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Introduction: An Invitation to Statistics | 1 | |

The Population and the Sample | 2 | |

Descriptive and Inferential Statistics | 3 | |

Achieving the Objective of Inferential Statistics: The Necessary Steps | 4 | |

1 | Describing Data with Graphs | 7 |

1.1 | Variables and Data | 8 |

1.2 | Types of Variables | 9 |

1.3 | Graphs for Categorical Data | 11 |

1.4 | Graphs for Quantitative Data | 17 |

1.5 | Relative Frequency Histograms | 23 |

2 | Describing Data with Numerical Measures | 50 |

2.1 | Describing a Set of Data with Numerical Measures | 51 |

2.2 | Measures of Center | 51 |

2.3 | Measures of Variability | 57 |

2.4 | On the Practical Significance of the Standard Deviation | 63 |

2.5 | A Check on the Calculation of s | 67 |

2.6 | Measures of Relative Standing | 73 |

2.7 | The Five-Number Summary and the Box Plot | 76 |

3 | Describing Bivariate Data | 93 |

3.1 | Bivariate Data | 94 |

3.2 | Graphs for Qualitative Variables | 94 |

3.3 | Scatterplots for Two Quantitative Variables | 98 |

3.4 | Numerical Measures for Quantitative Bivariate Data | 100 |

4 | Probability and Probability Distributions | 119 |

4.1 | The Role of Probability in Statistics | 120 |

4.2 | Events and the Sample Space | 120 |

4.3 | Calculating Probabilities Using Simple Events | 123 |

4.4 | Useful Counting Rules (Optional) | 129 |

4.5 | Event Relations and Probability Rules | 136 |

4.6 | Conditional Probability, Independence, and the Multiplicative Rule | 140 |

4.7 | Bayes’ Rule (Optional) | 149 |

4.8 | Discrete Random Variables and Their Probability Distributions | 154 |

5 | Several Useful Discrete Distributions | 174 |

5.1 | Introduction | 175 |

5.2 | The Binomial Probability Distribution | 175 |

5.3 | The Poisson Probability Distribution | 187 |

5.4 | The Hypergeometric Probability Distribution | 191 |

6 | The Normal Probability Distribution | 205 |

6.1 | Probability Distributions for Continuous Random Variables | 206 |

6.2 | The Normal Probability Distribution | 208 |

6.3 | Tabulated Areas of the Normal Probability Distribution | 210 |

6.4 | The Normal Approximation to the Binomial Probability Distribution (Optional) | 220 |

7 | Sampling Distributions | 236 |

7.1 | Introduction | 237 |

7.2 | Sampling Plans and Experimental Designs | 237 |

7.3 | Statistics and Sampling Distributions | 241 |

7.4 | The Central Limit Theorem | 243 |

7.5 | The Sampling Distribution of the Sample Mean | 247 |

7.6 | The Sampling Distribution of the Sample Proportion | 253 |

7.7 | A Sampling Application: Statistical Process Control (Optional) | 258 |

8 | Large-Sample Estimation | 274 |

8.1 | Where We’ve Been | 275 |

8.2 | Where We’re Going–Statistical Inference | 275 |

8.3 | Types of Estimators | 276 |

8.4 | Point Estimation | 277 |

8.5 | Interval Estimation | 284 |

8.6 | Estimating the Difference between Two Population Means | 294 |

8.7 | Estimating the Difference between Two Binomial Proportions | 299 |

8.8 | One-Sided Confidence Bounds | 303 |

8.9 | Choosing the Sample Size | 305 |

9 | Large-Sample Tests of Hypotheses | 320 |

9.1 | Testing Hypotheses about Population Parameters | 321 |

9.2 | A Statistical Test of Hypothesis | 321 |

9.3 | A Large-Sample Test about a Population Mean | 324 |

9.4 | A Large-Sample Test of Hypothesis for the Difference between Two Population Means | 337 |

9.5 | A Large-Sample Test of Hypothesis for a Binomial Proportion | 343 |

9.6 | A Large-Sample Test of Hypothesis for the Difference between Two Binomial Proportions | 348 |

9.7 | Some Comments on Testing Hypotheses | 353 |

10 | Inference from Small Samples | 362 |

10.1 | Introduction | 363 |

10.2 | Student’s t Distribution | 363 |

10.3 | Small-Sample Inferences Concerning a Population Mean | 367 |

10.4 | Small-Sample Inferences for the Difference between Two Population Means: Independent Random Samples | 375 |

10.5 | Small-Sample Inferences for the Difference between Two Means: A Paired-Difference Test | 386 |

