Table of Contents

Introduction: Basic Ideas of Statistics

1 Data

Topics

• What is Data?
        Task:   Identify Types of Statistics       Task:   Identify Data Types
• Where are the Data?
        Tools:
            Interactive Data Sets for Examining Maximum, Minimum and Range of Data Sets.
            Interactive Data Sets for Examining Mean, Median and Mode of Data Sets.
        Task:   Find Maximum, Minimum and Range of Data Set       Task:   Find Mean, Median and Mode of Data Set
• Presentation of Data and Histograms: Frequency, Relative Frequency, and Weights
        Tools:
            Build Histograms from Interactive Data Sets
            Histograms from Frequency Information
            Bins and Data Organization
            Approximating Averages
        Task:   Build a Histogram       Task:   Compute Relative Frequencies       Task:   Approximate Mean from Relative Frequency Information       Task:   Build a Histogram and Obtain Information about Data
• Measure of Dispersion: How Spread is the Data?
        Task:   Determine Variance and Standard Deviation       Task:   Approximate Standard Deviation from Frequency Data
• Other Descriptions of Data: Skewness, Kurtosis
        Task:   Determine Skewness and Kurtosis of a Data Set

2 Probability

Topics

• Introductory Examples
        Tools:
            Interactive Model of Coin Flips
            Interactive Model of Die Rolls
            Interactive Model of Waiting Times
• Axioms of Probability and Immediate Consequences
        Task:   Compute Probabilities of Simple Events
• Counting and More Examples
        Task:   Several Counting Problems
• Some Basic Set Theory
        Task:   Using Venn Diagrams
• Conditional Probability, Bayes’ Theorem, and Independence
        Task:   Determine Conditional Probabilities       Task:   Use Bayes’ Theorem
• Random Variables
        Task:   Identify Random Variables
• Expected Value and Basic Properties
        Task:   Compute Expected Values
• Moments and the Moment Generating Function
        Task:   Compute Moments
• Chebyshevs’ Theorem
        Task:   Using Chebyshev’s Inequality
• Basic Models: Discrete Random Variables
          Uniform
          Bernoulli
          Binomial
          Geometric and Inverse Binomial
          Poisson
        Task:   Explore Binomial Densities       Task:   Explore Geometric Densities       Task:   Explore Poisson Densities
• Basic Models: Continuous Random Variables
          Uniform
          Exponential
          Normal
        Task:   Explore Rectangular Densities       Task:   Explore Exponential Densities       Task:   Explore Normal Densities

Tasks

• Compute Probabilities of Simple Events
• Several Counting Problems
• Using Venn Diagrams
• Determine Conditional Probabilities
• Use Bayes’ Theorem
• Identify Random Variables
• Compute Expected Values
• Compute Moments
• Using Chebyshev’s Inequality
• Explore Binomial Densities
• Explore Geometric Densities
• Explore Poisson Densities
• Explore Rectangular Densities
• Explore Exponential Densities
• Explore Normal Densities

Evaluation Tools

• Compute Probabilities of Simple Events
• Several Counting Problems
• Using Venn Diagrams
• Determine Conditional Probabilities
• Use Bayes’ Theorem
• Identify Random Variables
• Compute Expected Values
• Compute Moments
• Using Chebyshev’s Inequality
• Basic Models   –   Discrete Random Variables
• Basic Models   –   Continuous Random Variables

3 Sampling

Topics

• The Idea – Understanding Underlying Probability
• Collection and Sample Bias
• Estimation
• Joint Density Functions and Independent Random Variables
• Further Properties of Expectation and Moment Generating Functions
• The Law of Large Numbers and Convergence to Probability
• Distribution of the Mean from a Normal Distribution
  
        Task:   Study Sample Means from a Normal Distribution
• Distribution of the Mean from a Non-normal Distribution
  
        Task:   Study Sample Means from a Non-normal Distribution

Tasks

• Study Sample Means from a Normal Distribution
• Study Sample Means from a Non-normal Distribution

Evaluation Tools

• Sample Means from a Normal Distribution
• Sample Means from a Non-normal Distribution

4 Interpretation and Inference   –   Drawing Conclusions

Topics

• Using Statistics – Analyzing Data through Understanding Underlying Probability
• Hypotheses, Hypothesis Testing, and Error
        Task:   Accepting/Rejecting Hypotheses
• Confidence Intervals for Normal Variables
        Task:   Confidence Intervals for a Normal Random Variable
• Distribution of Averages for Normal Variables
        Task:   Confidence Intervals for the Average of a Sample of a Normal Random Variable       Task:   Controlling Confidence Intervals with Sample Size
• Estimating the Mean of a Normal Variable from a Sample
• Sums of Chi-square Variables and Approximation of Variance
• Estimating Means and Variances in General
        Task:   Find Confidence Intervals for Proportions       Task:   Estimate the Difference of the Means of Two Normal Random Variables       Task:   Estimate the Difference of Two Proportions
• Small Sample Sizes
• Hypothesis Testing Using Confidence Intervals

Tasks

• Accepting/Rejecting Hypotheses
• Confidence Intervals for a Normal Random Variable
• Confidence Intervals for the Average of a Sample of a Normal Random Variable
• Controlling Confidence Intervals with Sample Size
• Find Confidence Intervals for Proportions
• Estimate the Difference of the Means of Two Normal Random Variables
• Estimate the Difference of Two Proportions

Evaluation Tools

• Accepting/Rejecting Hypotheses
• Confidence Intervals for a Normal Random Variable
• Confidence Intervals for the Average of a Sample of a Normal Random Variable
• Controlling Confidence Intervals with Sample Size
• Find Confidence Intervals for Proportions
• Estimate the Difference of the Means of Two Normal Random Variables
• Estimate the Difference of Two Proportions

5 Correlation and Regression

Topics

• Convergence of Averages to Normal
• Student’s t-distribution and Small Sample Size
• Confidence Intervals
• Hypothesis Testing
• One Sample
• Two Sample

6 Advanced Topics

Topics

• Chi-square and Goodness of Fit
• Analysis of Variance
• Correlation and Regression