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Mathematical Statistics II


Course Description

Introduction to the fundamentals of statistical inference. Point estimation, including the properties of estimators and ways of evaluating or comparing them, confidence intervals, and hypothesis testing. Statistical inference in linear models, including regression and analysis of variance, is also discussed.


Athena Title

Mathematical Statistics II


Semester Course Offered

Offered spring


Grading System

A - F (Traditional)


Student Learning Outcomes

  • Students will learn about statistical inference from a variety of perspectives, including point and interval estimation, and hypothesis testing.
  • Students will learn how to derive estimators and tests for some common situations (comparing two or more means, comparing two proportions), as well as ways of evaluating the statistical properties of the procedures in question.
  • Students will be introduced to the linear regression model. Simple experimental design, and models for analyzing those designs, will also be considered.
  • Students will learn how to use specific statistical methods and general modes of statistical thinking to make inferences from data, and to support (or refute) an argument or point of view with quantitative information.
  • Students will learn the mathematical and probabilistic underpinnings of statistical theory, they will develop an understanding of the underlying rationale for specific statistical methods, and they will learn how to assess the relative merits and applicability of competing statistical techniques.

Topical Outline

  • Point estimation
  • confidence intervals
  • properties of estimators, including unbiasedness, consistency, sufficiency and efficiency
  • methods of estimation including method of moments, maximum likelihood and least squares
  • hypothesis testing, including Neyman-Pearson tests, uniformly most powerful tests, likelihood ratio and other large sample tests
  • relationship between hypothesis testing and interval estimation
  • estimation and testing in one- and two-sample problems
  • linear models and least squares
  • analysis of variance and simple experimental designs

Syllabus