Statistical Thinking: Elementary Statistics
Edition: 3
Copyright: 2017
Edition: 3
Copyright: 2017
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This example-driven publication provides students with help understanding concepts and methodology with a goal of lessening the fear that statistics brings to many students - and even helping them to enjoy the subject. To accomplish this, the text is methodical, and offers more than one example per chapter. At the end of the analyses (which may involve calculation or computation), explanations are offered for the results. Traditional manual analysis is provided in order to lay basic foundations for understanding of the concepts. At the end of each chapter the use of technology is discussed, and quite a few examples of analyses using technology are presented. In fact, for some examples in which analyses were carried out manually, a technology approach using MINITAB is presented. The steps required to leverage technology for the analyses are presented as templates that can be used for similar problems the reader would encounter. In short, not just the output of computations, but also the code, is presented. There are also several exercise problems at the end of each chapter. Full-blown solutions showing steps that lead to the final results, as opposed to only answers, are presented for at least half of the ex- ercises. In addition, online exercise materials are presented. Most assignments and tests would be carried out online. Each purchaser of the text receives an access code that will enable them to access the online material.
CHAPTER 1 Elements of Sampling
1.0 Introduction
1.1 Data Collection by Sampling
1.1.1 Some Definitions
1.2 Some Unrecommended Sampling Methods
1.3 Probability Sampling Methods
1.3.1 Simple Random Sampling
1.3.2 Systematic Sampling
1.3.3 Cluster Sampling
1.3.4 Stratified Sampling
1.3.5 Multi-stage Sampling
EXERCISES
TABLE OF RANDOM DIGITS
CHAPTER 2 Basic Data Presentation and Analysis
2.0 Introduction
2.1 Presentation by Charts (Bar Charts and Pie Charts)
2.1.1 Pie Charts
2.1.2 Bar Charts (or Graphs)
2.2 Summarizing a Raw Numeric Data Set Pictorially
2.2.1 Using Minitab to Obtain an Array
2.2.2 Use of Minitab to Construct Stem-and-Leaf Plots
2.3 Grouping Data
2.3.1 Use of Minitab as an Aid for Preparing Frequency Tables
2.3.2 Histograms
2.3.3 The Frequency Polygon
2.3.4 Use of Minitab to Construct Histograms
2.3.5 Histogram with Rectangles of Unequal Bases
(Class Widths)
