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Applications Index
by Terry T. Sincich, James T. McClave
A First Course in Statistics, 12th Edition
Available in MyStatLabTM for Your Introductory Statistics Courses
Applet Correlation
A First Course in Statistics
A First Course in Statistics
Contents
Preface
New in the 12th Edition
Content-Specific Changes to This Edition
Hallmark Strengths
Get the most out of MyStatLab™
Resources for Success
Reviewers of Previous Editions
Other Contributors
Applications Index
1 Statistics, Data, and Statistical Thinking
Contents
Where We’re Going
1.1 The Science of Statistics
1.2 Types of Statistical Applications
1.3 Fundamental Elements of Statistics
Problem
Problem
Problem
1.4 Types of Data
Problem
1.5 Collecting Data: Sampling and Related Issues
Problem
1.6 The Role of Statistics in Critical Thinking and Ethics
Problem
Problem
Chapter Notes
Key Terms
Key Ideas
Types of Statistical Applications
Descriptive
Inferential
Types of Data
Data Collection Methods
Types of Random Samples
Problems with Nonrandom Samples
Exercises 1.1–1.36
Understanding the Principles
Applet Exercise 1.1
Applet Exercise 1.2
Applying the Concepts—Basic
Applying the Concepts–Intermediate
Applying the Concepts—Advanced
Critical Thinking Challenges
References
2 Methods for Describing Sets of Data
Contents
Where We’ve Been
Where We’re Going
2.1 Describing Qualitative Data
Problem
Exercises 2.1–2.24
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
2.2 Graphical Methods for Describing Quantitative Data
Dot Plots
Stem-and-Leaf Display
Histograms
Problem
Exercises 2.25–2.48
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
2.3 Numerical Measures of Central Tendency
Problem
Problem
Problem
Problem
Problem
Problem
Exercises 2.49––2.72
Understanding the Principles
Learning the Mechanics
Applet Exercise 2.1
Applet Exercise 2.2
Applet Exercise 2.3
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
2.4 Numerical Measures of Variability
Problem
Problem
Exercises 2.73–2.92
Understanding the Principles
Learning the Mechanics
Applet Exercise 2.4
Applet Exercise 2.5
Applet Exercise 2.6
Applying the Concepts—Basic
Applying the Concepts—Intermediate
2.5 Using the Mean and Standard Deviation to Describe Data
Problem
Problem
Problem
Exercises 2.93––2.113
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
2.6 Numerical Measures of Relative Standing
Problem
Problem
Exercises 2.114–2.131
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
2.7 Methods for Detecting Outliers: Box Plots and z-Scores
Problem
Problem
Problem
Exercises 2.132––2.153
Understanding the Principles
Learning the Mechanics
Applet Exercise 2.7
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
2.8 Graphing Bivariate Relationships (Optional)
Problem
Exercises 2.154––2.169
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
2.9 Distorting the Truth with Descriptive Statistics
Graphical Distortions
Misleading Numerical Descriptive Statistics
Problem
Problem
Exercises 2.170–2.173
Applying the Concepts—Intermediate
Chapter Notes
Key Terms
Key Symbols
Key Ideas
Describing Qualitative Data
Graphing Quantitative Data
Rules for Describing Quantitative Data
Rules for Detecting Quantitative Outliers
Guide to Selecting the Data Description Method
Supplementary Exercises 2.174–2.208
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
Critical Thinking Challenge
References
Using Technology MINITAB: Describing Data
Graphing Data
Numerical Descriptive Statistics
TI-83/TI–84 Plus Graphing Calculator: Describing Data
Histogram from Raw Data
Histogram from a Frequency Table
One-Variable Descriptive Statistics
Sorting Data (to Find the Mode)
Box Plot
Scatterplots
3 Probability
Contents
Where We’ve Been
Where We’re Going
3.1 Events, Sample Spaces, and Probability
Problem
Problem
Problem
Problem
Problem
Problem
Problem
Exercises 3.1–3.37
Understanding the Principles
Learning the Mechanics
Applet Exercise 3.1
Applet Exercise 3.2
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
3.2 Unions and Intersections
Problem
Look Back
Problem
3.3 Complementary Events
Problem
3.4 The Additive Rule and Mutually Exclusive Events
Problem
Problem
Exercises 3.38–3.67
Understanding the Principles
Learning the Mechanics
Applet Exercise 3.3
Applet Exercise 3.4
