Welcome to MATH 476 Statistics

Spring 2026

Course Description

Estimation theory; hypothesis tests; confidence intervals; goodness-of-fit tests; correlation and linear regression; analysis of variance; non-parametric methods

Instructor: Fred J. Hickernell

Fred J. Hickernell

Brief bio: Fred J. Hickernell is professor of applied mathematics. His research focuses on improving the efficiency of computer simulations and developing justifiable stopping criteria. He has spent most of his career at Hong Kong Baptist University and Illinois Institute of Technology, often in academic administrative roles. He has served on the editorial boards of the Journal of Complexity, Mathematics of Computation, and the SIAM Journal on Numerical Analysis. He is a Fellow of the Institute of Mathematical Statistics and the recipient of the 2016 Joseph F. Traub Prize for Achievement in Information-Based Complexity.

Hickernell speaks Cantonese and enjoys Chinese food. He is married with adult children. He enjoys discussing matters of substance. His most important identity is a disciple of Jesus.
Teaching Assistant: Sam Mei

Textbook: D. S. Wackerly, W. Mendenhall III, & R. L. Scheaffer, Mathematical Statistics with Applications, 7th ed (2008)

Recommended resources
Prerequisites
  • Multivariate calculus
  • Linear algebra
  • Calculus-based probability
  • Comfortable with code
Objectives

You will learn

  • The concept of statistical inference and the difference between population characteristics and sample estimate;
  • The probabilistic basis for statistical inference and the qualities of a good estimator;
  • How to correctly perform hypothesis tests and construct confidence intervals;
  • How to fit proper linear models; and
  • How to use statistical software—primarily Python or R—to facilitate the calculations involved.
Where to find it
This course website Canvas
Big Questions Grades
Schedule Assignments and Submissions
Jupyter Notebooks Announcements
Homework Discussions
Tests and Exams
Policies

Course Outline

Introduction
  • What is statistical inference?
  • Review of probability
    • Random variables and their distributions
    • Populations and samples
    • Sample statistics
Estimates of Population Parameters
  • Bias of estimates
  • Confidence intervals
  • Relative efficiency, consistency and sufficiency
  • Minimum variance unbiased estimation
  • Moment Estimators
  • Maximum Likelihood Estimates
Hypothesis Testing
  • Common tests for means and variances
  • Relationship between hypothesis tests and confidence intervals
  • Power of tests
  • Likelihood ratio tests
  • Comparison of more than two means
  • Analysis of categorical data
Linear Models and Least Squares
  • Linear Model
  • Method of Least Squares
  • Inferences concerning regression coefficients
  • Hypothesis testing and model selection
  • Correlation
Nonparametric Statistics
  • Matched pairs of experiments
  • Comparison of two populations
  • Comparison of more than two populations

Assessment

  • Homework: 15% (will drop the lowest 2 homework scores)

  • Midterm Tests: 25% (2/3 times best score + 1/3 times second best score)

  • Project: 20% (see project page for details)

  • Final Exam: 40%

  • Extra Credit: up to 10%
    Beginning January 20, if you are the first to find an error in

    • My lecture slides, Jupyter Notebooks, or assignments at least 24 hours after I have presented them in class, or
    • The textbook,

    Then I will award you 0.5 or 1 extra credit points, up to a maximum of 10 points.  

    For course materials hosted on GitHub, you may submit a pull request correcting the error. Alternatively, you may report the error by email with sufficient detail. Extra credit points are added to your final weighted total. Note that the weighted total may not correctly reflect the extra credit until grades are recorded for all categories.