Beginning Statistics
1.1 Getting Started
1.2 Data Classification
- Examples
- Example 1.4: Classifying Data as Qualitative or Quantitative
- Example 1.5: Classifying Data as Continuous or Discrete
- Example 1.6: Understanding the Nominal Level of Measurement
- Example 1.7: Classifying Data as Nominal or Ordinal
- Example 1.8: Classifying Data by the Level of Measurement
- Example 1.9: Classifying Data by the Level of Measurement
- Example 1.10: Classifying Data
1.3 The Process of a Statistical Study
- Examples
- Example 1.11: Identifying Population and Variables
- Example 1.12: Identifying Observational Studies and Experiments
- Example 1.13: Identifying Sampling Methods
- Example 1.14: Classifying Studies as Cross-Sectional or Longitudinal
- Example 1.15: Classifying Studies as Meta-Analysis or Case Study
- Example 1.16: Analyzing an Experiment
1.4 How to Critique a Published Study
3.1 Measures of Center
- Examples
- Example 3.1: Calculating the Sample Mean
- Example 3.2: Using the Mean to Find a Data Value
- Example 3.3: Calculating a Weighted Mean
- Example 3.4: Calculating a Weighted Mean
- Example 3.5: Finding the Median
- Example 3.6: Finding the Mode
- Example 3.7: Calculating Measures of Center—Mean, Median, and Mode
- Example 3.8: Choosing the Most Appropriate Measure of Center
- Example 3.9: Determining Mean, Median, and Mode from a Graph
3.2a Measures of Dispersion
3.2b Applying the Standard Deviation
- Examples
- Example 3.14: Interpreting Standard Deviations
- Example 3.15: Calculating and Interpreting Coefficient of Variation
- Example 3.16: Applying the Empirical Rule for Bell-Shaped Distributions
- Example 3.17: Applying Chebyshev's Theorem
- Example 3.18: Standard Deviation of Grouped Data
- Example 3.19: Standard Deviation of Grouped Data
3.3 Measures of Relative Position
- Examples
- Example 3.20: Finding Data Values Given the Percentiles
- Example 3.21: Finding the Percentile of a Given Data Value
- Example 3.22: Finding the Quartiles of a Given Data Set
- Example 3.23: Finding the Quartiles of a Given Data Set
- Example 3.24: Writing the Five-Number Summary of a Given Data Set
- Example 3.25: Creating a Box Plot
- Example 3.26: Interpreting Box Plots
- Example 3.27: Calculating a Standard Score
- Example 3.28: Comparing Standard Scores
4.1 Introduction to Probability
- Examples
- Example 4.1: Identifying Outcomes in a Sample Space or Event
- Example 4.2: Using a Pattern to List All Outcomes in a Sample Space
- Example 4.3: Using a Tree Diagram to List All Outcomes in a Sample Space
- Example 4.4: Identifying Types of Probability
- Example 4.5: Calculating Classical Probability
- Example 4.6: Calculating Classical Probability
- Example 4.7: Calculating Classical Probability
- Example 4.8: Calculating Classical Probability
4.2 Addition Rules for Probability
- Examples
- Example 4.9: Describing the Complement of an Event
- Example 4.10: Using the Complement Rule for Probability
- Example 4.11: Using the Complement Rule for Probability
- Example 4.12: Using the Addition Rule for Probability
- Example 4.13: Using the Addition Rule for Probability
- Example 4.14: Using the Addition Rule for Probability
- Example 4.15: Using the Addition Rule for Probability of Mutually Exclusive Events
- Example 4.16: Using the Extended Addition Rule for Probability of Mutually Exclusive Events
4.3 Multiplication Rules for Probability
- Examples
- Example 4.17: Using the Multiplication Rule for Probability of Independent Events
- Example 4.18: Using the Extended Multiplication Rule for Probability of Independent Events
- Example 4.19: Calculating Probability of Dependent Events
- Example 4.20: Calculating Conditional Probability
- Example 4.21: Using the Multiplication Rule for Probability of Dependent Events
- Example 4.22: Using the Multiplication Rule for Probability of Dependent Events
- Example 4.23: Using the Rule for Conditional Probability
- Example 4.24: Using the Fundamental Counting Principle