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
3.5 Conditional Probability
Problem
Problem
Problem
3.6 The Multiplicative Rule and Independent Events
Problem
Problem
Problem
Problem
Statistics in Action Revisited The Probability of Winning Cash 3 or Play 4
Exercises 3.68–3.103
Understanding the Principles
Learning the Mechanics
Applet Exercise 3.5
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
Chapter Notes
Key Terms
Key Symbols
Key Ideas
Probability Rules for k Sample Points, S1,S2,S3,…,Sk
Combinations Rule
Guide to Selecting Probability Rules
Supplementary Exercises 3.104–3.146
Understanding the Principles
Learning the Mechanics
Applet Exercise 3.6
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
Critical Thinking Challenges
References
4 Random Variables and Probability Distributions
Contents
Where We’ve Been
Where We’re Going
4.1 Two Types of Random Variables
Problem
Problem
Problem
Exercises 4.1–4.16
Understanding the Principles
Applying the Concepts—Basic
Applying the Concepts—Intermediate
4.2 Probability Distributions for Discrete Random Variables
Problem
Problem
Problem
Problem
Problem
Exercises 4.17–4.47
Understanding the Principles
Learning the Mechanics
Applet Exercise 4.1
Applet Exercise 4.2
Applying the Concepts—Basic
Applying the Concepts—Intermediate
4.3 The Binomial Random Variable
Problem
Problem
Problem
Problem
Using Tables and Technology for Binomial Probabilities
Problem
Exercises 4.48–4.72
Understanding the Principles
Learning the Mechanics
Applet Exercise 4.3
Applet Exercise 4.4
Applet Exercise 4.5
Applying the Concepts—Basic
Apply the Concepts—Intermediate
Applying the Concepts—Advanced
4.4 Probability Distributions for Continuous Random Variables
Problem
4.5 The Normal Distribution
Problem
Problem
Problem
Problem
Problem
Problem
Problem
Problem
Problem
Exercises 4.73–4.102
Understanding the Principles
Learning the Mechanics
Applet Exercise 4.6
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
4.6 Descriptive Methods for Assessing Normality
Problem
Statistics in Action Revisited Assessing whether the Normal Distribution Is Appropriate for Modeling the Super Weapon Hit Data
Exercises 4.103–4.124
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
4.7 Approximating a Binomial Distribution with a Normal Distribution (Optional)
Problem
Exercises 4.125–4.142
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
4.8 Sampling Distributions
Problem
Problem
Exercises 4.143–4.151
Understanding the Principles
Learning the Mechanics
4.9 The Sampling Distribution of x¯ and the Central Limit Theorem
Problem
Problem
Problem
Exercises 4.152–4.175
Understanding the Principles
Learning the Mechanics
Applet Exercise 4.7
Applet Exercise 4.8
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
Chapter Notes
Key Terms
Key Symbols
Key Ideas
Properties of Discrete Probability Distributions
Properties of Continuous Probability Distributions
Methods for Assessing Normality
Normal Approximation to Binomial
Key Formulas
Guide to Selecting a Probability Distribution
Generating the Sampling Distribution of x ¯
Supplementary Exercises 4.176–4.220
Understanding the Principles
Apply the Concepts–Basic
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
Critical Thinking Challenge
References
Using Technology MINITAB: Binomial Probabilities, Normal Probability, and Simulated Sampling Distribution
Binomial Probabilites
Normal Probabilities
Normal Probability Plot
TI-83/TI-84 Plus Graphing Calculator: Discrete Random Variables, Binomial, and Normal Probabilities
Calculating the Mean and Standard Deviation of a Discrete Random Variable
Calculating Binomial Probabilities
I. P(x=k)
II. P(x≤k)
III. P(x<k),P(x>k),P(x≥k)
Graphing the Area under the Standard Normal Curve
Finding Normal Probabilities without a Graph
Example
Finding Normal Probabilities with a Graph
Example
Graphing a Normal Probability Plot
Simulating a Sampling Distribution
5 Inferences Based on a Single Sample Estimation with Confidence Intervals
Contents
Where We’ve Been
Where We’re Going
5.1 Identifying and Estimating the Target Parameter
5.2 Confidence Interval for a Population Mean: Normal (z) Statistic
Problem
Problem
Problem
Exercises 5.1–5.28
Understanding the Principles
Learning the Mechanics
Applet Exercise 5.1
Applet Exercise 5.2
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
