Lewis Solutions

The following is a compilation of historic exam problems collected over the course of many years and modified to reinforce concept mastery through repetition. They are intended to offer students additional examples for test preparation and to increase practice decoding Lewis’s writing style, as well as model well-organized solutions in Lewis’s preferred notation. These resources are not guaranteed to be comprehensive, exhaustive, or predictive of current semester exams. Use the current semester’s class notes and ask Lewis to determine what concepts will be included in any given exam.

Fundamentals of Introductory Statistics

  • Resources for this section
    • Study Guide Notes
    • Example Problems and Solutions
    • Extra Practice and Answers
  • Statistics Vocabulary
    • Populations vs. Samples
    • Experiments
    • Observational Units
    • Variables of Interest
  • Notation
    • Population Parameters
    • Sample Statistics
    • Summation Notation Review
    • Working with Formulas
  • Distributions and Visualizing Data
    • Diagrams of Experiments
    • Shape
      • Skew
      • Symmetry
    • Center
      • Averages (Mean, Median, Mode)
      • Proportions
    • Spread
      • Population Variance and Population Standard Deviation
      • Sample Variance and Sample Standard Deviation
      • Range
    • Percentiles
      • Empirical Rule
      • Z-Scores
      • Intervals About the Mean

Probability Theory:

  • Resources for this section
    • Study Guide Notes
    • Example Problems and Solutions
    • Extra Practice and Answers
  • Experiments
    • Sample Space
    • Events
    • Venn Diagrams
    • One-Way Contingency Tables
    • Two-Way Contingency Tables
    • Tree Diagrams
    • To Replace or Not to Replace…it is an important question
    • Pigeon Holes
    • How Many Ways and Does Order Matter?
  • Rules of the Game
    • Complementary Events
    • Intersections (AND)
    • Unions (OR)
    • Conditional Probabilities
    • Independent Events
    • Mutually Exclusive Events
    • At Least
    • At Most
  • Games People Play
    • Cards
    • Dice
    • Coins
    • Combined Scenarios

Descriptive Statistics:

  • Resources for this section
    • Study Guide Notes
    • Example Problems and Solutions
    • Extra Practice and Answers
  • Binomial Random Variables
  • Discrete Random Variables
  • Uniform Random Variables
  • Normal Distribution
  • Standard Normal Distribution
  • Sampling Distribution

Inferential Statistics:

  • Resources for this section
    • Study Guide Notes
    • Example Problems and Solutions
    • Extra Practice and Answers
  • Inferences for Means (one sample)
    • One Sample Confidence Interval for Population Mean
    • One Sample Hypothesis Tests for Population Mean
  • Inferences for Means (two samples)
    • Two Sample Confidence Interval for Difference of Populations Means
    • Two Sample Hypothesis Test for Difference of Population Means
    • Two Sample Hypothesis Test for Paired Means
  • Inferences for Means (multiple samples)
    • ANOVA
  • Inferences for Categorical Variables
    • Goodness of Fit
    • Test for Independence
    • Test for Homogeneity

Analysis of Bi-variate Data: Linear Regression

  • Resources for this section
    • Study Guide Notes
    • Example Problems and Solutions
    • Extra Practice and Answers
  • Is There a Connection?
    • Correlation vs. Causation
    • Independent and Dependent Variables
    • Scatter plots
    • Line of Best Fit
    • Residuals
  • Describing the Connection
    • r = Correlation Coeefficceient
    • r2 = Coefficient of Determination
  • Making Predictions
    • Interpolation
    • Extrapolation