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I Introduction to Statistics 1
1.1 Introduction 1
What Is Statistics? 1
1.2 Why Sample? 8
Why Sample? 8
1.3 Sampling Techniques 10
Random or Probability Sampling Techniques 11
1.4 Uses of Statistics 16
1.5 Misuses of Statistics 18
Misleading Graphs 18
Non-Representative Samples 20
Inappropriate Comparisons 21
The Omission of Variation About an Average 21
1.6 Overview and Summary 21
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2 Organizing and Presenting Data 31
2.1 Introduction 31
2.2 Classifications of Data 33
Categorical and Numerical Variables 34
Continuous and Discrete Data 34
2.3 Exploring Data Using the Stem-and-Leaf Display 36
Back-to-Back Stem-and-Leaf Display 40
2.4 Frequency Distribution Tables 41
Frequency Distribution Table for Categorical Data 41
Frequency Distribution Table for Numerical Data 42
Relative Frequency Distributions 47
Cumulative Frequency Distributions 49
2.5 Graphs: Bar Graph, Histogram, Frequency Polygon and Ogive 52
Bar Graph 52
Histogram 54
Frequency Polygon and Ogive 61
2.6 Specialty Graphs: Pie Chart and Pictograph 65
2.7 Identifying Shapes and Interpreting Graphs 66
Shapes of Distributions 66
Interpreting Graphs 69
2.8 Using Technology 71
Graphing Calculator Display of a Histogram, Frequency Polygon and Ogive 73
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3 Numerical Techniques for Describing Data 85
3.1 Measures of Central Tendency 86
The Mean 86
Sample Mean 87
Population Mean 88
Other Calculations Using Σ 89
The Median 92
The Mode 95
The Relationship of the Mean, Median and Mode 98
The Mode and Its Location within the Distribution Shapes 99
The Median and Its Location within the Distribution Shapes 99
The Mean and Its Location within the Distribution Shapes 99
Symmetric Bell-Shaped Distribution 99
Skewed to the Left Distribution 100
Skewed to the Right Distribution 100
Comparing the Mean, the Median and the Mode 101
3.2 Measures of Variability 103
The Range 103
The Variance and Standard Deviation of a Sample 105
Interpretation of the Standard Deviation 108
The Variance and Standard Deviation of a Population 110
Using the Sample Standard Deviation to Estimate the Population Standard
Deviation 114
3.3 Applications of the Standard Deviation 115
Chebyshev’s Theorem 115
Empirical Rule 117
Using the Range to Obtain an Estimate of the Standard Deviation 118
3.4 Measures of Relative Standing 122
z Score 123
Detecting Outliers Using z Scores 126
Converting z Scores to Raw Scores 126
Percentile Rank and Percentiles 128
Deciles and Quartiles 130
3.5 Box-and-Whisker Plot: An Exploratory Data Analysis Technique 133
3.6 Using Technology 143
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4 Linear Correlation and Regression Analysis 169
4.1 Introduction 169
4.2 The Scatter Diagram 170
4.3 The Coefficient of Linear Correlation 177
Some Cautions Regarding the Interpretation of Correlation Results 181
4.4 More on the Relationship Between the Correlation Coefficient
and the Scatter Diagram 181
4.5 The Coefficient of Determination 182
4.6 Linear Regression Analysis 183
Interpolation versus Extrapolation 188
Regression Analysis Concept Revisited 190
4.7 Using Technology 193
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5 Probability 205
5.1 Introduction 205
The Birthday Problem 205
Chance! Chance! Chance! 206
5.2 Some Terms Used in Probability 206
Using a Tree Diagram to Construct a Sample Space 208
5.3 Permutations and Combinations 213
Permutation 213
Combination 219
Methods of Selection 223
Explaining the Difference Between the Idea of a Permutation
and a Combination 224
5.4 Probability 225
Alternate Approaches to Assigning a Probability 226
Another Approach to Defining Probability 231
Relative Frequency Concept of Probability or Posteriori Probability 231
Another Approach to Defining Probability 233
Subjective or Personal Probability 233
5.5 Fundamental Rules and Relationships of Probability 235
Probability Problems Using Permutations and Combinations 247
5.6 Conditional Probability 251
5.7 Using Technology 260
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6 Random Variables and Discrete Probability
Distributions 277
6.1 Introduction 277
6.2 Random Variables 278
6.3 Probability Distribution of a Discrete Random Variable 282
6.4 Mean and Standard Deviation of a Discrete Random Variable 288
The Mean Value of a Discrete Random Variable 288
The Variance and Standard Deviation of a Discrete Random Variable 292
6.5 Binomial Probability Distribution 299
Binomial Probability Formula 302
An Application of the Binomial Distribution: Acceptance Sampling 314
6.6 The Poisson Distribution 318
Shape of the Poisson Distribution 323
6.7 Using Technology 324
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7 Continuous Probability Distributions
and the Normal Distribution 341
7.1 Introduction 341
7.2 Continuous Probability Distributions 341
7.3 The Normal Distribution 346
7.4 Properties of a Normal Distribution 348
The Standard Normal Curve 350
7.5 Using the Normal Curve Area Table 353
Finding a z-score Knowing the Proportion of Area to the Left 366
7.6 Applications of the Normal Distribution 371
7.7 Percentiles and Applications of Percentiles 376
7.8 Probability Applications 387
7.9 The Normal Approximation to the Binomial Distribution 392
7.10 Using Technology 404
