Applied statistical inference with MINITAB

497 Pages·2019·29.822 MB·English

by  Lesik, Sally A

Applied Statistical Inference
with MINITAB®

Applied Statistical Inference
with MINITAB®
Second  Edition
Sally A. Lesik
Central Connecticut State University
CRC Press
Taylor & Francis Group
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Contents
Preface ...........................................................................................................................................xiii
Acknowledgments .....................................................................................................................xvii
1. Introduction .............................................................................................................................1
1.1 What is Statistics? ..........................................................................................................1
1.2 What This Book Is About .............................................................................................2
1.3 Summary Tables and Graphical Displays .................................................................2
1.4 Descriptive Representations of Data ..........................................................................3
1.5 Inferential Statistics ......................................................................................................4
1.6 Populations ....................................................................................................................5
1.7 Different Ways of Collecting Data ..............................................................................5
1.8 Types of Variables .........................................................................................................6
1.9 Scales of Variables .........................................................................................................7
1.10 Types of Analyses .........................................................................................................9
1.11 Entering Data into Minitab ........................................................................................10
1.12 Best Practices ...............................................................................................................11
Exercises ..................................................................................................................................12
2. Graphs and Charts ...............................................................................................................15
2.1 Introduction .................................................................................................................15
2.2 Frequency Distributions and Histograms ...............................................................15
2.3 Using Minitab to Create Histograms .......................................................................17
2.4 Stem-and-Leaf Plots ....................................................................................................21
2.5 Using Minitab to Create Stem-and-Leaf Plots ........................................................22
2.6 Bar Charts ....................................................................................................................24
2.7 Using Minitab to Create a Bar Chart ........................................................................24
2.8 Boxplots ........................................................................................................................27
2.9 Using Minitab to Create Boxplots .............................................................................31
2.10 Scatterplots ...................................................................................................................32
2.11 Using Minitab to Create Scatterplots .......................................................................33
2.12 Marginal Plots .............................................................................................................33
2.13 Using Minitab to Create Marginal Plots ..................................................................35
2.14 Matrix Plots ..................................................................................................................36
2.15 Using Minitab to Create a Matrix Plot .....................................................................38
2.16 Best Practices ...............................................................................................................38
Exercises ..................................................................................................................................41
Extending the Ideas ...............................................................................................................44
3. Descriptive Representations of Data and Random Variables .....................................47
3.1 Introduction .................................................................................................................47
3.2 Descriptive Statistics ...................................................................................................47
3.3 Measures of Central Tendency ..................................................................................48
3.4 Measures of Variability ..............................................................................................52
3.5 Using Minitab to Calculate Descriptive Statistics ..................................................55
vii
viii Contents
3.6 More on Statistical Inference .....................................................................................56
3.7 Discrete Random Variables .......................................................................................58
3.8 Sampling Distributions ..............................................................................................61
3.9 Continuous Random Variables .................................................................................64
3.10 Standard Normal Distribution ..................................................................................65
3.11 Non-Standard Normal Distributions .......................................................................69
3.12 Other Discrete and Continuous Probability Distributions ...................................73
3.13 The Binomial Distribution .........................................................................................74
3.14 The Poisson Distribution ...........................................................................................75
3.15 The t-Distribution........................................................................................................77
3.16 The Chi-Square Distribution .....................................................................................78
3.17 The F-Distribution .......................................................................................................79
3.18 Using Minitab to Graph Probability Distributions ................................................79
Exercises ..................................................................................................................................85
4. Statistical Inference for One Sample ................................................................................93
4.1 Introduction .................................................................................................................93
4.2 Confidence Intervals ...................................................................................................93
4.3 Using Minitab to Calculate Confidence Intervals for a Population Mean ..........99
4.4 Hypothesis Testing: A One-Sample t-Test for a Population Mean .....................100
4.5 Using Minitab for a One-Sample t-Test ..................................................................106