- Example 4.25: Using the Fundamental Counting Principle (Without Replacement)
- Example 4.26: Using the Fundamental Counting Principle to Calculate Probability
4.4 Combinations and Permutations
- Examples
- Example 4.27: Calculating Factorial Expressions
- Example 4.28: Calculating Numbers of Combinations and Permutations by Hand and by Using Formulas
- Example 4.29: Calculating the Number of Permutations
- Example 4.30: Calculating the Number of Combinations
- Example 4.31: Calculating Probability Using Permutations
- Example 4.32: Calculating Probability Using Combinations
- Example 4.33: Calculating the Number of Special Permutations
4.5 Combining Probability and Counting Techniques
5.1 Discrete Random Variables
5.2 Binomial Distribution
- Examples
- Example 5.5: Calculating a Binomial Probability Using the Formula
- Example 5.6: Calculating a Binomial Probability Using the Formula or a TI-83/84 Plus Calculator
- Example 5.7: Calculating Binomial Probabilities Using the Formula or a TI-83/84 Plus Calculator
- Example 5.10: Finding a Binomial Probability Using a Table
5.3 Poisson Distribution
- Examples
- Example 5.11: Calculating a Poisson Probability Using the Formula
- Example 5.12: Calculating a Poisson Probability Using the Formula or a TI-83/84 Plus Calculator
- Example 5.13: Calculating a Poisson Probability Using the Formula or a TI-83/84 Plus Calculator
- Example 5.14: Calculating Poisson Probabilities Using the Formula or a TI-83/84 Plus Calculator
- Example 5.17: Finding a Poisson Probability Using a Table
5.4 Hypergeometric Distribution
- Examples
- Example 5.18: Calculating a Hypergeometric Probability
- Example 5.19: Calculating a Hypergeometric Probability
- Example 5.20: Calculating a Cumulative Hypergeometric Probability
- Example 5.21: Calculating Hypergeometric Probabilities
- Example 5.22: Determining Which Discrete Probability Distribution to Use
6.1 Introduction to the Normal Distribution
6.2 Finding Area Under a Normal Distribution
- Examples
- Example 6.2: Finding Area to the Left of a Positive z-value Using a Cumulative Normal Table
- Example 6.3: Finding Area to the Left of a Negative z-value Using a Table or a TI-83/84 Plus Calculator
- Example 6.4: Finding Area to the Right of a Positive z-value Using a Cumulative Normal Table
- Example 6.5: Finding Area to the Right of a Negative z-value Using a Table or a TI-83/84 Plus Calculator
- Example 6.6: Finding Area between Two z-values Using Tables or a TI-83/84 Plus Calculator
- Example 6.10: Interpreting Probability for the Standard Normal Distribution as an Area under the Curve
6.3 Finding Probability Using a Normal Distribution
- Examples
- Example 6.12: Finding the Probability that a Normally Distributed Random Variable Will Be Less Than a Given Value
- Example 6.13: Finding the Probability that a Normal Distributed Random Variable Will Be Greater Than a Given Value
- Example 6.14: Finding the Probability that a Normally Distributed Random Variable Will Be between Two Given Values
- Example 6.15: Finding the Probability that a Normally Distributed Random Variable Will Be in the Tails Defined by Two Given Values
- Example 6.16: Finding the Probability that a Normally Distributed Random Variable Will Differ from the Mean by More Than a Given Value
6.4 Finding Values of a Normally Distributed Random Variable
- Examples
- Example 6.17: Finding the z-value with a Given Area to Its Left
- Example 6.18: Finding the z-value with a Given Area to Its Left
- Example 6.19: Finding the z-value That Represents a Given Percentile
- Example 6.20: Finding the z-value with a Given Area to Its Right
- Example 6.21: Finding the z-value with a Given Area between −z and z
- Example 6.22: Finding the z-value with a Given Area in the Tails to the Left of −z and to the Right of z
- Example 6.23: Finding the Value of a Normally Distributed Random Variable with a Given Area to Its Right
6.5 Approximating a Binomial Distribution Using a Normal Distribution