10.6 | Inferences Concerning a Population Variance | 394 |

10.7 | Comparing Two Population Variances | 401 |

10.8 | Revisiting the Small-Sample Assumptions | 409 |

11 | The Analysis of Variance | 426 |

11.1 | The Design of an Experiment | 427 |

11.2 | What Is an Analysis of Variance? | 428 |

11.3 | The Assumptions for an Analysis of Variance | 428 |

11.4 | The Completely Randomized Design: A One-Way Classification | 429 |

11.5 | The Analysis of Variance for a Completely Randomized Design | 430 |

11.6 | Ranking Population Means | 442 |

11.7 | The Randomized Block Design: A Two-Way Classification | 445 |

11.8 | The Analysis of Variance for a Randomized Block Design | 446 |

11.9 | The a x b Factorial Experiment: A Two-Way Classification | 458 |

11.10 | The Analysis of Variance for an a x b Factorial Experiment | 459 |

11.11 | Revisiting the Analysis of Variance Assumptions | 467 |

11.12 | A Brief Summary | 470 |

12 | Linear Regression and Correlation | 483 |

12.1 | Introduction | 484 |

12.2 | A Simple Linear Probabilistic Model | 484 |

12.3 | The Method of Least Squares | 486 |

12.4 | An Analysis of Variance for Linear Regression | 489 |

12.5 | Testing the Usefulness of the Linear Regression Model | 494 |

12.6 | Diagnostic Tools for Checking the Regression Assumptions | 502 |

12.7 | Estimation and Prediction Using the Fitted Line | 506 |

12.8 | Correlation Analysis | 513 |

13 | Multiple Regression Analysis | 532 |

13.1 | Introduction | 533 |

13.2 | The Multiple Regression Model | 533 |

13.3 | A Multiple Regression Analysis | 534 |

13.4 | A Polynomial Regression Model | 540 |

13.5 | Using Quantitative and Qualitative Predictor Variables in a Regression Model | 548 |

13.6 | Testing Sets of Regression Coefficients | 556 |

13.7 | Interpreting Residual Plots | 559 |

13.8 | Stepwise Regression Analysis | 560 |

13.9 | Misinterpreting a Regression Analysis | 561 |

13.10 | Steps to Follow When Building a Multiple Regression Model | 563 |

14 | Analysis of Categorical Data | 575 |

14.1 | A Description of the Experiment | 576 |

14.2 | Pearson’s Chi-Square Statistic | 577 |

14.3 | Testing Specified Cell Probabilities: The Goodness-of-Fit Test | 578 |

14.4 | Contingency Tables: A Two-Way Classification | 582 |

14.5 | Comparing Several Multinomial Populations: A Two-Way Classification with Fixed Row or Column Totals | 590 |

14.6 | The Equivalence of Statistical Tests | 594 |

14.7 | Other Applications of the Chi-Square Test | 595 |

15 | Nonparametric Statistics | 610 |

15.1 | Introduction | 611 |

15.2 | The Wilcoxon Rank Sum Test: Independent Random Samples | 611 |

15.3 | The Sign Test for a Paired Experiment | 620 |

15.4 | A Comparison of Statistical Tests | 625 |

15.5 | The Wilcoxon Signed-Rank Test for a Paired Experiment | 626 |

15.6 | The Kruskal-Wallis H Test for Completely Randomized Designs | 632 |

15.7 | The Friedman F[subscript r] Test for Randomized Block Designs | 638 |

15.8 | Rank Correlation Coefficient | 643 |

15.9 | Summary | 650 |

Appendix I | 663 | |

Table 1 | Cumulative Binomial Probabilities | 664 |

Table 2 | Cumulative Poisson Probabilities | 670 |

Table 3 | Areas under the Normal Curve | 672 |

Table 4 | Critical Values of t | 675 |

Table 5 | Critical Values of Chi-Square | 676 |

Table 6 | Percentage Points of the F Distribution | 678 |

Table 7 | Critical Values of T for the Wilcoxon Rank Sum Test, n[subscript 1] [less than or equal] n[subscript 2] | 686 |

Table 8 | Critical Values of T for the Wilcoxon Signed-Rank Test, n = 5(1)50 | 688 |

Table 9 | Critical Values of Spearman’s Rank Correlation Coefficient for a One-Tailed Test | 689 |

Table 10 | Random Numbers | 690 |

Table 11 | Percentage Points of the Studentized Range, q[subscript [alpha](k, df) | 692 |

Answers to Selected Exercises | 696 | |

Index |