Introductory Statistics

913 Pages·2013·25.34 MB·English

by  OpenStax College, Barbara Illowsky, Susan Dean

Introductory Statistics

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BARBARA ILLOWSKY, DE ANZA COLLEGE
SUSAN DEAN, DE ANZA COLLEGE
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Table of Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Chapter1: Sampling and Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.1 Definitions of Statistics, Probability, and Key Terms . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Data, Sampling, and Variation in Data and Sampling . . . . . . . . . . . . . . . . . . . . . 10
1.3 Frequency, Frequency Tables, and Levels of Measurement . . . . . . . . . . . . . . . . . . 26
1.4 Experimental Design and Ethics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
1.5 Data Collection Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
1.6 Sampling Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Chapter2: Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
2.1 Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs . . . . . . . . . . . . . . 68
2.2 Histograms, Frequency Polygons, and Time Series Graphs . . . . . . . . . . . . . . . . . . 77
2.3 Measures of the Location of the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
2.4 Box Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
2.5 Measures of the Center of the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
2.6 Skewness and the Mean, Median, and Mode . . . . . . . . . . . . . . . . . . . . . . . . . 106
2.7 Measures of the Spread of the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
2.8 Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
Chapter3: Probability Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
3.1 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
3.2 Independent and Mutually Exclusive Events . . . . . . . . . . . . . . . . . . . . . . . . . . 181
3.3 Two Basic Rules of Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
3.4 Contingency Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
3.5 Tree and Venn Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
3.6 Probability Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
Chapter4: Discrete Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
4.1 Probability Distribution Function (PDF) for a Discrete Random Variable . . . . . . . . . . . 244
4.2 Mean or Expected Value and Standard Deviation . . . . . . . . . . . . . . . . . . . . . . . 247
4.3 Binomial Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
4.4 Geometric Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
4.5 Hypergeometric Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
4.6 Poisson Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266
4.7 Discrete Distribution (Playing Card Experiment) . . . . . . . . . . . . . . . . . . . . . . . . 271
4.8 Discrete Distribution (Lucky Dice Experiment) . . . . . . . . . . . . . . . . . . . . . . . . . 274
Chapter5: Continuous Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
5.1 Continuous Probability Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313
5.2 The Uniform Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316
5.3 The Exponential Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326
5.4 Continuous Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338
Chapter6: The Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365
6.1 The Standard Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366
6.2 Using the Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371
6.3 Normal Distribution (Lap Times) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379
6.4 Normal Distribution (Pinkie Length) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381
Chapter7: The Central Limit Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399
7.1 The Central Limit Theorem for Sample Means (Averages) . . . . . . . . . . . . . . . . . . 400
7.2 The Central Limit Theorem for Sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
7.3 Using the Central Limit Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408
7.4 Central Limit Theorem (Pocket Change) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417
7.5 Central Limit Theorem (Cookie Recipes) . . . . . . . . . . . . . . . . . . . . . . . . . . . 420
Chapter8: Confidence Intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443
8.1 A Single Population Mean using the Normal Distribution . . . . . . . . . . . . . . . . . . . 445
8.2 A Single Population Mean using the Student t Distribution . . . . . . . . . . . . . . . . . . 456
8.3 A Population Proportion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460
8.4 Confidence Interval (Home Costs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467
8.5 Confidence Interval (Place of Birth) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469
8.6 Confidence Interval (Women's Heights) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471
Chapter9: Hypothesis Testing with One Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . 505
9.1 Null and Alternative Hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506
9.2 Outcomes and the Type I and Type II Errors . . . . . . . . . . . . . . . . . . . . . . . . . . 508
9.3 Distribution Needed for Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . 510
9.4 Rare Events, the Sample, Decision and Conclusion . . . . . . . . . . . . . . . . . . . . . . 511
9.5 Additional Information and Full Hypothesis Test Examples . . . . . . . . . . . . . . . . . . 514
9.6 Hypothesis Testing of a Single Mean and Single Proportion . . . . . . . . . . . . . . . . . . 530
Chapter10: Hypothesis Testing with Two Samples . . . . . . . . . . . . . . . . . . . . . . . . . 567
10.1 Two Population Means with Unknown Standard Deviations . . . . . . . . . . . . . . . . . 568
10.2 Two Population Means with Known Standard Deviations . . . . . . . . . . . . . . . . . . 576
10.3 Comparing Two Independent Population Proportions . . . . . . . . . . . . . . . . . . . . 579
10.4 Matched or Paired Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584
10.5 Hypothesis Testing for Two Means and Two Proportions . . . . . . . . . . . . . . . . . . . 590
Chapter11: The Chi-Square Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 621
11.1 Facts About the Chi-Square Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 622
11.2 Goodness-of-Fit Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623
11.3 Test of Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633
11.4 Test for Homogeneity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 638
11.5 Comparison of the Chi-Square Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 641
11.6 Test of a Single Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 641
11.7 Lab 1: Chi-Square Goodness-of-Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644
