Fundamentals of Statistics

Michael Sullivan
November 2006
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For one semester algebra-based Introductory Statistics Courses.


This very popular text promotes student success while maintaining the statistical integrity of the course. Three objectives motivate this text: (1) to generate and maintain student interest, thereby promoting student success and confidence; (2) to provide extensive and effective opportunity for student practice; (3) to permit flexibility of teaching styles. This revision follows the Guidelines for Assessment and Instruction in Statistics Education (GAISE) for the college introductory statistics course.

Datasets and other resources (where applicable) for this book are available here.



Guidelines for Assessment and Instruction in Statistics Education (GAISE) for the college introductory statistics course - Adheres closely to the  guidelines endorsed recently by the American Statistical Association:

- 1. Emphasize statistical literacy and develop statistical thinking;

- 2. Use real data in teaching statistics;

- 3. Stress conceptual understanding;

- 4. Foster active learning;

- 5. Use technology for developing conceptual understanding; - 6. Use assessments to improve and evaluate student learning.

See for more information.



• Emphasizes statistical literacy and develops statistical thinking in 5 ways:

                I.      Extensive discussion of data production - Sections 1.2 through 1.4 discuss sampling techniques and pitfalls of sampling.  Section 1.5 has a thorough discussion of design and experiments.

                II.      Readingand interpretation of statistical graphs - The emphasis in Chapter 2 is on constructing and interpreting statistical graphs.  In addition, in Section 2.3, the author illustrates the idea off misrepresenting data through graphs.  The remainder of the text requires students to use graphs as a preliminary step in any statistical analysis.

                III.      Discussion making about appropriate techniques - When a research question is posed, the researcher must decide on the type of analysis to conduct using the data to answer the question. Different models may be used to answer the question.  For example, in Section 1.5, students are asked to design an experiment to answer a research question.  Different designs may all be legitimate choices.  The student is asked to justify his/her design choice.  New Putting It All Together sections in chapters 9-10 (Confidence Intervals and Hypothesis Testing) to help students in determining which technique to use.

                  IV.      Decisions Projects - Each chapter opens with a Decisions Project that requires students to collect, summarize, and interpret data to help make decisions that occur in every day life.

                 V.      Concepts and Vocabulary - Each section exercise set has a category of problems that require students to learn the language of statistics and explain statistical concepts in their own words.



• Use Real Data in Teaching Statistics - The examples and exercises use real, sourced data to illustrate statistical concepts and procedures.  The data come from a wide variety of disciplines such as psychology, sociology, finance, economics, biology, environmental studies, business, and chemistry so that all students can see the importance of data analysis in their field of study.

    • Among the many interesting data sets are data sets from the authors' students so that students understand that thinking statistically applies to ordinary situations.
    • See the Applications Index on pg. xxiv for a full listing.


• Stress Conceptual Understanding in the following ways:

                I.      Applying the Concepts Problems - Asks the student to analyze real data by drawing graphs or going through procedures, and help to develop a student's ability to think statistically.

  • Exercises 21 and 22, pg. 117
  • Exercise 25, pg. 118
  • Exercise 41, pg. 121
  • Exercise 31, pg. 190
  • Exercises 35-37, pg. 191-192

                II.      Simulation and Applets - Throughout the text, exercises require students to perform simulations or use applets that will contribute to their conceptual understanding.  Simulations and applets are powerful because they let students work actively with data.  Further, many students who are visual learners find that applets give them the reinforcement that they need to master a concept.

·        Students use simulation to enhance their understanding of sampling distributions (ex. #34-35, pg. 434)

·        Students use an applet to enhance their understanding of confidence intervals (ex. XXX

                III.      The Presentation of Formulas - When formulas are presented, the author uses both a “computational” formula and “definition” formula.

o  Pg. 127: Definition and formula for "Sample Variance"; Pg. 128: Example #4 - works the example BOTH ways.



