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Statistics, 3E

Book Description

Statistics is a class that is required in many college majors, and it's an increasingly popular Advanced Placement high school course. In addition to math and technical students, many business and liberal arts students are required to take it as a fundamental component of their majors. A knowledge of statistical interpretation is vital for many careers. Idiot's Guides: Statistics explains the fundamental tenets in language anyone can understand. Content includes:
- Calculating descriptive statistics
- Measures of central tendency: mean, median, and mode
- Probability
- Variance analysis
- Inferential statistics
- Hypothesis testing
- Organizing data into statistical charts and tables

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright Page
  4. Foreword
  5. Introduction
  6. Part 1: The Basics
    1. 1 Let’s Get Started
      1. What Is Statistics and Why Do You Need It?
      2. Types of Statistics
        1. Descriptive Statistics–the Minor League
        2. Inferential Statistics–the Major League
      3. Population vs. Sample
      4. Parameter vs. Statistic
      5. Ethics and Statistics–It’s a Dangerous World Out There
      6. Practice Problems
    2. 2 Data, Data Everywhere and Not a Drop to Drink
      1. The Importance of Data
      2. The Sources of Data–Where Does All This Stuff Come From?
        1. Direct Observation–I’ll Be Watching You
        2. Experiments–Who’s in Control?
        3. Surveys–Is That Your Final Answer?
      3. Data and Types of Variables
        1. Quantitative vs. Qualitative Variables
        2. Discrete vs. Continuous Variables
        3. Dependent vs. Independent Variables
      4. Types of Measurement Scales–a Weighty Topic
        1. Nominal Level of Measurement
        2. Ordinal Level of Measurement
        3. Interval Level of Measurement
        4. Ratio Level of Measurement
      5. Computers to the Rescue
        1. The Role of Computers in Statistics
        2. Installing the Data Analysis Add-In
      6. Practice Problems
    3. 3 Displaying Descriptive Statistics
      1. Frequency Distributions
        1. The Frequency Distribution
        2. (A Distant) Relative Frequency Distribution
        3. The Cumulative Frequency Distribution
        4. The Contingency Table
      2. Charting Your Course: Graphs
        1. Histogram
        2. Letting Excel Do Our Dirty Work
        3. Bar Chart
        4. Pie Chart
        5. Line Chart
      3. The Stem and Leaf Display–Statistical Flower Power
      4. Practice Problems
    4. 4 Calculating Descriptive Statistics: Measures of Central Tendency (Mean, Median, and Mode)
      1. Measures of Central Tendency
        1. Mean
        2. Median
        3. Mode
        4. Weighted Mean
        5. Measures of Central Tendency for Grouped Data:
        6. How Does One Choose?
      2. Using Excel to Calculate Central Tendency
      3. Practice Problems
    5. 5 Calculating Descriptive Statistics: Measures of Dispersion
      1. Measures of Dispersion for Ungrouped Data
        1. Range
        2. Variance
        3. Using the Raw Score Method (When Grilling)
        4. Variance of a Population
        5. Standard Deviation
      2. Measures of Dispersion for Grouped Data
      3. Measures of Relative Position
        1. Quartiles
        2. Interquartile Range (IQR)
      4. Excel to the Rescue
      5. Practice Problems
  7. Part 2: Probability Topics
    1. 6 Introduction to Probability
      1. What is Probability?
        1. Classical Probability
        2. Empirical Probability
        3. Subjective Probability
      2. Relationship Between Events
        1. Mutually Exclusive Events
        2. Independent Events
        3. Complementary Events
      3. Union and Intersection of Events
        1. The Union of Events: A Marriage Made in Heaven
        2. The Intersection of Events
      4. Practice Problems
    2. 7 Probability and Counting Rules
      1. Addition Rule of Probabilities
      2. Conditional Probability
      3. Multiplication Rule of Probabilities
      4. Bayes’ Theorem
      5. Counting Principles
        1. The Fundamental Counting Rule
        2. Permutations
        3. Combinations
        4. Using Excel to Calculate Factorials, Permutations, and Combinations
      6. Practice Problems
    3. 8 Probability Distributions
      1. Basic Concepts of Probability Distributions
        1. Random Variables
        2. Probability Distributions
        3. Rules for Discrete Probability Distributions
      2. The Mean of Discrete Probability Distributions
      3. The Variance and Standard Deviation of Discrete Probability Distributions
      4. Practice Problems
    4. 9 The Binomial Probability Distribution
      1. Characteristics of a Binomial Experiment
      2. The Binomial Probability Distribution
      3. Binomial Probability Tables
      4. Using Excel to Calculate Binomial Probabilities
      5. The Mean and Standard Deviation for the Binomial Distribution
      6. Practice Problems
    5. 10 The Poisson Probability Distribution
      1. Characteristics of a Poisson Process