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8 Sampling and Sampling Distributions 421
8.1 The Sampling Distribution of the Mean 421
8.2 The Mean and Standard Deviation of the Sampling Distribution
of the Mean 429
Mean of the Sampling Distribution of the Mean 429
Standard Deviation of the Sampling Distribution of the Mean 429
Interpretation of the Standard Error of the Mean 432
8.3 The Finite Correction Factor 433
8.4 The Shape of the Sampling Distribution of the Mean 436
Sampling from a Normal Population 436
Sampling from a Non-Normal Population 439
The Central Limit Theorem 439
8.5 Calculating Probabilities Using the Sampling Distribution of the Mean 444
8.6 The Effect of Sample Size on the Standard Error of the Mean 450
8.7 The Sampling Distribution of the Proportion 452
Sampling Error of the Proportion 461
Interpretation of the Standard Error of the Proportion 462
Shape of the Sampling Distribution of the Proportion 462
Calculating Probabilities Using the Sampling Distribution
of the Proportion 464
8.8 Using Technology 468
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9 Estimation 481
9.1 Introduction 481
9.2 Point Estimate of the Population Mean and the Population Proportion 482
9.3 Interval Estimation 484
9.4 Interval Estimation: Confidence Intervals for the Population Mean 485
Constructing a Confidence Interval for a Population Mean: When the Population
Standard Deviation Is Unknown 493
The t Distribution 494
9.5 Interval Estimation: Confidence Intervals for the Population Proportion 500
9.6 Determining Sample Size and the Margin of Error 504
Sample Size for Estimating a Population Mean, μ 504
Sample Size for Estimating a Population Proportion, p 508
Summary of Confidence Intervals 513
9.7 Using Technology 513
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10 Introduction to Hypothesis Testing 523
10.1 Introduction 523
10.2 Hypothesis Testing 523
Null and Alternative Hypotheses 524
10.3 The Development of a Decision Rule 532
10.4 p-Values for Hypothesis Testing 547
Procedure to Calculate the p-Value of a Hypothesis Test 550
10.5 Using Technology 552
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11 Hypothesis Testing Involving One Population 563
11.1 Introduction 563
11.2 Hypothesis Testing Involving a Population Proportion 563
Hypothesis Testing Procedure Involving a Population Proportion 565
11.3 Hypothesis Testing Involving a Population Mean: Population Standard Deviation
Known 574
11.4 The t Distribution 579
Using Table III: Critical Value for the t Distribution 580
11.5 Hypothesis Testing Involving a Population Mean: Population Standard Deviation
Unknown 582
11.6 p-Value Approach to Hypothesis Testing Using the TI-84 Plus Calculator 591
11.7 Using Technology 598
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12 Hypothesis Testing Involving Two Population Proportions
Using Independent Samples 609
12.1 Introduction to Hypothesis Tests Involving a Difference Between Two Population
Proportions Using Independent Samples 609
12.2 The Sampling Distribution of the Difference Between Two Proportions 610
12.3 Hypothesis Testing Involving Two Population Proportions Using Large Samples 619
Hypothesis Testing Procedure Involving the Difference Between the Proportions
of Two Populations for Large Samples 619
12.4 Hypothesis Testing Involving Two Population Proportions Comparing
Treatment and Control Groups 630
12.5 p-Value Approach to Hypothesis Testing Involving Two Population Proportions
Using the TI-84 Calculator 636
12.6 Two Population Hypothesis Testing Summaries Using Independent Samples 640
12.7 Using Technology 642
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13 Hypothesis Test Involving Two Population Means
Using Independent Samples 657
13.1 Introduction 657
13.2 The Sampling Distribution of the Difference Between Two Means 657
13.3 Hypothesis Testing Involving Two Population Means and Unknown Population
Standard Deviations 660
Two Sample t Test 660
13.4 Hypothesis Tests Comparing Treatment and Control Groups 666
13.5 p-Value Approach to Hypothesis Testing Involving Two Population Means
Using the TI-84 Plus Calculator 672
13.6 Using Technology 677
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14 Chi-Square 687
14.1 Introduction 687
14.2 Properties of the Chi-Square Distribution 689
14.3 Chi-Square Hypothesis Test of Independence 690
14.4 Assumptions Underlying the Chi-Square Test 700
14.5 Test of Goodness-of-Fit 700
14.6 p-Value Approach to Chi-Square Hypothesis Test of Independence
Using the TI-84 Plus Calculator 707
14.7 Using Technology 712
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15 Inferences for Correlation and Regression 723
15.1 Introduction 723
15.2 Testing the Significance of the Correlation Coefficient 725
Procedure to Test the Significance of the Population Correlation
Coefficient, 725
15.3 Assumptions for Linear Regression Analysis 733
15.4 p-Value Approach to Testing the Significance of the Correlation Coefficient
Using the TI-84 Calculator 733
15.5 Introduction to Multiple Regression 738
15.6 Using Technology 745
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Answer Section 757
Appendices 791
A: Databases 792
B: Chapter Formulas 797
C: Summary of Hypothesis Tests 803
D: Statistical Tables 805
Index 811
16 The F-Distribution and An Introduction
to Analysis of Variance (ANOVA)
17 NonParametric Statistics
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