# Introductory Statistics

Author(s): Lukun Zheng

Edition: 2

Pages: 250

## \$93.99

ISBN 9798765742334

Details Electronic Delivery EBOOK 180 days

Dedication
Preface

Part I Introduction

1 Introduction to Statistics
1.1 What Is Statistics?
1.2 Sampling Methods
1.2.1 Biased Sampling Methods
1.2.2 Simple Random Sampling
1.3 Types of Data
Problems

Part II Descriptive Statistics

2 Presentation of Data
2.1 Frequency Distribution Table
2.2 Histograms
2.3 Other graphs
2.3.1 Bar Graphs
2.3.2 Circle Graphs
2.3.3 Stem-and-Leaf Displays
Problems

3 Descriptive Statistics
3.1 Measures of Center (Ungrouped Data)
3.1.1 Arithmetic Mean
3.1.2 Median
3.1.3 Mode
3.1.4 Comparison of the Mean, Median, and Mode
3.2 Measures of Variation (ungrouped data)
3.2.1 Range
3.2.2 Standard Deviation
3.3 Measures of Center and Variation (grouped data)
3.3.1 Mean
3.3.2 Standard Deviation
3.3.3 Modal Class
3.4.1 Z Scores
3.4.2 Box-and-Whisker Plot
3.4.3 Quartiles
3.4.4 Percentiles
Problems

Part III Probability

4 Probability
4.1 Basic Concepts and Definitions
4.1.1 Sample Spaces and Events
4.1.2 Probability
4.2 Complements, Unions, and Intersections
4.2.1 Event Operations
4.2.2 Probability Rules
4.3 Conditional Probability and Independence
4.3.1 Conditional Probability
4.3.2 Product Rule
4.3.3 Independence
4.4 Bayes’ Theorem
Problems

5 Discrete Probability Distributions
5.1 Random Variables and Probability Distributions
5.1.1 Random Variables
5.1.2 Probability Distributions
5.2 The Mean and Standard Deviation of a Discrete Random Variable
5.2.1 The mean μ
5.2.2 The standard deviation s
5.3 The Binomial Distribution
5.3.1 Definition
5.3.2 Properties of The Binomial Distribution
Problems

6 The Normal Distribution
6.1 Area and Probability
6.1.1 Continuous Data and Probability Distribution Functions
6.1.2 Finding Probabilities for Uniform Distributions
6.1.3 Properties of a Normal Distribution
6.1.4 Using the Standard Normal Table to Find Z-Scores
6.2 The Standard Normal Distribution
6.2.1 Finding Probabilities for the Standard Normal Distribution
6.2.2 Finding Z-Scores for a Given Area
6.3 Normal Distributions
6.3.1 Finding Normal Probabilities
6.3.2 Finding the Value of X Given a Proportion/Probability
Problems

Part IV Inferential Statistics

7 Confidence Intervals and Sample Sizes
7.1 Sampling Distributions: Mean
7.1.1 Central Limit Theorem for Sample Means
7.1.2 Computing Probabilities of a Sample Mean
7.2 Sampling Distributions: Proportion
7.2.1 Central Limit Theorem for Sample Proportions
7.3 Confidence Intervals for Population Means
7.3.1 Confidence Intervals when s is Known
7.3.2 Confidence Intervals when s is Unknown
7.4 Confidence Intervals for Population Proportions
7.4.1 Confidence Intervals for a Population Proportion, p
7.4.2 Determining Sample Size
Problems

8 Hypothesis Testing
8.1 Basics of Hypothesis Testing
8.1.1 The Null and Alternative Hypotheses
8.1.2 The Test Statistic
8.1.3 The p-value and the Rejection Region
8.1.4 Decision Rules and Two Types of Errors
8.2 Hypothesis testing about a Population Mean (Large Sample n ≥ 30)
8.3 Hypothesis testing about a Population Mean (Small Sample n < 30)
Problems

9 Correlation and Regression
9.1 Scatterplots and Correlation
9.1.1 Strength of Association
9.1.2 Linear Correlation Coefficient, r
9.1.3 Properties of the Correlation Coefficient, r
9.1.4 Calculator Steps
9.2 Hypothesis Testing for Correlation
9.2.1 Hypothesis Testing – Linear Correlation
9.3 Linear Regression
9.3.1 Regression Equation
9.3.2 Calculator Steps
Problems

