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MA 132


I. Let’s Get Started 

  • Statistics Overview
  • Statistics vs. Probability
  • Descriptive  and Inferential Statistics
  • Designing the Study
  • Sampling Strategies
  • Data – Classification of
  • Data Collection Methods

II. Organizing and Graphing Data

  • Graphing Qualitative Data
    • Pie Char
    • Bar Chart
    • Pareto Char
  • Graphing Quantitative Data
    • Frequency Distributions and Histograms – Varieties of
    • Stem and Lea
    • Ogive
    • Dot Plot
    • Scatter Plot

III.  Describing our Data

  • Measures of Central Tendency
  • Measures of Dispersion
  • Measures of Position
  • Overview of Excel 

IV.  Probability and Probability Distributions

  • An overview of probability
  • Theoretical and empirical probability
  • Probability experiments
  • Random variables
  • Law of Large Numbers
  • Discrete Probability Distributions
    • Binomial Probability Distribution
    • Probability Distribution
  • Continuous Probability Distributions
    • Gaussian or Normal Probability Distribution
    • T-distribution
  • Calculating Theoretical Probabilities when working with a Normal Probability Distribution
  • Creating a Normal Quantile Plot in Excel to assess the normalcy of your data

V.  Point Estimates, The Central Limit Theorem and Confidence Intervals 

  • Point estimates
  • The Sampling Distribution of Sample Means
  • Central Limit Theorem
  • Confidence Intervals for the Population Mean
  • Confidence Intervals for the Population Variance

VI. Hypothesis Testing 

  • Overview
    • The process itself
    • What can we test?
    • All tests are not created equal – A summary of different tests by type
    • Why is normalcy in a data set so important
    • What can we do if the data is not normal
    • Large sample vs. small sample – Bigger is better
  • Hypothesis testing involving the mean – parametric and non-parametric data
  • Hypothesis testing involving the standard deviation/variance
  • Hypothesis testing to determine whether data collected actually ‘fits’ a recognized probability distribution
    • Goodness of Fit Test for discrete data
  • Type I and Type II errors
  • P value vs. critical value 
  • Working with actual data – Constructing and executing a hypothesis test 
    • Hypothesis testing involving horseshoe crab sizes
    • Hypothesis testing involving self pollination of plants
    • Hypothesis testing involving spontaneous vs. acquired mutation

VII. Linear Correlation and Regression

VIII. Additional Topics in Probability

  • Three types of Probability
  • Events and sample spaces
  • Complements of an event
  • Independent , Dependent and Mutually Exclusive Events
  • Using visual Tools to better understand the scenario – Tree Diagrams/Venn Diagrams
  • Simple Probability
  • Conditional Probability
  • Addition and Multiplication Rules of Probability
  • Fundamental Counting Principle
  • Law of Large Numbers