Introductory Statistics

About the Author
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 Additional Descriptive Topics 
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 
B.1 Answers to Selected Problems