• Foster Active Learning in the Classroom - to promote active learning, the author includes:

    • Numerous in-class activities that encourage students to collect, summarize and analyze data.  Doing these activities promotes conceptual understanding of statistical con concepts.
      • Approximately 2-3 Activities Per chapter.
      • Sample Standard Deviation Activity, pg. 129
      • Correlation Activity, pg. 184
      • Expected Value Activity, pg. 292
    • Applets that can be used in the classroom or as a group project Thes are on the text CD. Full listing of applets on pg. xxiii.
      • Subset of the applets include, among others: Sampling, Sampling Distribution, long run probability, Central Limit Theorem, Binomial Distribution.
      • Students use simulation to enhance their understanding of sampling distributions (ex. #34-35, pg. 434)
      • Students use an applet to enhance their understanding of confidence intervals (ex. XXX)
    • End of Chapter Case Study on the CD that accompanies the text that can be assigned as a small-group project.
      • Chapter 5: The Case of the Body Bag


• Use Technology for Developing Concepts and Analyzing Data - Technology allows us to explore statistical ideas in new and exciting ways.  Graphing calculators and statistical software packages can be used to explore “what if” scenarios.  Doing so helps to develop the students' understanding of statistical concepts.  Each example is presented using computation “by hand”.  When appropriate, the results for the same example are obtained using a graphing calculator or software.

    • Exercise 24 (Section 4.1) asks the student to determine the impact of removing an observation from a data set.  This problem foreshadows the idea of influential observations and is done easily with the help of technology.
    • Steps for obtaining output using the graphing calculator, MINITAB and Excel are included at the ends of section: Technology Step-by-Step.
    • Output is included, where appropriate, so students get used to "eyeballing" different statistical packages.
      • Pg. 114: MINITAB
      • Pg. 115: TI-Calculator


• Use Assessments to Improve and Evaluate Student Learning - The exercises at the end of each section are divided into three categories, all oriented towards helping student master concepts and gain a deeper statistical literacy.

    • The Concepts and Vocabulary exercises are fill-in-the-blank, and open-ended questions that assess students' understanding of vocabulary and statistical concepts.
    • The SkillBuilding exercises can be thought of as “drill and practice” problems that allow students to develop a level of comfort with the formulas and procedures in the section.
    • The Applying the Concepts exercises are based in real data that ask a variety of questions to help develop statistical thinking.  While these exercises  do ask the standard questions, such as finding the mean, they also ask the student to explain the results or to respond to a variety of “what if” questions that broaden the scope of the concept and the analysis.


CD Contents:

·  Case Studies  

  • Case Study: Chrysalises for Cash - chapter 1
  • Case Study: The Day the Sky Roared - chapter 2
  • Case Study: Who Was 'A Mourner'? - chapter 3
  • Case Study: Thomas Malthus, Population, and Subsistence - chapter 4
  • Case Study: The Case of the Body in the Bag - chapter 5
  • Case Study: The Voyage of the St. Andrew - chapter 6
  • Case Study: A Tale of Blood, Chemistry, and Health - chapter 7
  • Case Study: Sampling Distribution of the Median - chapter 8
  • Case Study: The Search for a Fire-Safe Cigarette - chapter 9
  • Case Study: How Old Is Stonehenge? - chapter 10
  • Case Study: Control in the Design of an Experiment - chapter 11
  • Case Study: Feeling Lucky? Well, Are You? - chapter 12

·  Additional Topics

  • C.1 Review of Lines
  • C.2 Confidence Intervals about a Population Standard Deviation
  • C.3 Testing Claims about the Population Standard Deviation
  • C.4 One-Way Analysis of Variance