2.3.6 Ogives
EXERCISES
CHAPTER 3 Descriptive Measures for a Data Set
3.0 Introduction
3.1 The Measures of the Center (Mean, Mode, Median) for a Sample
3.1.1 The Sample Mean
3.1.2 The Sample Median
3.1.3 The Sample Mode for Ungrouped Observations
3.2 The Five Number Summary and Interquartile Range
3.2.1 Boxplots and Outliers
3.3 Measure of Dispersion or Spread
3.3.1 The Semi-Interquartile Range
3.4 The Standard Deviation
3.4.1 Calculation of Standard Deviation
3.4.2 Mean Absolute Deviation
3.5 Relationships between Measures of Dispersion
3.6 Descriptive Measures for a Population
3.7 Analyzing and Finding Descriptive Statistics for Grouped Data
3.7.1 Sample Mean for Grouped Data
3.7.2 Sample Median for Grouped Data
3.7.3 The Sample Mode for Grouped Data
3.7.4 Percentile for Grouped Data
3.7.5 Calculating the Variance and Standard Deviation for Grouped Data
3.7.6 Mean Absolute Deviation for Grouped Data
3.8 Minitab Solutions
3.8.1 Descriptive Statistics: Heights
3.8.2 Boxplot of Heights
3.8.3 Descriptive Statistics: c1
EXERCISES
CHAPTER 4 Elements of Probability and Related Topics
4.0 Introduction
4.1 Sets
4.1.1 Use of Venn Diagrams
4.1.2 The Complement of a Set
4.1.3 The Intersection of Sets
4.1.4 Union of Sets
4.1.5 Exhaustive Sets
4.1.6 Laws of Set Operations
4.2 Basic Concepts of Probability
4.2.1 What is an Event?
4.2.2 Random Variable
4.2.3 Classical Definition of Probability
4.2.4 Relative Frequency Definition of Probability
4.3 Defining Probability Axiomatically
4.3.1 Relationships between Events and Use of Venn Diagrams
4.4 Bayes’ Theorem
4.5 Some Useful Mathematical Techniques
4.5.1 Combinatorial Analysis
4.5.2 Permutations
EXERCISES
CHAPTER 5 Discrete Probability Distributions
5.0 Introduction
5.1 Probability Distributions for Discrete Random Variables
5.2 The Concept of Expectation, Mean, Variance, and Standard Deviation for a Discrete Distribution
5.3 Other Discrete Distributions
5.3.1 The Bernoulli Distribution
5.3.2 The Binomial Distribution
5.3.3 The Poisson Distribution
5.4 A Different Form for Poisson Distribution
5.5 The use of MINITAB to Calculate Probabilities for Some Discrete Distributions
5.5.1 Calculating Binomial Probabilities using MINITAB
5.5.2 Calculating Poisson Probabilities using MINITAB
EXERCISES
CHAPTER 6 Continuous Distributions
6.0 Introduction
6.1 The Uniform Distribution
6.1.1 The Mean, Variance, and Standard Deviation of the Uniform Distribution
6.2 The Normal Distribution
6.2.1 The Standard Normal Distribution
6.2.2 The 68–95–99 Rule, or the Empirical Rule
6.2.3 Application of Empirical Rule to Normal Distribution with Mean and Variance
6.2.4 Percentiles of the Normal Distribution
6.3 Relationship Between the Binomial and the Normal Distributions
6.4 Correcting for Continuity
6.5 Normal Approximation of the Poisson Distribution
6.6 Use of MINITAB to Evaluate Normal and Rectangular Distributions
6.6.1 Use of MINITAB to Evaluate Probabilities for Rectangular Distribution
6.6.2 Use of MINITAB to Evaluate Probabilities for Normal Distribution
EXERCISES
TABLE OF THE STANDARD NORMAL DISTRIBUTION
CHAPTER 7 Sampling Distributions of the Mean, the Proportion, and the Central Limit Theorem
7.0 Introduction—Revisiting Sampling
7.1 Sampling Distribution of the Sample Mean
7.1.1 Mean, Variance, and Standard Deviation of a Sample Mean
7.1.2 Sampling Distribution of the Sample Mean when the Variable is Normally Distributed
7.2 Sampling Distribution of the Sample Mean when Population is Not Normal
7.2.1 Sampling Without Replacement
7.2.2 Sampling With Replacement from a Finite Population
7.3 The Central Limit Theorem
7.4 Sampling Distribution of the Proportion
EXERCISES
CHAPTER 8 Confidence Interval for the Single
Population Mean and Proportion
8.0 Introduction
8.1 Estimation
