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L A ROSE • DISCOVERIN G STAT ISTICS
TA B L E O F CO N T E N T S
CHAPTER 1. THE NATURE OF STATISTICS
Case Study: Does Friday the 13th
Change Human Behavior?
1.1 Data Stories: The People Behind
the Numbers
1.2 An Introduction to Statistics
What is Statistics?
Descriptive Statistics: The Building
Blocks of Data Analysis
Inferential Statistics: How Do We Get
There From Here?
1.3 Gathering Data
Random Sampling
More Sampling Methods
Surveys and Questionnaires
Experimental Studies and Observational Studies
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Chapter 1 Vocabulary
Chapter 1 Review Exercises
Chapter 1 Quiz
CHAPTER 2. DESCRIBING DATA USING
GRAPHS AND TABLES
Case Study: The Caesar Cipher
2.1 Graphs and Tables for Categorical Data
Frequency Distributions and Relative
Frequency Distributions
Bar Graphs and Pareto Charts
Pie Charts
2.2 Graphs and Tables for Quantitative Data
Frequency Distributions and Relative
Frequency Distributions
Histograms and Frequency Polygons
Stem-and-Leaf Displays and Dotplots
Distribution Shape, Symmetry, and Skewness
2.3 Further Graphs and Tables for
Quantitative Data
Cumulative Frequency Distributions and
Cumulative Relative Frequency
Distributions
Ogives
Time Series Graphs
2.4 Graphical Misrepresentations of Data
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Chapter 2 Vocabulary
Chapter 2 Review Exercises
Chapter 2 Quiz
CHAPTER 3. DESCRIBING DATA NUMERICALLY
Case Study: Can the Financial Experts Beat the Darts?
3.1 Measures of Center
The Mean
The Median
The Mode
Skewness and Measures of Center
3.2 Measures of Variability
The Range
What Is a Deviation?
The Standard Deviation and the Variance
3.3 Working with Grouped Data
The Weighted Mean
Estimating the Mean for Grouped Data
Estimating the Variance and Standard
Deviation for Grouped Data
3.4 Measures of Position
Percentiles
z-Scores
Detecting Outliers Using z-Scores
3.5 Chebyshev’s Rule and the Empirical Rule
Chebyshev’s Rule
The Empirical Rule
3.6 Robust Measures
Quartiles and the Interquartile Range
The Five-Number Summary
The Boxplot
Robust Detection of Outliers
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Chapter 3 Formulas and Vocabulary
Chapter 3 Review Exercises
Chapter 3 Quiz
CHAPTER 4. DESCRIBING THE RELATIONSHIP
BETWEEN TWO VARIABLES
Case Study: Female Literacy and Fertility Worldwide
4.1 Tables and Graphs for the Relationship
Between Two Variables
Crosstabulations
Clustered Bar Graphs
Scatterplots
4.2 Introduction to Correlation
4.3 Introduction to Regression
The Regression Line
Using the Regression Equation to Make
Predictions
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Chapter 4 Formulas and Vocabulary
Chapter 4 Review Exercises
Chapter 4 Quiz
CHAPTER 5. PROBABILITY
Case Study: The ELISA Test for the Presence of HIV
5.1 Introducing Probability
Building Blocks of Probability: Experiments,
Outcomes, Events, and Sample Spaces
Classical Method of Assigning Probability
Law of Large Numbers and Relative Frequency
Method of Assigning Probability
5.2 Combining Events
Combining Events Using Complement, Union,
and Intersection
Addition Rule
5.3 Conditional Probability
Introduction to Conditional Probability
Independent Events
Multiplication Rule
Sampling With and Without Replacement
5.4 Counting Methods
Multiplication Rule for Counting
Permutations and Combinations
Computing Probabilities Using Combinations
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Chapter 5 Formulas and Vocabulary
Chapter 5 Review Exercises
Chapter 5 Quiz
CHAPTER 6. RANDOM VARIABLES AND
THE NORMAL DISTRIBUTION
Case Study: Be Careful What You Assume: Major
League Baseball Salaries
6.1 Discrete Random Variables
Random Variables
Discrete Probability Distributions
Mean and Variability of a Discrete Random
Variable
6.2 Binomial Probability Distribution
Binomial Experiment
Binomial Probability Distribution Formula
Binomial Distribution Tables
Binomial Mean, Variance, and Standard
Deviation
6.3 Continuous Random Variables and the
Normal Probability Distribution
Continuous Probability Distributions
Introduction to the Normal Probability
Distribution
6.4 Standard Normal Distribution
Finding Areas Under the Standard Normal
Curve for a Given Z-Value
Finding Standard Normal Values for a
Given Area
6.5 Applications of the Normal Distribution
Finding Probabilities for Any Normal
Distribution
Finding Normal Data Values for Specified
Probabilities
The Normal Approximation to the Binomial
Probability Distribution
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Chapter 6 Formulas and Vocabulary
Chapter 6 Review Exercises
Chapter 6 Quiz
CHAPTER 7. SAMPLING DISTRIBUTIONS
Case Study: The Trial of the Pyx: How Much
Gold is in Your Gold Coins?
