Statistics

1. Statistics, Data, and Statistical Thinking

1.1 The Science of Statistics

1.2 Types of Statistical Applications

1.3 Fundamental Elements of Statistics

1.4 Types of Data

1.5 Collecting Data

1.6 The Role of Statistics in Critical Thinking

Statistics in Action: Social Media Networks and the Millennial Generation

Using Technology: Creating and Listing Data



2. Methods for Describing Sets of Data

2.1 Describing Qualitative Data

2.2 Graphical Methods for Describing Quantitative Data

2.3 Summation Notation

2.4 Numerical Measures of Central Tendency

2.5 Numerical Measures of Variability

2.6 Interpreting the Standard Deviation

2.7 Numerical Measures of Relative Standing

2.8 Methods for Detecting Outliers: Box Plots and z-Scores

2.9 Graphing Bivariate Relationships (Optional)

2.10 Distorting the Truth with Descriptive Techniques

Statistics In Action: Body Image Dissatisfaction: Real or Imagined?

Using Technology: Describing Data



3. Probability

3.1 Events, Sample Spaces, and Probability

3.2 Unions and Intersections

3.3 Complementary Events

3.4 The Additive Rule and Mutually Exclusive Events

3.5 Conditional Probability

3.6 The Multiplicative Rule and Independent Events

3.7 Random Sampling

3.8 Some Additional Counting Rules (Optional)

3.9 Bayes' Rule (Optional)

Statistics In Action: Lotto Buster! -Can You Improve Your Chances of Winning the Lottery?

Using Technology: Generating a Random Sample



4. Discrete Random Variables

4.1 Two Types of Random Variables

4.2 Probability Distributions for Discrete Random Variables

4.3 Expected Values of Discrete Random Variables

4.4 The Binomial Random Variable

4.5 The Poisson Random Variable (Optional)

4.6 The Hypergeometric Random Variable (Optional)

Statistics in Action: Probability in a Reverse Cocaine Sting- Was Cocaine Really Sold?

Using Technology: Discrete Probabilities



5. Continuous Random Variables

5.1 Continuous Probability Distributions

5.2 The Uniform Distribution

5.3 The Normal Distribution

5.4 Descriptive Methods for Assessing Normality

5.5 Approximating a Binomial Distribution with a Normal Distribution (Optional)

5.6 The Exponential Distribution (Optional)

Statistics in Action: Super Weapons Development - Is the Hit Ratio Optimized?

Using Technology: Continuous Random Variables, Probabilities, and Normal Probability Plots



6. Sampling Distributions

6.1 What is a Sampling Distribution?

6.2 Properties of Sampling Distributions: Unbiasedness and Minimum Variance

6.3 The Sampling Distribution of (x-bar) and the Central Limit Theorem

Statistics in Action: The Insomnia Pill-Will It Take Less Time to Fall Asleep?

Using Technology: Simulating a Sampling Distribution



7. Inferences Based on a Single Sample: Estimation with Confidence Intervals

7.1 Identifying and Estimating the Target Parameter

7.2 Confidence Interval for a Population Mean: Normal (z) Statistic

7.3 Confidence Interval for a Population Mean: Student's t-statistic

7.4 Large-Sample Confidence Interval for a Population Proportion

7.5 Determining the Sample Size

7.6 Confidence Interval for a Population Variance (Optional)

Statistics in Action: Medicare Fraud Investigations

Using Technology: Confidence Intervals



8. Inferences Based on a Single Sample: Tests of Hypothesis

8.1 The Elements of a Test of Hypothesis

8.2 Formulating Hypotheses and Setting Up the Rejection Region

8.3 Test of Hypothesis About a Population Mean: Normal (z) Statistic

8.4 Observed Significance Levels: p-Values

8.5 Test of Hypothesis About a Population Mean: Student's t-statistic

8.6 Large-Sample Test of Hypothesis About a Population Proportion

8.7 Calculating Type II Error Probabilities: More About ss (Optional)

8.8 Test of Hypothesis About a Population Variance (Optional)

Statistics in Action: Diary of a Kleenex User-How Many Tissues in a Box?

