examples
• Example 6.4.1: Finding the z-value with a Given Area to Its Left
• Example 6.4.2: Finding the z-value That Represents a Given Percentile
• Example 6.4.3: Finding the z-value with a Given Area to Its Right
• Example 6.4.4: Finding the z-value with a Given Area between −z and z

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
• Example 6.5.2: Using the Continuity Correction Factor with a Normal Distribution to Approximate a Binomial Probability
• Example 6.5.3: Using a Normal Distribution to Approximate a Binomial Probability of the Form P(X > x)
• Example 6.5.4: Using a Normal Distribution to Approximate a Binomial Probability of the Form P(X ≤ x)
• Example 6.5.5: Using a Normal Distribution to Approximate a Binomial Probability of the Form P(X = x)

7.1 Sampling Distributions and the Central Limit Theorem

• Examples
• Example 7.1.1: Calculating the Mean and Standard Deviation of a Sampling Distribution of Sample Means
• Example 7.1.2: Applying the Central Limit Theorem
• Example 7.1.3: Applying the Central Limit Theorem
• Example 7.1.3: Applying the Central Limit Theorem

7.2 Central Limit Theorem with Means

• Examples
• Example 7.2.1: Finding the Probability that a Sample Mean Will Be Less Than a Given Value
• Example 7.2.2: Finding the Probability that a Sample Mean Will Be Greater Than a Given Value
• 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

• Examples
• Example 7.3.1: Finding the Probability that a Sample Proportion Will Be At Least a Given Value
• Example 7.3.2: Finding the Probability that a Sample Proportion Will Be No More Than a Given Value

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)
• Example 8.3.2: Constructing a Confidence Interval for a Population Mean (σ Unknown)
• Example 8.3.3: Constructing 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 8.5.2: 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 8.5.4: Constructing a Confidence Interval for a Population Variance
• Example 8.5.5: Constructing a Confidence Interval for a Population Standard Deviation
• Example 8.5.5: 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 9.1.1: Finding the Point Estimate and Margin of Error of a Confidence Interval for the Difference between Two Population Means (σ Known, Independent Samples)
• Example 9.1.2: Constructing a Confidence Interval for the Difference between Two Population Means (σ Known, Independent Samples)
• Example 9.1.2: Constructing a Confidence Interval for the Difference between Two Population Means (σ Known, Independent Samples)
• Example 9.1.3: 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)
• Example 9.2.2: Constructing a Confidence Interval for the Difference between Two Population Means with Unequal Variances (σ Unknown, Independent Samples)
• Example 9.2.3: Constructing a Confidence Interval for the Difference between Two Population Means with Equal 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

• Examples
• Example 9.4.1: Calculating Sample Proportions and Verifying Sample Size Conditions

9.5 Comparing Two Population Variances

• Examples
• Example 9.5.1: Calculating the Point Estimate for Comparing Two Population Variances and Finding Critical F-Values

10.1 Fundamentals of Hypothesis Testing

• Examples
• Example 10.1.1: Determining the Null and Alternative Hypotheses
• Example 10.1.2: Determining the Null and Alternative Hypotheses
• Example 10.1.3: Determining the Null and Alternative Hypotheses
• Example 10.1.4: Interpreting the Conclusion to a Hypothesis Test

10.2 Hypothesis Testing for Population Means (Sigma Known)

• Examples
• Example 10.2.1: Hypothesis Test for a Population Mean (Right-Tailed, σ 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
• Example 10.3.2: Hypothesis Test for a Population Mean (Left-Tailed, σ Unknown)

10.4 Hypothesis Testing for Population Proportions

• Examples
• Example 10.4.1: Determining Which Distribution to Use for the Test Statistic in a Hypothesis Test
• Example 10.4.2: Hypothesis Test for a Population Proportion (Left-Tailed)

10.5 Hypothesis Testing for Population Variances

• Examples
• Example 10.5.1: Hypothesis Test for a Population Variance (Left-Tailed)

10.6 Chi-Square Test for Goodness of Fit

• Examples
• Example 10.6.1: Chi-Square Test for Goodness of Fit

10.7 Chi-Square Test for Association

• Examples
• Example 10.7.1: Performing a Chi-Square Test for Association

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

• Examples
• Example 11.1.1: Hypothesis Test for Two Population Means (Left-Tailed, Independent Samples, σ Known)

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

• Examples
• Example 11.2.1: Hypothesis Test for Two Population Means (Right-Tailed, σ Unknown, Independent Samples, Unequal Variances)

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

• Examples
• Example 11.3.1: Determining the Null and Alternative Hypotheses for a Dependent Samples

11.4 Hypothesis Testing: Two Population Proportions

• Examples
• Example 11.4.1: Hypothesis Test for Two Population Proportions (Left-Tailed)

11.5 Hypothesis Testing: Two Population Variances

• Examples
• Example 11.5.1: Hypothesis Test for Two Population Variances (Left-Tailed)

11.6 ANOVA (Analysis of Variance)

• Examples
• Example 11.6.1: Completing a One-Way ANOVA Table and Performing a One-Way ANOVA Test

12.1 Scatter Plots and Correlation

• Examples
• Example 12.1.1: Creating a Scatter Plot to Identify Trends in Data
• Example 12.1.2: Determining Whether a Scatter Plot Would Have a Positive Slope, Negative Slope, or Not Follow a Straight-Line Pattern
• Example 12.1.4: Describing the Linear Relationship Between Two Variables, Graphically and Numerically

12.2 Linear Regression

• Examples
• Example 12.2.1: Finding a Least-Squares Regression Line
• Example 12.2.2: Making Predictions Using a Least-Squares Regression Line
• Example 12.2.2: Making Predictions Using a Least-Squares Regression Line
• Example 12.2.3: Finding the Least-Squares Regression Line for a Given Data Set

12.3 Regression Analysis

• Examples
• Example 12.3.1: Calculating Residuals Using an Estimated Regression Equation
• Example 12.3.2: Calculating the Sum of Squared Errors
• Example 12.3.3: Calculating the Standard Error of Estimate

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