7.1 Introduction to Sampling Distributions
Point Estimates and Sampling Error Sampling
–
Distribution of the Sample Mean –
Sampling Distribution of for a Normal
Population
Assessing Normality Using Normal Probability
Plots
Finding Probabilities and Percentiles Using a
Sampling Distribution
7.2 The Central Limit Theorem for Means
Sampling Distribution of – for Skewed and
Symmetric Populations
Using Central Limit Theorem for Means to Solve
Probability Problems About the Sample Mean
7.3 The Central Limit Theorem for
Proportions
Sampling Distribution of the Sample
Proportion pˆ
Sampling Distribution of pˆ for Extreme and
Moderate Values of p
The Central Limit Theorem for Proportions
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Chapter 7 Formulas and Vocabulary
Chapter 7 Review Exercises
Chapter 7 Quiz
L A ROSE • DISCOVERIN G STAT ISTICS
TA B L E O F CO N T E N T S
CHAPTER 8. CONFIDENCE INTERVALS
Case Study: Analyzing Stock Performance on
the New York Stock Exchange
8.1 Z Intervals for the Mean
Introduction to Confidence Intervals:
Developing the Formula
What Do Confidence Intervals Mean?
Z Interval for the Population Mean :
Two Cases
Margin of Error
8.2 t Interval for the Mean
Introducing the t Distribution
t Interval for the Mean: Two Cases
Margin of Error for the t Interval
8.3 Z Interval for a Population Proportion
Point Estimate pˆ of the Population Proportion p
Z Interval for the Population Proportion p
Margin of Error for the Z Interval for the
Population Proportion p
8.4 Confidence Intervals for the Population
Variance and Standard Deviation
Properties of the 2 (Chi-Square) Distribution
Finding Critical Values for the 2 (Chi-Square)
Distribution
Constructing Confidence Intervals for the
Population Variance and Standard
Deviation
Using Confidence Intervals for to Perform
Two-Tailed Hypothesis Tests About Probability of a Type II Error and the Power
of a Hypothesis Test
9.4 t Test for the Population Mean ␮
t Test for Using the p-Value Method
t Test for Using the Critical-Value Method
Standard Error of the Sample Mean
9.5 Z Test for the Population Proportion p
The Essential Idea About Hypothesis Testing
for the Proportion
Z Test for p Using the p-Value Method
Z Test for p Using the Critical-Value Method
Using Confidence Intervals for p to Perform
Two-Tailed Hypothesis Tests About p
9.6 Chi-Square Test for the Population
Standard Deviation ␴
The Essential Idea about Hypothesis Testing
for the Population Standard Deviation 2 Test for Using the p-value Method
2 Test for Using the Critical-Value Method
Using Confidence Intervals for to Perform
Two-Tailed Hypothesis Tests for Try This in Class!