- Examples
- Example 6.26: Using the Continuity Correction Factor with a Normal Distribution to Approximate a Binomial Probability
- Example 6.27: Using the Continuity Correction Factor with a Normal Distribution to Approximate a Binomial Probability
- Example 6.28: Using a Normal Distribution to Approximate a Binomial Probability of the Form P(X > x)
- Example 6.29: Using a Normal Distribution to Approximate a Binomial Probability of the Form P(X ≤ x)
- Example 6.30: Using a Normal Distribution to Approximate a Binomial Probability of the Form P(X = x)
7.1 Introduction to the Central Limit Theorem
7.2 Central Limit Theorem with Means
- Examples
- Example 7.4: Finding the Probability that a Sample Mean Will Be Less Than a Given Value
- Example 7.5: Finding the Probability that a Sample Mean Will Be Greater Than a Given Value
- Example 7.6: Finding the Probability that a Sample Mean Will Differ from the Population Mean by Less Than a Given Amount
- Example 7.7: Finding the Probability that a Sample Mean Will Differ from the Population Mean by More Than a Given Amount
7.3 Central Limit Theorem with Proportions
- Examples
- Example 7.8: Finding the Probability that a Sample Proportion Will Be At Least a Given Value
- Example 7.9: Finding the Probability that a Sample Proportion Will Be No More Than a Given Value
- Example 7.10: Finding the Probability that a Sample Proportion Will Differ from the Population Proportion by Less Than a Given Amount
- Example 7.11: Finding the Probability that a Sample Proportion Will Differ from the Population Proportion by More Than a Given Amount
8.1 Estimating Population Means (Sigma Known)
- Examples
- Example 8.1: Finding a Point Estimate for a Population Mean
- Example 8.2: Constructing a Confidence Interval with a Given Margin of Error
- Example 8.3: Finding the Margin of Error of a Confidence Interval for a Population Mean (σ Known)
- Example 8.4: Constructing a Confidence Interval for a Population Mean (σ Known)
- Example 8.5: Constructing a Confidence Interval for a Population Mean (σ Known)
- Example 8.7: Interpreting a Confidence Interval
- Example 8.8: Finding the Minimum Sample Size Needed for a Confidence Interval for a Population Mean
8.2 Student's t-Distribution
- Examples
- Example 8.9: Finding the Value of tα
- Example 8.10: Finding the Value of t Given the Area to the Right
- Example 8.11: Finding the Value of t Given the Area to the Left
- Example 8.12: Finding the Value of t Given the Area in Two Tails
- Example 8.13: Finding the Value of t Given Area between −t and t
- Example 8.14: Finding the Critical t-value for a Confidence Interval
8.3 Estimating Population Means (Sigma Unknown)
8.4 Estimating Population Proportions
- Examples
- Example 8.19: Finding a Point Estimate for a Population Proportion
- Example 8.20: Constructing a Confidence Interval for a Population Proportion
- Example 8.22: Finding the Minimum Sample Size Needed for a Confidence Interval for a Population Proportion
- Example 8.23: Finding the Minimum Sample Size, Point Estimate, and Confidence Interval for a Population Proportion
8.5 Estimating Population Variances
- Examples
- Example 8.24: Finding Point Estimates for the Population Standard Deviation and Variance
- Example 8.25: Constructing a Confidence Interval for a Population Variance
- Example 8.26: Constructing a Confidence Interval for a Population Standard Deviation
- Example 8.27: Constructing a Confidence Interval for a Population Variance
- Example 8.28: Constructing a Confidence Interval for a Population Standard Deviation
- Example 8.29: Finding the Minimum Sample Size Needed for a Confidence Interval for a Population Standard Deviation
9.1 Comparing Two Population Means (Sigma Known)
9.2 Comparing Two Population Means (Sigma Unknown)
- Examples
- Example 9.4: Finding the Margin of Error of a Confidence Interval for the Difference between Two Population Means (σ Unknown, Unequal Variances)