Appendices
A.1 Table A Normal Curve (z) Table
A.2 Table B t Table

Lukun Zheng

Dedication
Preface

Part I Introduction

1 Introduction to Statistics
1.1 What Is Statistics?
1.2 Sampling Methods
1.2.1 Biased Sampling Methods
1.2.2 Simple Random Sampling
1.3 Types of Data
Problems

Part II Descriptive Statistics

2 Presentation of Data
2.1 Frequency Distribution Table
2.2 Histograms
2.3 Other graphs
2.3.1 Bar Graphs
2.3.2 Circle Graphs
2.3.3 Stem-and-Leaf Displays
Problems

3 Descriptive Statistics
3.1 Measures of Center (Ungrouped Data)
3.1.1 Arithmetic Mean
3.1.2 Median
3.1.3 Mode
3.1.4 Comparison of the Mean, Median, and Mode
3.2 Measures of Variation (ungrouped data)
3.2.1 Range
3.2.2 Standard Deviation
3.3 Measures of Center and Variation (grouped data)
3.3.1 Mean
3.3.2 Standard Deviation
3.3.3 Modal Class
3.4.1 Z Scores
3.4.2 Box-and-Whisker Plot
3.4.3 Quartiles
3.4.4 Percentiles
Problems

Part III Probability

4 Probability
4.1 Basic Concepts and Definitions
4.1.1 Sample Spaces and Events
4.1.2 Probability
4.2 Complements, Unions, and Intersections
4.2.1 Event Operations
4.2.2 Probability Rules
4.3 Conditional Probability and Independence
4.3.1 Conditional Probability
4.3.2 Product Rule
4.3.3 Independence
4.4 Bayes’ Theorem
Problems

5 Discrete Probability Distributions
5.1 Random Variables and Probability Distributions
5.1.1 Random Variables
5.1.2 Probability Distributions
5.2 The Mean and Standard Deviation of a Discrete Random Variable
5.2.1 The mean μ
5.2.2 The standard deviation s
5.3 The Binomial Distribution
5.3.1 Definition
5.3.2 Properties of The Binomial Distribution
Problems

6 The Normal Distribution
6.1 Area and Probability
6.1.1 Continuous Data and Probability Distribution Functions
6.1.2 Finding Probabilities for Uniform Distributions
6.1.3 Properties of a Normal Distribution
6.1.4 Using the Standard Normal Table to Find Z-Scores
6.2 The Standard Normal Distribution
6.2.1 Finding Probabilities for the Standard Normal Distribution
6.2.2 Finding Z-Scores for a Given Area
6.3 Normal Distributions
6.3.1 Finding Normal Probabilities
6.3.2 Finding the Value of X Given a Proportion/Probability
Problems

Part IV Inferential Statistics

7 Confidence Intervals and Sample Sizes
7.1 Sampling Distributions: Mean
7.1.1 Central Limit Theorem for Sample Means
7.1.2 Computing Probabilities of a Sample Mean
7.2 Sampling Distributions: Proportion
7.2.1 Central Limit Theorem for Sample Proportions
7.3 Confidence Intervals for Population Means
7.3.1 Confidence Intervals when s is Known
7.3.2 Confidence Intervals when s is Unknown
7.4 Confidence Intervals for Population Proportions
7.4.1 Confidence Intervals for a Population Proportion, p
7.4.2 Determining Sample Size
Problems

8 Hypothesis Testing
8.1 Basics of Hypothesis Testing
8.1.1 The Null and Alternative Hypotheses
8.1.2 The Test Statistic
8.1.3 The p-value and the Rejection Region
8.1.4 Decision Rules and Two Types of Errors
8.2 Hypothesis testing about a Population Mean (Large Sample n ≥ 30)
8.3 Hypothesis testing about a Population Mean (Small Sample n < 30)
Problems

9 Correlation and Regression
9.1 Scatterplots and Correlation
9.1.1 Strength of Association
9.1.2 Linear Correlation Coefficient, r
9.1.3 Properties of the Correlation Coefficient, r
9.1.4 Calculator Steps
9.2 Hypothesis Testing for Correlation
9.2.1 Hypothesis Testing – Linear Correlation
9.3 Linear Regression
9.3.1 Regression Equation
9.3.2 Calculator Steps
Problems

Appendices
A.1 Table A Normal Curve (z) Table
A.2 Table B t Table