Chapter 9 Formulas and Vocabulary
Chapter 9 Review Exercises
Chapter 9 Quiz
8.5 Sample Size Considerations
Sample Size for Estimating the Population
Mean
Sample Size for Estimating the Population
Proportion with No Prior Information About p
Sample Size Requirement when Prior
Information About p Is Available
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Chapter 8 Formulas and Vocabulary
Chapter 8 Review Exercises
Chapter 8 Quiz
Case Study: The Golden Ratio
9.1 Introduction to Hypothesis Testing
Constructing the Hypotheses
Significant Difference or Chance Variation?
Type I and Type II Errors
9.2 Z Test for the Population Mean ␮:
p-Value Method
The Essential Idea About Hypothesis Testing
for the Mean
p-Values
Performing the Z test for the Population Mean
Using the p-Value Method
Assessing the Strength of Evidence Against
the Null Hypothesis
9.3 Z Test for the Population Mean ␮:
Critical-Value Method
Critical Regions and the Critical Value Zcrit
Performing the Z Test for the Population
Mean Using the Critical-Value Method
The Relationship Between the p-Value
Method and the Critical-Value Method
Introduction to the 2 Test for Independence
Performing the 2 Test for Independence
Test for the Homogeneity of Proportions
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Chapter 11 Formulas and Vocabulary
Chapter 11 Review Exercises
Chapter 11 Quiz
CHAPTER 12. ANALYSIS OF VARIANCE
Case Study: Professors on Facebook
12.1 Introduction to the Analysis of
Variance (ANOVA)
F Distribution
How Analysis of Variance (ANOVA) Works
ANOVA Table
12.2 Performing Analysis of Variance
ANOVA: p-Value Method
ANOVA: Estimated p-Value Method
ANOVA: Critical-Value Method
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Chapter 12 Formulas and Vocabulary
Chapter 12 Review Exercises
Chapter 12 Quiz
CHAPTER 13 REGRESSION ANALYSIS
CHAPTER 10. TWO-SAMPLE INFERENCE
Case Study: How Fair is the Scoring in Scrabble?
Case Study: Do Prior Student Evaluations Influence
Students’ Ratings of Professors?
13.1 Introduction to Linear Regression
10.1 Inference for Difference in Means–
Dependent Samples
Independent Samples and Dependent Samples
Dependent Sample t Interval for the
Population Mean of the Differences
Dependent Sample t Test for the Population
Mean of the Differences
10.2 Inference About Two Independent Means
CHAPTER 9. HYPOTHESIS TESTING
11.2 ␹2 Test for Independence and for
Homogeneity of Proportions
–
Sampling Distribution of –1 – 2
Confidence Intervals for 1 – 2
Independent Sample t Test for 1 – 2
Using Confidence Intervals for 1 – 2 to
Perform Two-Tailed Hypothesis Tests About
1 – 2
10.3 Inference for Two Independent
Proportions
Sampling Distribution of p1 – p2
Independent Sample Z Interval for p1 – p2
Independent Sample Z Test for p1 – p2
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Chapter 10 Formulas and Vocabulary
Chapter 10 Review Exercises
Chapter 10 Quiz
CHAPTER 11. CATEGORICAL DATA ANALYSIS
Case Study: Online Dating
11.1 ␹2 Goodness of Fit Test
The Multinomial Random Variable
What is a 2 Goodness of Fit Test?
Performing the 2 Goodness of Fit Test
Review of Regression Concepts
Prediction Error, SSE, and Standard Error
of the Estimate s
13.2 Coefficient of Determination r2
SST, SSR, and SSE
Calculating and Interpreting the
Coefficient of Determination r2
13.3 Inference About the Slope of
the Regression Line
Regression Model
Confidence Interval for Slope 1
Hypothesis Tests for Slope 1
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Chapter 13 Formulas and Vocabulary
Chapter 13 Review Exercises
Chapter 13 Quiz
ANSWERS TO ODD-NUMBERED EXERCISES
AND CHAPTER QUIZZES
TABLES APPENDIX
Table A: Random Numbers
Table B: Binomial Distribution
Table C: Standard Normal Distribution
Table D: t-Distribution
Table E: Chi-square (2) Distribution
Table F: F-Distribution
NOTES AND DATA SOURCES
INDEX