## STAT-332 Probability & Mathematical Statistics II

Mathematics, Statistics & Computer Science Department

COURSE NO./TITLE: STAT-332 (354-332) Probability & Mathematical Statistics II

CREDIT: 3

COURSE DESCRIPTION: Point estimation. Properties of point estimators: unbiasedness, efficiency, consistency, sufficiency. The method of maximum likelihood. Basic concepts of interval estimation and hypothesis testing. Inference in one-sample and two-sample problems. Simple linear regression analysis; the method of least squares. Goodness-of-fit tests. Analysis of categorical data.

Prerequisites: STAT-331.

TEXTBOOK:

• Intro to Mathematical Statistics & Its Applications, 4th Ed., by Marx (F07) (Adopted 8/01: Introduction to Mathematical Statistics & Its Applications, 3rd Ed. by Marx
• (Prior to Fall 01: Probability & Statistical Inference, 5th Ed., by Hogg & Tanis)
• (Prior to Spring 98: Mathematical Statistics & Data Analysis, 2nd Ed., by Rice)
• (Prior to Fall 95: Introduction to Mathematic Statistics, 2nd Ed., by Larsen)

COURSE OBJECTIVES: The course will enable students to:

1. Appreciate the importance of statistical inference in science and technology.
2. Apply the methods of statistical inference: estimation and hypothesis testing.
3. Demonstrate skills by problem solving and the writing of clear, complete, logically correct solutions.
4. Use a statistical computing package such as SPSS or STATGRAPHICS.

COURSE OUTLINE:

1. Estimation
A. Concepts of Point Estimation
B. Properties of Estimators
C. Minimum Variance Estimators
D. The Method of Maximum Likelihood & The Method of Moments
E. Interval Estimation
2. Hypothesis Testing
A. Concepts of Hypothesis Testing
B. Optimal Tests
3. One-Sample Problems
A. Inference About the Mean & Variance in a Normal Distribution
B. The Central Limit Theorem
C. Inference About a Proportion
4. Two-Sample Problems
A. The Two-Sample t-test for Equality of Means
B. The F-test for Equality of Variance
C. The Two-Sample Test for Equality of Proportions
D. Confidence Intervals for the Two-Sample Problem
5. Simple Linear Regression Analysis
A. The Method of Least Squares
B. Inferences for the Regression Parameters
6. Introduction to some or all of the following topics (as time permits):
A. Goodness-of-Fit Tests
B. Analysis of Categorical Data
C. Analysis of Variance
D. Nonparametric Inference
E. Bayesian Inference Revised 6/08