Using Technology: Tests of Hypothesis



9. Inferences Based on a Two Samples: Confidence Intervals and Tests of Hypotheses

9.1 Identifying the Target Parameter

9.2 Comparing Two Population Means: Independent Sampling

9.3 Comparing Two Population Means: Paired Difference Experiments

9.4 Comparing Two Population Proportions: Independent Sampling

9.5 Determining the Sample Size

9.6 Comparing Two Population Variances: Independent Sampling (Optional)

Statistics in Action: Zixit Corp. vs. Visa USA Inc.-A Libel Case

Using Technology: Two-Sample Inferences



10. Analysis of Variance: Comparing More Than Two Means

10.1 Elements of a Designed Study

10.2 The Completely Randomized Design: Single Factor

10.3 Multiple Comparisons of Means

10.4 The Randomized Block Design

10.5 Factorial Experiments: Two Factors

Statistics in Action: On the Trail of the Cockroach: Do Roaches Travel at Random?

Using Technology: Analysis of Variance



11. Simple Linear Regression

11.1 Probabilistic Models

11.2 Fitting the Model: The Least Squares Approach

11.3 Model Assumptions

11.4 Assessing the Utility of the Model: Making Inferences About the Slope ss1

11.5 The Coefficients of Correlation and Determination

11.6 Using the Model for Estimation and Prediction

11.7 A Complete Example

Statistics in Action: Can "Dowsers" Really Detect Water?

Using Technology: Simple Linear Regression



12. Multiple Regression and Model Building

12.1 Multiple Regression Models

12.2 The First-Order Model: Inferences About the Individual ss-Parameters

12.3 Evaluating the Overall Utility of a Model

12.4 Using the Model for Estimation and Prediction

12.5 Model Building: Interaction Models

12.6 Model Building: Quadratic and other Higher-Order Models

12.7 Model Building: Qualitative (Dummy) Variable Models

12.8 Model Building: Models with both Quantitative and Qualitative Variables

12.9 Model Building: Comparing Nested Models (Optional)

12.10 Model Building: Stepwise Regression (Optional)

12.11 Residual Analysis: Checking the Regression Assumptions

12.12 Some Pitfalls: Estimability, Multicollinearity, and Extrapolation

Statistics in Action: Modeling Condo Sales: Are There Differences in Auction Prices?

Using Technology: Multiple Regression



13. Categorical Data Analysis

13.1 Categorical Data and the Multinomial Distribution

13.2 Testing Categorical Probabilities: One-Way Table

13.3 Testing Categorical Probabilities: Two-Way (Contingency) Table

13.4 A Word of Caution About Chi-Square Tests

Statistics in Action: College Students and Alcohol-Is Drinking Frequency Related to Amount?

Using Technology: Chi-Square Analyses



14. Nonparametric Statistics*

14.1 Introduction: Distribution-Free Tests

14.2 Single Population Inferences

14.3 Comparing Two Populations: Independent Samples

14.4 Comparing Two Populations: Paired Difference Experiment

14.5 Comparing Three or More Populations: Completely Randomized Design

14.6 Comparing Three or More Populations: Randomized Block Design

14.7 Rank Correlation

Statistics in Action: How Vulnerable are Wells to Groundwater Contamination?

Using Technology: Nonparametric Analyses



Appendix A. Tables

Table I. Random Numbers

Table II. Binomial Probabilities

Table III. Poisson Probabilities

Table IV. Normal Curve Areas

Table V. Exponentials

Table VI. Critical Values of t

Table VII. Critical Values of x2

Table VIII. Percentage Points of the F Distribution, a=.10

Table IX. Percentage Points of the F Distribution, a=.05

Table X. Percentage Points of the F Distribution, a=.025

Table XI. Percentage Points of the F Distribution, a=.01

Table XII. Critical Values of TL and TU for the Wilcoxon Rank Sum Test

Table XIII. Critical Values of T0 in the Wilcoxon Signed Rank Test

Table XIV. Critical Values of Spearman's Rank Correlation Coefficient



Appendix B. Calculation Formulas for Analysis of Variance



Short Answers to Selected Odd-Numbered Exercises



*This chapter is included on the CD-ROM that comes with the textbook.