Introductory Statistics

Cover
Title
Copyright
End User License Agreement
Contents
Preface
	CONSENT FOR PUBLICATION
	CONFLICT OF INTEREST
	ACKNOWLEDGEMENT
Introduction to Statistics
	INTRODUCTION
	DATA TYPES
		Sample Data
	CONCLUSION
Summarizing and Graphing
	INTRODUCTION
	FREQUENCY DISTRIBUTIONS AND HISTOGRAMS
	GRAPHS
	CONCLUSION
Basic Concepts of Probability
	INTRODUCTION
	SAMPLES EVENTS AND THEIR PROBABILITIES
		Sample Spaces
		Event
		Examples
			Example 1
			Example 2
			Example 3
			Example 4
	EXPERIMENT
		Definition:
			Example 5
	PROBABILITY
		Examples
			Example 1
			Example 2
			Example 3
			Example 4
			Example 5
	COMPLEMENTS, INTERSECTIONS, AND UNIONS
		Complement
		Examples
			Example 1
		Probability Rule for Complements
			Example 2
		Intersection of Events
		Examples
			Example 1
			Example 2
		Probability Rule for Mutually Exclusive Events
			Example
		Union of Events
		Examples
			Example 1
			Example 2
		Additive Rule of Probability
			Example 3
			Example 4
			Example 5
	CONDITIONAL PROBABILITY AND INDEPENDENT OCCURRENCES
		Conditional Probability
		Examples
			Example 1
			Example 2
			Example 3
		Independent Events
		Examples
			Example 1
			Example 2
			Example 3
			Example 4
		Probability in Tree Diagrams
			Example
		Principles
	CONCLUSION
Discrete Random Variables
	INTRODUCTION
		Random Variables
			Understanding Random Variables
			Types of Random Variables
			Example of Random Variable
		Example:
		Examples of Probability Distributions for Discrete Random Variables (DRV)
			Example 1
			Example 2
		Examples
			Example # 1
			Example # 2
			Example # 3
		Variance of Discrete Random Variables
		Characteristics and Notations
			Binominal Distribution
			Understanding Binominal Distribution
			Analyzing Binominal Distribution
			Criteria for Binominal Distribution
			Examples of Binominal Distributions
			Trial 1
			Trial 2
			Trial 3
			Cumulative Binominal Probability
			Negative Binominal Distribution
			Notations
			The Mean of Negative Binominal Distribution
	CONCLUSION
Continuous Random Variables
	INTRODUCTION
		Probability Distribution of Continuous Random Variable
			Properties
			Probability Density Functions
			Cumulative Distribution Functions
		Examples of Probability Distribution of Continuous Random Variable
			Example # 1
			The Normal Distribution
			Understanding Normal Distribution
			Kurtosis and Skewness
			Central Limit Theorem
			Sample Mean
			Convergence to Normal Distribution
			The Standard Normal Distribution
			The Standard Normal Distribution Vs. Normal Distribution
			Standardizing Normal Distribution
			How to Calculate Z-score
			Example of Finding Z -score
			To Find Probability using The Normal Standard Distribution
			P values and Z-Tests
			How to Use Z-Table
			Example: Using Z distribution to Find Probability
			Areas of Tails of Distribution
			Tails of Standard Normal Distribution
	CONCLUSION
Sampling Distributions
	INTRODUCTION
	THE MEAN AND STANDARD DEVIATION (SD) OF THE SAMPLE MEAN
		Examples
			Example 1
			Example 2
			The Sampling Distribution of the Sample Mean
			The Central Limit Theorem
		Examples
			Example 1
			Example 2
		Solution [44]
			Example 3
			Example 4
		Normally Distributed Populations
		Standard Deviation of x¯ (Standard Error) [44]
		Z-Score of the Sample Mean [44]
		Examples
			Example 1
			Example 2
			Example 3
		The Sample Proportion
		Sample Proportions in a Small Population:
		The Sampling Distribution of the Sample Proportion
		Examples
			Example 1
			Example 2
			Example 3
		CONCLUSION
Estimation
	INTRODUCTION
		Construction of Confidence Intervals
		Interval Estimate vs. Point Estimate
		Intervals of Confidence
		Confidence Level
		The Error Margin
		Estimator
			Interval vs. Point Estimator
			Types of Estimators
		WHAT IS STANDARD ERROR (SDE)?
		Standard Deviation (SD) of Sample Estimates
		Standard Error (SE) of Sample Estimates
		Margin of Error
			How to Calculate the Error Margin
		What is the Critical Value and How Do I Find it?
		What is a Confidence Interval, and How Does It Work?
		Confidence Intervals and How to Interpret Them
		Data Requirements for Confidence Interval
		What is a Confidence Interval, and How Do I Make One?
		Bias and Error
		MSE stands for Mean Squared Error
		Sample Size and Estimates
		Determining the Sample Size is Necessary to Estimate the Population Mean
		Examples
			Example
		Large Sample Estimation of a Population Mean
		Large Sample 100 (1 - α) % Confidence Interval for a Population Mean
			Example
		Small Sample Estimation of a Population Mean
		Small Sample 100 (1 -α) % Confidence Interval for a Population Mean [53]
			Example 1
			Example 2
		Determining Sample Size Required to Estimate Population Proportion (p)
			Example
		Estimating the Target Parameter: Point Estimation
		Maximum Likelihood
		Linear Least Squares (LLS)
		Estimating the Target Parameter: Interval Estimation
			Example
		The t Distribution
		Estimating a Population Proportion
		Using Confidence Intervals to Determine the Population Proportion
		Examples
			Example 1
		The “Plus Four” Confidence Interval
		Calculating the Sample Size n
		Sample Size Considerations
		The Cost of Collecting Samples
			Pre-existing knowledge
			Variability That is Inherent
		Determination of the Sample Size
		Proportions of Samples Taken
	CONCLUSION
Hypothesis Testing
	INTRODUCTION
		Z-Test
		T-Test
	CONCLUSION
Correlation and Regression
	INTRODUCTION
	CORRELATION
	REGRESSION
	CONCLUSION
Ethics
	INTRODUCTION
	ETHICS
	CONCLUSION
References
Subject Index
Back Cover