8.2 Estimating the Population Mean when the Variable is Normally Distributed
8.2.1 Confidence Interval for the Population Mean when Variable is Normally Distributed, Assuming 2 is Known
8.2.2 Finding Confidence Intervals for the Mean when 2 is Unknown
8.3 Confidence Intervals for the Population Proportion
8.3.1 The Need to Know a Population Proportion
8.3.2 Estimating Population Proportion—Point and Confidence Interval Estimates
8.4 Finding the Sample Size for Attaining a Confidence Level and a Margin of Error in Estimating the Population Mean
8.5 Finding the Sample Size for Attaining a Confidence Level and a Set Margin of Error in Estimating p, the Population Proportion
8.6 Large Samples—Using Central Limit Theorem (CLT) to Find Confidence Intervals for the Mean
8.7 Confidence Intervals Using MINITAB
8.7.1 Use of MINITAB for Confidence Intervals for the Single Population Mean when Variance is Known and Data is Normally Distributed or Sample Size is Large
8.7.2 Confidence Interval for a Single Population Mean Using MINITAB when Data are Normally Distributed and Variance is Unknown
8.7.3 Confidence Interval for a Single Population Proportion Using MINITAB
EXERCISES
TABLE OF THE t-DISTRIBUTION
CHAPTER 9 Tests of Hypotheses
9.0 Introduction
9.1 The Null and Alternative Hypotheses
9.1.1 Definitions
9.2 Errors Associated with Hypotheses Tests
9.2.1 Sizes of Types I and II Errors
9.2.2 Level of Significance
9.2.3 Finding the Values of the Size of Type I Error, the Size of Type II Error, and the Power of Test
9.2.4 Power of a Test 9.3 Tests of Hypotheses
9.3.1 Tests for a Single Population Mean Based on Normal Distribution
9.3.2 Classical Approach to Tests of Hypotheses
9.4 The p-Value Approach to Testing Hypothesis
9.4.1 Direction of Extreme and Extreme Values
9.4.2 Using p-Value to Make Decisions when Testing Hypotheses
9.5 Tests about Single Population Mean Drawn from Normal Populations when Variance is Unknown—Use of t-Distribution
9.5.1 Large Sample Approach Based on Central Limit Theorem
9.5.2 Hypotheses Tests about a Population Proportion
9.6 Use of MINITAB for Hypotheses Tests Involving a Single Mean or Proportion
9.6.1 Use of MINITAB to Perform Tests for a Single Population Mean when Variance is Known
9.6.2 Use of MINITAB to Perform Tests for a Single Population Mean when Variance is Unknown
9.6.3 Use of MINITAB to Perform Tests for a Single Population Proportion
EXERCISES
CHAPTER 10 Simple Linear Regression Analysis
10.0 Introduction
10.1 The Simple Linear Regression
10.1.1Exploration of Relationships Using Scatterplots
10.1.2 Regression Using Least Squares Approach
10.1.3 The Least Squares Simple Linear Regression
10.1.4 Assumptions of the Least Squares Linear Model
10.2 Fitted Values and Residuals in Least Squares Simple Linear Regression
10.2.1 Residuals, Sum of Squares Error, and Sum of Squares Regression
10.2.2 Interpolation and Extrapolation
10.3 Testing Hypothesis about the Slope of the Line,
10.4 Another Form for the Regression Equations
10.5 Use of MINITAB for Simple Linear Regression
EXERCISES
CHAPTER 11 Correlation
11.0 Introduction
11.1 Linear Correlation Coefficient
11.2 Testing Whether the Population Correlation Coefficient is Zero
11.3 Coefficient of Determination
11.4 Use of MINITAB to Find the Correlation Coefficient and Test its Population Value is Not Zero
EXERCISES
CHAPTER 12 Two Sample Confidence Intervals
12.0 Introduction
12.1 Sampling Distribution of Sample Means
12.1.1Distribution of the Difference Between Two Sample Means When the Populations Are Not Normal (Central Limit Theorem)
12.2 Sampling Distribution of the Difference Between Two Sample Proportions
12.3 The Two Sample Confidence Intervals
12.4 Confidence Intervals for Difference Between Two Parameters
12.5 Confidence Interval for the Difference Between Two Population Proportions