4.6 Power Analysis for a One-Sample t-Test ................................................................115
4.7 Using Minitab for a Power Analysis for a One-Sample t-Test ............................116
4.8 Confidence Intervals and Hypothesis Tests for One Proportion .......................120
4.9 Using Minitab for a One-Sample Proportion ........................................................124
4.10 Power Analysis for a One-Sample Proportion ......................................................127
4.11 Confidence Intervals and Hypothesis Tests for One-Sample Variance ............129
4.12 Confidence Intervals for One-Sample Variance ...................................................130
4.13 Hypothesis Tests for One-Sample Variance ..........................................................132
4.14 Using Minitab for One-Sample Variance ..............................................................134
4.15 Power Analysis for One-Sample Variance .............................................................136
4.16 Confidence Intervals for One-Sample Count Data...............................................140
4.17 Using Minitab to Calculate Confidence Intervals for a One-Sample
Count Variable ...........................................................................................................142
4.18 Hypothesis Test for a One-Sample Count Variable ..............................................144
4.19 Using Minitab to Conduct a Hypothesis Test for a One-Sample Count
Variable .......................................................................................................................146
4.20 Using Minitab for a Power Analysis for a One-Sample Poisson ........................147
4.21 A Note About One- and Two-Tailed Hypothesis Tests .......................................149
Exercises ................................................................................................................................151
References .............................................................................................................................155
5. Statistical Inference for Two-Sample Data ...................................................................157
5.1 Introduction ...............................................................................................................157
5.2 Confidence Interval for the Difference Between Two Means .............................157
5.3 Using Minitab to Calculate a Confidence Interval for the Difference
Between Two Means .................................................................................................160
5.4 Hypothesis Tests for the Difference Between Two Means ..................................162
5.5 Using Minitab to Test the Difference Between Two Means ................................166
Contents ix
5.6 Using Minitab to Create an Interval Plot ...............................................................167
5.7 Using Minitab for a Power Analysis for a Two-Sample t-Test ............................170
5.8 Paired Confidence Interval and t-Test ....................................................................172
5.9 Using Minitab for a Paired Confidence Interval and t-Test ................................176
5.10 Differences Between Two Proportions ..................................................................178
5.11 Using Minitab for Two-Sample Proportion Confidence Intervals and
Hypothesis Tests .......................................................................................................182
5.12 Power Analysis for a Two-Sample Proportion ......................................................184
5.13 Confidence Intervals and Hypothesis Tests for Two Variances .........................184
5.14 Using Minitab for Testing Two Sample Variances ...............................................191
5.15 Power Analysis for Two-Sample Variances ...........................................................193
5.16 Confidence Intervals and Hypothesis Tests for Two-Count Variables .............195
5.17 Using Minitab for a Two-Sample Poisson .............................................................198
5.18 Power Analysis for a Two-Sample Poisson Rate ...................................................199
5.19 Best Practices .............................................................................................................201
Exercises ................................................................................................................................203
6. Simple Linear Regression .................................................................................................213
6.1 Introduction ...............................................................................................................213
6.2 The Simple Linear Regression Model ....................................................................214
6.3 Model Assumptions for Simple Linear Regression .............................................220
6.4 Finding the Equation of the Line of Best Fit .........................................................221
6.5 Using Minitab for Simple Linear Regression ........................................................224
6.6 Standard Errors for Estimated Regression Parameters .......................................227
6.7 Inferences about the Population Regression Parameters ....................................227
6.8 Using Minitab to Test the Population Slope Parameter .......................................230
6.9 Confidence Intervals for the Mean Response for a Specific Value of the
Predictor Variable ......................................................................................................232
6.10 Prediction Intervals for a Response for a Specific Value of the
Predictor Variable ......................................................................................................233
6.11 Using Minitab to Find Confidence and Prediction Intervals .............................235
Exercises ................................................................................................................................242
7. More on Simple Linear Regression .................................................................................247
7.1 Introduction ...............................................................................................................247
7.2 The Coefficient of Determination ...........................................................................247
7.3 Using Minitab to Find the Coefficient of Determination ....................................249
7.4 The Coefficient of Correlation .................................................................................250
7.5 Correlation Inference ................................................................................................254
7.6 Using Minitab for Correlation Analysis ................................................................257
7.7 Assessing Linear Regression Model Assumptions ..............................................259
7.8 Using Minitab to Create Exploratory Plots of Residuals .....................................259
7.9 A Formal Test of the Normality Assumption .......................................................264
7.10 Using Minitab for the Ryan–Joiner Test.................................................................266
7.11 Assessing Outliers ....................................................................................................268
7.12 Assessing Outliers: Leverage Values ......................................................................269
7.13 Using Minitab to Calculate Leverage Values ........................................................269
7.14 Assessing Outliers: Standardized Residuals ........................................................272
7.15 Using Minitab to Calculate Standardized Residuals ...........................................273