11.8 Lab 2: Chi-Square Test of Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . 648
Chapter12: Linear Regression and Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . 679
12.1 Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 680
12.2 Scatter Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 682
12.3 The Regression Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685
12.4 Testing the Significance of the Correlation Coefficient . . . . . . . . . . . . . . . . . . . . 691
12.5 Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 696
12.6 Outliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 697
12.7 Regression (Distance from School) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 704
12.8 Regression (Textbook Cost) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 706
12.9 Regression (Fuel Efficiency) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 708
Chapter13: F Distribution and One-Way ANOVA . . . . . . . . . . . . . . . . . . . . . . . . . . . 743
13.1 One-Way ANOVA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 744
13.2 The F Distribution and the F-Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 745
13.3 Facts About the F Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 749
13.4 Test of Two Variances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 756
13.5 Lab: One-Way ANOVA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 759
AppendixA:Review Exercises (Ch 3-13) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 785
AppendixB:Practice Tests (1-4) and Final Exams . . . . . . . . . . . . . . . . . . . . . . . . . . 813
AppendixC:Data Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 869
AppendixD:Group and Partner Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 873
AppendixE:Solution Sheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 879
AppendixF:Mathematical Phrases, Symbols, and Formulas . . . . . . . . . . . . . . . . . . . . 883
AppendixG:Notes for the TI-83, 83+, 84, 84+ Calculators . . . . . . . . . . . . . . . . . . . . . . 889
AppendixH:Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 901
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 903
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Preface 1
PREFACE
Welcome to Introductory Statistics, an OpenStax resource. This textbook was written to increase student access to high-
quality learning materials, maintaining highest standards of academic rigor at little to no cost.
The foundation of this textbook is Collaborative Statistics, by Barbara Illowsky and Susan Dean. Additional topics,
examples,andinnovationsinterminologyandpracticalapplicationshavebeenadded,allwithagoalofincreasingrelevance
and accessibility for students.
About OpenStax
OpenStax is a nonprofit based at Rice University, and it’s our mission to improve student access to education. Our first
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About OpenStax's resources
Customization
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Because our books are openly licensed, you are free to use the entire book or pick and choose the sections that are most
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InstructorsalsohavetheoptionofcreatingacustomizedversionoftheirOpenStaxbook.Thecustomversioncanbemade
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Format
YoucanaccessthistextbookforfreeinwebvieworPDFthroughOpenStax.org,andinlow-costprintandiBookseditions.
Coverage and scope
Chapter 1 Sampling and Data
Chapter 2 Descriptive Statistics
Chapter 3 Probability Topics
Chapter 4 Discrete Random Variables
Chapter 5 Continuous Random Variables
Chapter 6 The Normal Distribution
Chapter 7 The Central Limit Theorem
Chapter 8 Confidence Intervals
Chapter 9 Hypothesis Testing with One Sample
Chapter 10 Hypothesis Testing with Two Samples
Chapter 11 The Chi-Square Distribution
Chapter 12 Linear Regression and Correlation
Chapter 13 F Distribution and One-Way ANOVA
2 Preface
Alternate sequencing
Introductory Statistics was conceived and written to fit a particular topical sequence, but it can be used flexibly to
accommodate othercoursestructures. Onesuchpotential structure, whichfitsreasonably wellwiththetextbookcontent,
isprovidedbelow.Pleaseconsider,however,thatthechapterswerenotwrittentobecompletelyindependent,andthatthe
proposed alternate sequence should be carefully considered for student preparation and textual consistency.
Chapter 1 Sampling and Data
Chapter 2 Descriptive Statistics
Chapter 12 Linear Regression and Correlation
Chapter 3 Probability Topics
Chapter 4 Discrete Random Variables
Chapter 5 Continuous Random Variables
Chapter 6 The Normal Distribution
Chapter 7 The Central Limit Theorem
Chapter 8 Confidence Intervals
Chapter 9 Hypothesis Testing with One Sample
Chapter 10 Hypothesis Testing with Two Samples
Chapter 11 The Chi-Square Distribution
Chapter 13 F Distribution and One-Way ANOVA
Pedagogical foundation and features
• Examples are placed strategically throughout the text to show students the step-by-step process of interpreting and
solving statistical problems. To keep the text relevant for students, the examples are drawn from a broad spectrum
ofpracticaltopics,includingexamplesaboutcollegelifeandlearning,healthandmedicine,retailandbusiness,and
sports and entertainment.
• TryItpracticeproblemsimmediatelyfollowmanyexamplesandgivestudentstheopportunitytopracticeastheyread
the text.They are usually based on practical and familiar topics, like the Examples themselves.
• Collaborative Exercisesprovide an in-class scenario for students to work together to explore presented concepts.
• Using the TI-83, 83+, 84, 84+ Calculator shows students step-by-step instructions to input problems into their
calculator.
• The Technology Iconindicates where the use of a TI calculator or computer software is recommended.
• Practice,Homework,andBringingItTogetherproblemsgivethestudentsproblemsatvariousdegreesofdifficulty
while also including real-world scenarios to engage students.
Statistics labs
TheseinnovativeactivitiesweredevelopedbyBarbaraIllowskyandSusanDeaninordertoofferstudentstheexperienceof
designing,implementing,andinterpretingstatisticalanalyses.Theyaredrawnfromactualexperimentsanddata-gathering
processesandofferauniquehands-onandcollaborativeexperience.Thelabsprovideafoundationforfurtherlearningand
classroom interaction that will produce a meaningful application of statistics.
StatisticsLabsappearattheendofeachchapterandbeginwithstudentlearningoutcomes,generalestimatesfortimeon
task,andanyglobalimplementation notes.Studentsarethenprovidedwithstep-by-stepguidance,includingsampledata
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lay the groundwork for future collaborative or individual work.
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