Investigating Statistical Concepts, Applications, and Methods

Table of Contents

Chapter 1: Comparisons and Conclusions

Section 1-1: Summarizing Categorical Data

Investigation 1-1: Popcorn and Lung Disease – Two-way tables, bar graphs p. 2

Practice problems 1-1, 1-2, 1-3 p. 9

Section 1-2: Analyzing Categorical Data

Investigation 1-2: Smoking and Lung Cancer - RR vs. OR, when can use p. 11

Practice problem 1-4 p. 19

Investigation 1-3: Smoking and Lung Cancer - Association, Independence p. 20

Excel Exploration p. 22

Practice problems 1-5, 1-6, 1-7 p. 25

Section 1-3: Confounding

Investigation 1-4: Near-sightedness and Night Lights – Confounding p. 27

Practice problems 1-8, 1-9 p. 30

Investigation 1-5: Graduate Admissions - Simpson’s Paradox p. 31

Practice problems 1-10, 1-11 p. 35

Section 1-4: Designing Experiments

Investigation 1-6: Foreign Language and SAT - Experiments p. 36

Investigation 1-7: Have a Nice Trip- Randomization p. 38

Practice problems 1-12, 1-13, 1-14, 1-15 p. 44

Investigation 1-8: Have a Nice Trip (optional) - Blocking p. 45

Practice problems 1-16, 1-17 p. 47

Section 1-5: Assessing Statistical Significance

Investigation 1-9: Friendly Observers - Simulation, Statistical significance p. 48

Practice problems 1-18, 1-19 p. 55

Brief Introduction to Minitab p. 56

Section 1-6: Probability and Counting Methods

Investigation 1-10: College Committee – Probability and Counting Methods p. 57

Investigation 1-11: Selecting Senators – Hypergeometric Distribution p. 65

Practice problems 1-20, 1-21 p. 69

Section 1-7: Fisher’s Exact Test

Investigation 1-12: Friendly Observers – Fisher’s Exact Test, sample size effects p. 71

Investigation 1-13: Minority Coaches – interpretation of p-values p. 76

Practice problems 1-22, 1-23, 1-24 p. 78

Summaries p. 79

Chapter 2: Comparisons with Quantitative Variables

Section 2-1: Summarizing Quantitative Data

Investigation 2-1: Anticipating Variable Behavior p. 82

Investigation 2-2: Cloud Seeding - dotplots, numerical summaries p. 85

Practice problems 2-1, 2-2 p. 95

Investigation 2-3: Geyser Eruptions - standard deviation, IQR, histograms p. 96

Investigation 2-4: Bumpiness, Variety, and Variability p. 101

Practice problems 2-3, 2-4, 2-5, 2-6 p. 103

Investigation 2-5: Body Temperatures – z-scores p. 105

Practice problems 2-7, 2-8 p. 109

Investigation 2-6: Fan Cost Index - resistance, percent change, rescaling p. 110

Practice problem 2-9 p. 115

Investigation 2-7: House Prices - minimization criteria, resistance p. 116

Practice problems 2-10, 2-11, 2-12 p. 122

Section 2-2: Statistical Significance

Investigation 2-8: Sleep Deprivation and Visual Learning - randomization test p. 123

Investigation 2-9: More on Sleep Deprivation p. 129

Investigation 2-10: Lifetimes of Notables - observational, stemplots p. 131

Practice problems 2-13, 2-14 p. 133

Summaries p. 134

Chapter 3: Sampling from Populations

Section 3-1: Selecting Samples from Populations I

Investigation 3-1: Sampling Words – bias, random samples, sampling variability p. 137

Practice problems 3-1, 3-2 p. 145

Investigation 3-2: Comparison Shopping - sampling plans p. 146

Practice problems 3-3, 3-4, 3-5 p. 149

Investigation 3-3: Sampling Variability of Sample Means p. 150

Practice problems 3-6, 3-7, 3-8 p. 154

Investigation 3-4: Sampling Variability of Sample Proportions p. 155

Practice problems 3-9, 3-10 p. 160

Investigation 3-5: Freshmen Voting Patterns – statistical inference p. 161

Practice problems 3-11, 3-12 p. 165

Investigation 3-6: Comparison of Sampling Methods (Minitab Exploration) p. 166

Section 3-2: Sampling from a Process

Investigation 3-7: Do Pets Look Like Their Owners? – Bernoulli process p. 167

Investigation 3-8: Pop Quiz! – binomial probability distribution p. 170

Practice problems 3-13, 3-14, 3-15 p. 177

Section 3-3: Exact Binomial Inference

Investigation 3-9: Water Oxygen Levels – hypotheses, p-value p. 178

Investigation 3-10: Heart Transplant Mortality – practice p. 182

Practice problems 3-16, 3-17, 3-18 p. 185

Investigation 3-11: Do Pets Look Like Their Owners? (cont.) – practice p. 187

Investigation 3-12: Halloween Treat Choices – symmetric two-sided p-value p. 189

Investigation 3-13: Kissing the Right Way - asymmetric two-sided p-values p. 192

Practice problems 3-19, 3-20, 3-21 p. 195

Investigation 3-14: Kissing the Right Way (cont.) - binomial confidence intervals p. 196