5.3 Confidence Interval for a Population Mean: Student’s t-Statistic Confidence Interval for a Population Mean: Student’s t-Statistic
Problem 1
Solution to Problem 1
Problem 2
Solution to Problem 2
Problem
Problem
Statistics in Action Revisited Estimating the Mean Overpayment
Exercises 5.29–5.51
Understanding the Principles
Applet Exercise 5.3
Applet Exercise 5.4
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
5.4 Large-Sample Confidence Interval for a Population Proportion
Problem
Problem
Look Ahead
Problem
Exercises 5.52–5.73
Understanding the Principles
Applet Exercise 5.5
Applet Exercise 5.6
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
5.5 Determining the Sample Size
Estimating a Population Mean
Problem
Estimating a Population Proportion
Problem
Exercises 5.74–5.98
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
5.6 Confidence Interval for a Population Variance (Optional)
Problem
Problem
Exercises 5.99–5.117
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basics
Applying the Concepts—Intermediate
Chapter Notes
Key Terms
Key Symbols
Key Ideas
Population Parameters, Estimators, & Standard Errors
Determining the Sample Size n:
Key Words for Identifying the Target Parameter:
Commonly Used z-values for a Large-Sample Confidence Interval for μ or p:
Illustrating the Notion of “95% Confidence”
Guide to Forming a Confidence Interval
Supplementary Exercises 5.118–5.152
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
Critical Thinking Challenge
References
6 Inferences Based on a Single Sample Tests of Hypothesis
Contents
Where We’ve Been
Where We’re Going
6.1 The Elements of a Test of Hypothesis
6.2 Formulating Hypotheses and Setting Up the Rejection Region
Problem
Problem
Problem
Exercises 6.1–6.21
Understanding the Principles
Learning the Mechanics
Applet Exercise 6.1
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
6.3 Observed Significance Levels: p-Values
Problem
Exercises 6.22–6.30
Learning the Mechanics
6.4 Test of Hypothesis about a Population Mean: Normal (z) Statistic
Problem
Problem
Problem
Exercises 6.31–6.50
Understanding the Principles
Learning the Mechanics
Applet Exercise 6.2
Applet Exercise 6.3
Applet Exercise 6.4
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
6.5 Test of Hypothesis about a Population Mean: Student’s t-Statistic Test of Hypothesis about a Population Mean: Student’s t-Statistic
Problem
Problem
Exercises 6.51–6.72
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
6.6 Large-Sample Test of Hypothesis about a Population Proportion
Problem
Problem
Small samples
Exercises 6.73–6.93
Understanding the Principles
Learning the Mechanics
Applet Exercise 6.5
Applet Exercise 6.6
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
6.7 Test of Hypothesis about a Population Variance (Optional)
Problem
Problem
Exercises 6.94–6.114
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
6.8 A Nonparametric Test about a Population Median (Optional)
Problem
Exercises 6.115–6.131
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Chapter Notes
Key Terms
Key Symbols
Key Ideas
Key Words for Identifying the Target Parameter
Elements of a Hypothesis Test
Forms of Alternative Hypothesis
Using p-Values to Decide
Guide to Selecting a One-Sample Hypothesis Test
Supplementary Exercises 6.132–6.169
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
Critical Thinking Challenges
References
7 Comparing Population Means
Contents
Where We’ve Been
Where We’re Going
7.1 Identifying the Target Parameter
7.2 Comparing Two Population Means: Independent Sampling
Large Samples
Problem
Problem
Problem
Small Samples
Problem
Exercises 7.1–7.28
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
7.3 Comparing Two Population Means: Paired Difference Experiments
Problem
Exercises 7.29–7.52
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
7.4 Determining the Sample Size
Problem
Problem
Exercises 7.53–7.65
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts—Intermediate
7.5 A Nonparametric Test for Comparing Two Populations: Independent Samples (Optional)
Problem
Exercises 7.66–7.85
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts-Intermediate
7.6 A Nonparametric Test for Comparing Two Populations: Paired Difference Experiment (Optional)
Problem
Exercises 7.86–7.102