12.6 Confidence Intervals for Differences Between Two Means
12.7 Confidence Intervals for the Difference Between the Means for Two Independent Samples
12.7.1 Confidence Interval for the Difference Between Means for Two Independent Samples When Variances are Equal
12.7.2Confidence Interval for the Difference Between Means When Variances Are Unknown and Are Not Equal
12.8 Use of Central Limit Theorem for Constructing Confidence Intervals for the Difference Between Two Population Means for Large Samples
12.9 Use of MINITAB for Confidence Intervals for Means and Proportions
EXERCISES
CHAPTER 13 Tests of Hypotheses Involving Two Samples
13.0 Introduction
13.1 Testing Hypotheses about Two Population Proportions
13.2 Making Inferences about the Means of Two Populations
13.3 Making Inferences about Two Population Means, the Pooled Variance t- Test
13.4 Comparing Two Means when Populations are Normal and Variances are Unknown
13.5 Linking Hypotheses Testing and Confidence Intervals
13.6 Paired Comparison or Matched Pair t- Test
13.7 Use of MINITAB for Testing Hypotheses and Constructing Confidence Intervals
13.7.1 Use of MINITAB for Testing for Difference Between Two Proportions, and Constructing 100(1-)% Confidence Interval for the Difference
13.7.2 Using MINITAB for Confidence Interval and Hypotheses Tests for the Difference Between Means when Variances are not Known but are Assumed Equal
13.7.3 Using MINITAB for Confidence Interval and Hypotheses Tests for the Difference Between Means when Variances are Unknown and are not Equal
13.7.4 Using MINITAB to Carry out Paired Comparison or Matched Pair t- Test and Obtaining the Confidence Interval for the Mean Difference
EXERCISES
CHAPTER 14 Chi-Square Goodness of Fit and Analysis of Categorized Data
14.1 Data Analyses Based on Chi-Square
14.2 The Chi-Square Distribution
14.2.1 Multinomial Experiments and Goodness of Fit Tests
14.3 Chi-Square Test of Homogeneity
14.4 Chi-Square Test for Independence or Association Between Two Categorical Variables
14.5 Use of MINITAB for Chi-Square Analysis
EXERCISES—CHI-SQUARE ANALYSIS
CHAPTER 15 The Completely Randomized Design—One Way Analysis of Variance
15.0 One-Way Layout—An Introduction
15.1 The One-Way ANOVA or the Completely Randomized Design
15.2 The Least Significant Difference Method
15.3 The Unbalanced One-Way Layout
EXERCISES
CHAPTER 16 The Randomized Complete Block Design
16.0 The Randomized Complete Block Design
16.1 Advantages and Disadvantages of RCBD
16.1.2 Model for RCBD and Analysis of Its Responses
16.2 Missing Data in RCBD—An Approximate Analysis
16.3 Using MINITAB to Carry Out ANOVA With Missing Data
16.3.1 Use of MINITAB for RCBD When Data Are Not Missing
EXERCISES—RANDOMIZED COMPLETE BLOCK DESIGN
CHAPTER 17 The Two-Way Layout
17.0 The Full Two Factor Factorial Experiment (A Two-Way Layout)
EXERCISES—TWO FACTOR FACTORIAL EXPERIMENT
(TWO-WAY LAYOUT)
CHAPTER 18 Introductory Nonparametric Statistics
18.0 Introduction—Nonparametric Tests
18.1 The Sign Tests
18.2 The Wilcoxon Signed-Rank Test
18.2.1 Normal Approximation for the Wilcoxon Signed-Rank Test
18.3 The Wilcoxon Rank-Sum Test
18.3.1 Normal Approximation of the Wilcoxon Rank-Sum Test
18.4 The Kruskal–Wallis Test (A Nonparametric Equivalent of One-Way ANOVA)
EXERCISES (NONPARAMETIC STATISTICS)
APPENDIX I Table of Random Digits
APPENDIX II Table of the Standard Normal Distribution
APPENDIX III Table of the t- Distribution APPENDIX IV Table of the Upper α -Percentile of the
Chi-Square Distribution
APPENDIX V Table of the Upper α -Percentile of the F –Distribution
APPENDIX VI Table for Wilcoxon Signed-Rank Test
APPENDIX VII Table of the Critical Values for the Smaller Rank Sum for Wilcoxon-Mann-Whitney Test
Solutions to Exercises