Practice problems 3-22, 3-23, 3-24 p. 200

Investigation 3-15: Improved Batting Averages – Type I and Type II Errors p. 201

Practice problems 3-25, 3-26 p. 209

Section 3-4: Sampling from a Population II

Investigation 3-16: Sampling Words (cont.) – Binomial approximation p. 210

Investigation 3-17: Feeling Good – Approximate binomial procedures p. 214

Practice problems 3-27, 3-28, 3-29 p. 216

Investigation 3-18: Long-term Effects of Agent Orange – Sign Test p. 218

Practice problems 3-30, 3-31 p. 220

Summaries p. 221

Chapter 4: Models and Sampling Distributions

Section 4-1: Models of quantitative data

Investigation 4-1: Pot Pourri – Models, Normal distribution p. 224

Practice problems 4-1, 4-2 p. 228

Investigation 4-2: Body Measurements – checking the normal model p. 229

Practice problems 4-3, 4-4 p. 233

Section 4-2: Applying the normal probability model

Investigation 4-3: Fuel Capacity – area under curve p. 234

Practice problems 4-5, 4-6, 4-7 p. 236

Investigation 4-4: Modeling Body Measurements p. 237

Investigation 4-5: Birth Weights – normal probability calculations p. 242

Practice problems 4-8, 4-9, 4-10 p. 246

Section 4-3: Distributions of sample counts and proportions

Investigation 4-6: Reese’s Pieces - Normal approximation to binomial p. 248

Probability Detour: mean and standard deviation of p. 252

Practice problems 4-11, 4-12, 4-13 p. 255

Investigation 4-7: Cohen v. Brown University – large sample z-test, test statistic p. 256

Investigation 4-8: Kissing the Right Way (cont.) – errors p. 261

Investigation 4-9: Cohen v. Brown University (cont.) – large sample z-interval p. 267

Practice problems 4-14, 4-15, 4-16, 4-17 p. 271

Investigation 4-10: Reese’s Pieces – meaning of confidence (applet exploration) p. 272

Investigation 4-11: Good News or Bad News First – Wilson adjustment p. 276

Practice problems 4-18, 4-19, 4-20, 4-21 p. 279

Section 4-4: Distributions of sample means

Investigation 4-12: Scottish Militiamen and American Moms – t distribution p. 280

Practice problems 4-22, 4-23 p. 293

Applet Explorations: Confidence and robustness p. 294

Investigation 4-13: Basketball Scoring – t test, prediction interval p. 295

Investigation 4-14: Comparison Shopping – paired p. 303

Practice problems 4-24, 4-25, 4-26 p. 306

Section 4-5: Bootstrapping

Investigation 4-15: Sampling Words (cont.) – Bootstrapping p. 307

Investigation 4-16: Comparison Shopping (cont.) – t vs. bootstrap p. 314

Investigation 4-17: Heroin treatment time – bootstrapping p. 315

Practice problems 4-27 p. 317

Summaries p. 318

Chapter 5: Comparing Two Populations

Section 5-1: Comparing two samples on a categorical response

Activity 5-1: Newspaper Credibility Decline - two proportion sampling distn p. 321

Activity 5-2: Newspaper Credibility Decline (cont.) - two-sample z-procedures p. 326

Practice problems 5-1, 5-2, 5-3 p. 331

Activity 5-3: Sleepless Drivers - CI for odds ratio p. 373

Practice problems 5-4, 5-5 p. 338

Section 5-2: Randomized experiments revisited

Activity 5-4: Letrozole and Breast Cancer - normal approximation for Fisher’s p. 339

Practice problems 5-6, 5-7 p. 344

Section 5-3: Comparing two samples on a quantitative response

Activity 5-5: NBA Salaries - two-sample t procedures (Minitab Exploration) p. 345

Probability Detour p. 349

Practice problems 5-8, 5-9 p. 350

Activity 5-6: Handedness and Life Expectancy - effect of sample size and SD p. 351

Practice problem 5-10 p. 355

Activity 5-7: Comparison Shopping (cont.) - two- vs. one-sample with paired data p. 356

Practice problems 5-11, 5-12, 5-13 p. 360

Section 5-4: Randomized experiments revisited

Activity 5-8: Sleep Deprivation (cont.)- t approximation p. 361

Practice problems 5-14, 5-15 p. 364

Section 5-5: Other statistics

Activity 5-9: Heart transplants and survival – bootstrapping p. 366

Practice problems 5-16, 5-17 p. 370

Chapter 6: Comparing Several Populations, Exploring Relationships

Section 6-1: Two Categorical Variables

Investigation 6-1: Dr. Spock’s Trial - Chi-Square test for homogeneity p. 374

Investigation 6-2: Near-Sightedness and Night Lights (cont.) – association p. 382

Investigation 6-3: Newspaper Credibility Decline (cont.) p. 386

Practice problems 6-1, 6-2, 6-3 p. 388

Section 6-2: Comparing Several Population Means

Investigation 6-4: Handicap Discrimination – reasoning of ANOVA p. 390

Investigation 6-5: Restaurant Spending and Music – ANOVA practice p. 398

Practice problems 6-4, 6-5 p. 401

Section 6-3: Relationships Between Quantitative Variables

Investigation 6-6: House Prices – scatterplots p. 402

Investigation 6-7: Drive for Show, Putt for Dough - correlation coefficients p. 404

Applet Exploration: Random Correlation Coefficients p. 410

Practice problems 6-6, 6-7 p. 412

Investigation 6-8: Height and Foot Size - least squares regression p. 413

Investigation 6-9: Money Making Movies - properties, coded scatterplots p. 421

Applet Exploration: Behavior of Regression Lines – resistance p. 424

Practice Problems 6-8, 6-9, 6-10 p. 425

Section 6-4: Inference for Regression

Investigation 6-10: Boys’ Heights – regression model p. 426

Investigation 6-11: House Prices (cont.) – transformation p. 430

Investigation 6-12: Hypothetical Housing Prices - sampling distributions p. 432

Investigation 6-13: House Price (cont.) – inference for regression p. 438

Minitab Exploration: The Regression Effect p. 442

Practice problems 6-11, 6-12, 6-13, 6-14 p. 441

Summaries p. 443