- Example 9.5: Constructing a Confidence Interval for the Difference between Two Population Means (σ Unknown, Unequal Variances)
- Example 9.6: Constructing a Confidence Interval for the Difference between Two Population Means (σ Unknown, Equal Variances)
9.3 Comparing Two Population Means (Sigma Unknown, Dependent Samples)
- Examples
- Example 9.8: Calculating Paired Differences
- Example 9.9: Finding a Point Estimate for the Mean of the Paired Differences for Two Populations (σ Unknown, Dependent Samples)
- Example 9.10: Constructing a Confidence Interval 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
- Examples
- Example 9.15: Calculating the Point Estimate for Comparing Two Population Variances and Finding Critical F-Values
- Example 9.16: Constructing a Confidence Interval for the Ratio of Two Population Variances
- Example 9.17: Constructing a Confidence Interval for the Ratio of Two Population Standard Deviations
10.1 Fundamentals of Hypothesis Testing
- Examples
- Example 10.1: Determining the Null and Alternative Hypotheses
- Example 10.2: Determining the Null and Alternative Hypotheses
- Example 10.3: Determining the Null and Alternative Hypotheses
- Example 10.4: Determining the Null and Alternative Hypotheses
- Example 10.5: Interpreting the Conclusion to a Hypothesis Test
- Example 10.6: Interpreting the Conclusion to a Hypothesis Test
- Example 10.7: Determining the Type of Error
- Example 10.8: Determining the Type of Error
- Example 10.9: Determining the Type of Error
10.2 Hypothesis Testing for Population Means (Sigma Known)
- Examples
- Example 10.10: Using a Rejection Region in a Hypothesis Test for a Population Mean (Right-Tailed, σ Known)
- Example 10.11: Calculating the p-Value for a z-test Statistic for a Left-Tailed Test
- Example 10.12: Calculating the p-Value for a z-test Statistic for a Right-Tailed Test
- Example 10.13: Calculating the p-Value for a z-test Statistic for a Two-Tailed Test
- Example 10.15: Determining the Conclusion to a Hypothesis Test Using the p-Value
- Example 10.16: Performing a Hypothesis Test for a Population Mean (Right-Tailed, σ Known)
- Example 10.17: Performing a Hypothesis Test for a Population Mean (Two-Tailed, σ Known)
10.3 Hypothesis Testing for Population Means (Sigma Unknown)
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)
- Examples
- Example 11.1: Determining the Null and Alternative Hypotheses for a Left-Tailed Test
- Example 11.2: Determining the Null and Alternative Hypotheses for a Right-Tailed Test
- Example 11.3: Determining the Null and Alternative Hypotheses for a Two-Tailed Test
- Example 11.4: Determining the Null and Alternative Hypotheses
- Example 11.5: Performing a Hypothesis Test for Two Population Means (Right-Tailed, σ Known)
- Example 11.6: Performing a Hypothesis Test for Two Population Means (Two-Tailed, σ Known)
- Example 11.7: Performing a Hypothesis Test for Two Population Means (Right-Tailed, σ Known)
11.2 Hypothesis Testing: Two Population Means (Sigma Unknown)
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)
12.1 Scatter Plots and Correlation
- Examples
- Example 12.1: Creating a Scatter Plot to Identify Trends in Data
- Example 12.2: Creating a Scatter Plot to Identify Trends in Data
- Example 12.3: Determining Whether a Scatter Plot Would Have a Positive Slope, Negative Slope, or Not Follow a Straight-Line Pattern
- Example 12.6: Using a Table of Critical Values to Determine Significance of a Linear Relationship
- Example 12.9: Calculating and Interpreting the Coefficient of Determination
12.2 Linear Regression
12.3 Regression Analysis
12.4 Multiple Regression Equations
A.1 Constructing Samples
A.2 Games of Chance
A.3 Name that Distribution
A.4 Type II Errors
A.5 Direct Mail
A.6 Hypothesis Testing Means (z Value)
A.7 Hypothesis Testing Proportions (z Value)
A.8 ANOVA Regression
A.9 R-Charts
- Examples
- Example A9.1: R-Charts
A.10 p-Charts
- Examples
- Example A10.1: p-Charts
A.11 c-Charts
- Examples
- Example A11.1: c-Charts