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
7.7 Comparing Three or More Population Means: Analysis of Variance (Optional)
Problem
Problem
Exercises 7.103–7.121
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
Chapter Notes
Key Terms
Key Symbols
Key Ideas
Key Words for Identifying the Target Parameter
Determining the Sample Size
Conditions Required for Inferences about μ1−μ2
Large samples:
Small samples:
*Conditions Required for ANOVA
Large or small samples:
Conditions Required for Inferences about μd
Large samples:
Small samples:
Using a Confidence Interval for (μ1−μ2) to Determine whether a Difference Exists
Guide to Comparing Population Means
Supplementary Exercises 7.122–7.147
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
Critical Thinking Challenge
References
8 Comparing Population Proportions
Contents
Where We’ve Been
Where We’re Going
8.1 Comparing Two Population Proportions: Independent Sampling
Problem
Problem
Exercises 8.1–8.23
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
8.2 Determining the Sample Size
Problem
Exercises 8.24–8.33
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts—Intermediate
8.3 Testing Category Probabilities: Multinomial Experiment
Problem
Problem
Exercises 8.34–8.53
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
8.4 Testing Categorical Probabilities: Two-Way (Contingency) Table
Problem
Contingency Tables with Fixed Marginals
Exercises 8.54–8.78
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
Chapter Notes
Key Terms
Key Symbols/Notation
Key Ideas
Multinomial Data
Properties of a Multinomial Experiment
One-Way Table
Two-Way (Contingency) Table
Chi-Square (χ2) Statistic
Chi-square tests for independence
Conditions Required for Valid χ2 Tests
Categorical Data Analysis Guide
Supplementary Exercises 8.79–8.107
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
Critical Thinking Challenge
References
9 Simple Linear Regression
Contents
Where We’ve Been
Where We’re Going
9.1 Probabilistic Models
Problem
Exercises 9.1–9.14
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basic
9.2 Fitting the Model: The Least Squares Approach
Problem
Exercises 9.15–9.36
Understanding the Principles
Learning the Mechanics
Applet Exercise 9.1
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
9.3 Model Assumptions
Problem
Exercises 9.37–9.52
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
9.4 Assessing the Utility of the Model: Making Inferences about the Slope β1
Problem
Exercises 9.53–9.76
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
9.5 The Coefficients of Correlation and Determination
Coefficient of Correlation
Problem
Coefficient of Determination
Problem
Exercises 9.77–9.100
Understanding the Principles
Learning the Mechanics
Applet Exercise 9.2
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
9.6 Using the Model for Estimation and Prediction
Problem
Problem
Exercises 9.99–9.119
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
9.7 A Complete Example
Exercises 9.120–9.123
Applying the Concepts—Intermediate
9.8 A Nonparametric Test for Correlation (Optional)
Problem
Exercises 9.124—9.139
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Chapter Notes
Key Terms
Key Symbols/Notation
Key Ideas
Simple Linear Regression Variables
Method of least squares properties
First-order (straight-line) model
Practical interpretation of y-intercept
Practical interpretation of slope
Coefficient of correlation, r
Coefficient of determination, r2
Practical interpretation of model standard deviation s
Comparing Intervals in Step 5
Nonparametric Test for Rank Correlation
Key Formulas
Guide to Simple Linear Regression
Supplementary Exercises 9.140–9.163
Understanding the Principles
Learning the Mechanics
Applying the Concepts—Basic
Applying the Concepts—Intermediate
Applying the Concepts—Advanced
Critical Thinking Challenge
References
Appendix A: Summation Notation
Problem
Problem
Problem
Appendix B: Tables
Appendix C: Calculation Formulas for Analysis of Variance (Independent Sampling)
Short Answers to Selected Odd Exercises
Index
Photo Credits
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 9
Selected Formulas
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A First Course in Statistics
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