·  Formula Cards

·  Data Sets

·  Applets

·  Graphing Calculator Links

New to this Edition

Content Changes

  • Over 45% new and updated exercises, with an emphasis on adding even greater variety, to give instructors an even larger range of exercises to choose from in selecting homework. The array of exercises includes many intriguing and meaningful topics, from M&Ms (always popular in statistics books) to the meaning of cholesterol counts, from identity theft to gas mileage, and from election results to cosmetic surgery. An interesting new exercise in chapter 3 based on an experiment by Trina McNamara of Joliet Junior College compares a name-brand chocolate-chip cookie with a store-brand chocolate-chip cookie-one of the many interesting data sets contributed by students to the textbook.
  • Over 60% new examples, most of which contain real world data, acting to further illustrate and reinforce concepts and techniques. Like the exercises, the choice of topics is practical, ranges widely, and will hold students' attention.
  • All sourced data have been updated and carefully selected to engage the students.
  • Each chapters open with a scenario, “Making an Informed Decision, that poses a question to the student and then, within the chapter, presents the content that is necessary to use statistics to make the Decision. This feature engages the student in the statistical-thinking process and highlights the practicality of statistics.
    • [See pg. 106 where the "Decision" is introduced, and pg. 164 where it is analyzed in detail.]
  • Using Technology examples show the way that software and calculators assist an analysis, once students have mastered “by hand” calculations. The Using Technology examples also give the students a feeling for statistics in practice, demonstrate when to rely on different devices and software, and show the output or screens to expect. 
    • See Example 5 (pg. 129), Obtaining the Standard Deviation [by Hand] and Example 6 (pg. 130), Determining the Variance and Standard Deviation Using Technology.
  • Section 4.1 on Correlation now has, at the request of reviewers, an optional objective which discusses checking the significance of the correlation coefficient.
  • Chapter 5 on probability has been revamped to ease the introduction of topics in probability. The early sections take greater care in delineating disjoint events and the complement rule. The concept of independence gets fuller coverage in this new edition, too.
    • To cater to different teaching styles, as much or as little (just section 5.1) probability can be covered.
  • Updated and rewritten Chapter 6 on discrete probability models addresses reviewers' concerns. Mike Sullivan focused especially on enhancing coverage of the binomial probability distribution. At the request of reviewers, the binomial tables have been added to the appendixes. 
  • New Chapter 8 on sampling distributions was added to strengthen the coverage of this important topic-which tends to cause students to stumble. The decision to give more play to sampling distributions by placing them in their own chapter was heartily endorsed by the reviewers of this new edition.
  • Chapters 9 and 10 continue to discuss confidence intervals and hypothesis testing about a mean by presenting the “s known use z, s unknown use t” approach. The author finds that students benefit from some discussion of confidence intervals and hypothesis testing when the population standard deviation is known, even if such situations seldom arise in practice. In both of these chapters, Mike Sullivan presents the sigma-known case as a pedagogical model or template, followed by sections on tests more likely to be used in practice.
  • Furthering comprehension of Confidence Intervals and Hypothesis Testing through new Putting It All Together sections in chapters 9 and 10.  These concepts are typically challenging for students and they have difficulty determining WHICH technique to apply.  These new sections require that students first determine the appropriate confidence interval or hypothesis test to conduct. This forces students to think about when each technique should be used, which is typically a stumbling block on exams.
    • Section 9.4 (Confidence Intervals)
    • Sectiono 10.5 (Hypothesis Testing)

Pedagogical Changes

  • New side-by-side presentation of hypothesis testing (chapter 10), which allows instructors the flexibility for presenting the classical approach, P-value approach, or both approaches. Recognizing that there are advocates of each of these two approaches, this format allows an instructor to choose the method that suits the philosophy of the course. [ See Example XXX]
  • Activities have been added to each chapter, giving instructors the flexibility to engage the class in an activity or assign them for homework.  There are approximately 2-3 activities per chapter. Use of activities promotes participation in the course by the students, makes concepts more vivid, and underscores the value of learning and using statistical techniques. [see Activity on Sample. Standard Deviation, pg. 129; Activity on Correlation, pg. 184; Activity on Expected Value, pg. 292).
  • More emphasis on statistical thinking and interpretation of results appears throughout the chapters. Mike Sullivan added more follow-up questions to exercises to require consideration and interpretation of what the students have calculated. Further, examples and exercises encourage the use of boxplots and normal probability plots so that students can use descriptive statistics throughout the text to interpret data and understand the workings of techniques. The author also redoubled his effort to include screen captures and computer printouts so that students will learn to “eyeball” and interpret results when using technology.
  • A division into parts makes the structure of the book more transparent to instructors and to the students. The parts show the student that the order of topics is logical and practical by following the statistical process.
  • MyStatLab, offering course management, online homework and tutorial and assessment, is fully integrated with the text.  Since 2001, over one million students have done better in math and statistics with  MyMathLab and MyStatLab!

Table of Contents

Part I: Getting the Information You Need

Chapter 1 Data Collection

1.1 Introduction to the Practice of Statistics

1.2 Observational Studies, Experiments, and Simple Random


1.3 Other Effective Sampling Methods

1.4 Sources of Error in Sampling

1.5 The Design of Experiments

Chapter Review

Case Study: Chrysalises for Cash (on CD)


Part II: Descriptive Statistics

Chapter 2 Organizing and Summarizing Data

2.1 Organizing Qualitative Data

2.2 Organizing Quantitative Data

2.3 Graphical Misrepresentations of Data

Chapter Review

Case Study: The Day the Sky Roared (on CD)


Chapter 3 Numerically Summarizing Data

3.1 Measures of Central Tendency

3.2 Measures of Dispersion

3.3 Measures of Central Tendency and Dispersion from Grouped


3.4 Measures of Position

3.5 The Five-Number Summary and Boxplots

Chapter Review

Case Study:Who Was 'A Mourner'? (on CD)


