**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. |

**Course Objectives:** | This course is a continuation of 4/6510, Mathematical Statistics I. Using the
concepts of probability and distribution developed in that course, 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. |