      2. The Poisson Probability Distribution
      3. Poisson Probability Tables
      4. Using Excel to Calculate Poisson Probabilities
      5. Using the Poisson Distribution as an Approximation to the Binomial Distribution
      6. Practice Problems
    6. 11 The Normal Probability Distribution
      1. Characteristics of the Normal Probability Distribution
      2. Calculating Probabilities for the Normal Distribution
        1. Calculating Probability Using the Z-Score
        2. Using the Standard Normal Table
        3. The Area Under the Normal Distribution and the Empirical Rule
        4. Calculating Normal Probabilities Using Excel
      3. Using the Normal Distribution as an Approximation to the Binomial Distribution
      4. Practice Problems
  8. Part 3: Inferential Statistics
    1. 12 Sampling
      1. Why Sample?
      2. Random Sampling
        1. Simple Random Sampling
        2. Systematic Sampling
        3. Cluster Sampling
        4. Stratified Sampling
      3. Sampling Error and Sampling Bias
        1. Sampling Error
        2. Sampling Bias
      4. Examples of Poor Sampling Techniques
      5. Practice Problems
    2. 13 Sampling Distributions
      1. What Is a Sampling Distribution?
      2. Sampling Distribution of the Sample Means
      3. Mean of the Sampling Distribution of the Sample Means
      4. Standard Error of the Sampling Distribution of the Sample Means
      5. The Central Limit Theorem
      6. Putting the Central Limit Theorem to Work
      7. Sampling Distribution of the Proportion
        1. Calculating the Sample Proportion
        2. Calculating the Standard Error of the Proportion
      8. Practice Problems
    3. 14 Confidence Intervals
      1. The Basics of Confidence Intervals
        1. Point Estimate and Interval Estimate
        2. The Principle of Confidence Intervals
        3. The Probability of an Error (the Alpha Value)
      2. Confidence Intervals for the Population Mean
        1. When the Population Standard Deviation Is Known
        2. Beware of Interpretation of the Confidence Interval!
        3. The Effect of Changing Confidence Levels
        4. The Effect of Changing the Sample Size
        5. When the Population Standard Deviation Is Unknown
      3. When the Population Standard Deviation Is Unknown and with Small Samples
        1. Determining Sample Size for the Population Mean
        2. Using Excel’s CONFIDENCE Function
      4. Confidence Intervals for the Population Proportion with Large Samples
        1. Calculating the Confidence Interval for the Population Proportion
        2. Determining Sample Size for the Proportion
      5. Practice Problems
    4. 15 Hypothesis Testing with One Population
      1. Hypothesis Testing: The Traditional Method
        1. Procedures for Hypothesis Testing
        2. 1. The Null and Alternative Hypotheses
        3. 2. The Level of Significance
        4. 3. The Test Statistic
        5. 4. The Critical Value
        6. 5. State Your Decision
      2. One-Tail vs. Two-Tail Tests
        1. Two-Tail Hypothesis Testing
        2. One-Tail Hypothesis Testing
      3. Hypothesis Testing for the Population Mean
        1. When Sigma Is Known
        2. When Sigma Is Unknown and Using a Large Sample
        3. When Sigma Is Unknown and Using a Small Sample
      4. The Role of Alpha in Hypothesis Testing
      5. The p-Value Method
        1. The p-Value for a One-Tail Test
        2. The p-Value for a Two-Tail Test
      6. Using Excel for Hypothesis Testing
        1. Using Excel’s NORM.S.DIST Function
        2. Using Excel’s T.DIST, T.DIST.RT, and T.DIST.2T Functions
        3. Using Excel’s T.INV and T.INV.2T Functions
      7. Hypothesis Testing for the Population Proportion with Large Samples
        1. One-Tail Hypothesis Test for the Proportion
        2. Two-Tail Hypothesis Test for the Proportion
      8. Practice Problems
    5. 16 Hypothesis Testing with Two Populations
      1. The Concept of Testing Two Populations
      2. Sampling Distribution for the Difference in Means
      3. Testing for the Differences Between Two Population Means with Independent Samples
        1. When the Population Standard Deviations Are Known
        2. Testing a Difference Other Than Zero
        3. When the Population Standard Deviations Are Unknown
        4. Unequal Population Variances When the Population Standard Deviations Are Unknown
        5. Equal Population Variances When the Population Standard Deviations Are Unknown
        6. To Pool or Not to Pool?
      4. Testing for Differences Between Means with Dependent Samples
      5. Letting Excel Do the Grunt Work
      6. Testing for Differences Between Proportions with Independent Samples
      7. Practice Problems
  9. Appendixes
    1. A Solutions to “Practice Problems”
    2. B Statistical Tables
    3. C Glossary
    4. D Statistics Reference Glossary
    5. E Excel Reference Glossary
    6. 1 Analysis of Variance
    7. 2 Chi-Square Tests
    8. 3 Correlation and Simple Linear Regression
    9. 4 Solutions to “Practice Problems”
    10. 5 Online Appendix
  10. About the Author