Chapter 4 Describing the Relation between Two Variables

4.1 Scatter Diagrams and Correlation

4.2 Least-Squares Regression

4.3 The Coefficient of Determination

Chapter Review

Case Study: Thomas Malthus, Population, and Subsistence (on CD)


Part III: Probability and Probability Distributions

Chapter 5 Probability

5.1 Probability Rules

5.2 The Addition Rule and Complements

5.3 Independence and the Multiplication Rule

5.4 Conditional Probability and the General Multiplication Rule

5.5 Counting Techniques

Chapter Review

Case Study: The Case of the Body in the Bag (on CD)


Chapter 6 Discrete Probability Distributions

6.1 Discrete Random Variables

6.2 The Binomial Probability Distribution

Chapter Review

Case Study: The Voyage of the St.Andrew (on CD)


Chapter 7 The Normal Probability Distribution

7.1 Properties of the Normal Distribution

7.2 The Standard Normal Distribution

7.3 Applications of the Normal Distribution

7.4 Assessing Normality

7.5 The Normal Approximation to the Binomial Probability Distribution

Chapter Review

Case Study: A Tale of Blood, Chemistry, and Health (on CD)


Putting It All Together: Probability


Part IV: Inference: From Samples to Population

Chapter 8 Sampling Distributions

8.1 Distribution of the Sample Mean

8.2 Distribution of the Sample Proportion

Chapter Review

Case Study: Sampling Distribution of the Median (on CD)


Chapter 9 Estimating the Value of a Parameter Using Confidence Intervals

9.1 The Logic in Constructing Confidence Intervals about a Population Mean Where the Population Standard Deviation is Known

9.2 Confidence Intervals about a Population Mean in Practice Where the Population Standard Deviation is Unknown

9.3 Confidence Intervals about a Population Proportion

9.4 Putting It All Together:Which Method Do I Use?

Chapter Review

Case Study: The Search for a Fire-Safe Cigarette (on CD)


Chapter 10 Testing Claims Regarding a Parameter

10.1 The Language of Hypothesis Testing

10.2 Testing Claims about a Population Mean Assuming the Population Standard Deviation Is Known

10.3 Testing Claims about a Population Mean in Practice

10.4 Testing Claims about a Population Proportion

10.5 Putting It All Together:Which Method Do I Use?

Chapter Review

Case Study: How Old Is Stonehenge? (on CD)


Chapter 11 Inference on Two Samples

11.1 Inference about Two Means: Dependent Samples

11.2 Inference about Two Means: Independent Samples

11.3 Inference about Two Population Proportions

11.4 Putting It All Together: Which Method Do I Use?

Chapter Review

Case Study: Control in the Design of an Experiment (on CD)


Chapter 12 Additional Inferential Procedures

12.1 Goodness of Fit Test

12.2 Tests for Independence and the Homogeneity of Proportions

12.3 Testing the Significance of the Least-Squares Regression Model

12.4 Confidence and Prediction Intervals

Chapter Review

Case Study: Feeling Lucky? Well, Are You? (on CD)


Additional Topics on CD

C.1 Review of Lines

C.2 Confidence Intervals about a Population Standard Deviation

C.3 Testing Claims about the Population Standard Deviation

C.4 One-Way Analysis of Variance


Appendix A Tables





Michael Sullivan III is a Professor of mathematics at Joliet Junior College.  He holds graduate degrees from DePaul University in both mathematics and economics.  Mike is a very successful textbook author, having co-authored the following texts

  • Precalculus Enhanced with Graphing Utilities 4e (CR 2006)
  • College Algebra Enhanced with Graphing Utilities 4e (CR2006)
  • Algebra and Trigonometry Enhanced with Graphing Utilities 4e (CR2006)


His time in the classroom and extensive authoring experience has given him an excellent foundation to write a successful introductory Statistics text: Statistics: Informed Decisions Using Data 2e (2007) and a briefer version of this text, Fundamentals of Statistics, 1/e (2005).


Because Mike's passion is making math more exciting and accessible to students, he is coauthoring a developmental math series for Prentice Hall that will be published in 2007. These titles will include:

  • Elementary Algebra (CR2007)
  • Intermediate Algebra (CR2007)
  • Elementary and Intermediate Algebra (CR2007)


Mike is the proud father of three children and when he isn't teaching or writing, he can be found coaching his children's baseball and soccer teams.