Stat 427 Mathematical Statistics Spring 2006

Instructor: Allan Rossman
Class Times: MTuWTh 10:10-11:00am, room 33-287
Office: Faculty Office Building East 25-102
Phone: 756-2861 (6-2861 on campus)
Email: arossman@calpoly.edu
Office Hours: Mondays-Thursdays 3:10-4:30, and by appointment and by chance
Text: Probability and Statistics (3rd edition), by Morris H. DeGroot and Mark J. Schervish

Course Webpage: http://statweb.calpoly.edu/rossman/stat427/

Overview: This course continues your study of the foundations of statistical inference, focusing on the important concept of testing. We will begin by considering the basic concepts of hypothesis testing, proceeding to important ideas such as likelihood ratio tests and uniformly most powerful tests. Then we will move to studying nonparameteric tests, including chi-square tests. Then we will conclude by studying basic ideas and methods of decision theory.

Goals: By the conclusion of the course, I hope that you have improved your ability to:

• understand concepts of hypothesis testing and decision theory
• derive and prove results in these areas
• apply probability and statistical methods to solve problems
• use the computer to investigate statistical phenomena
• communicate your knowledge of statistical ideas effectively

Class Policies: I expect class meetings to be fairly informal. Often I will present new material, and at times I will ask you to work on problems or activities. I strongly encourage you to bring questions to class and to interrupt me with questions as they occur to you.

Please come prepared to participate in class. By this I primarily mean two things:

• Please read relevant sections of the text before coming to class. Read carefully, and come to class with questions on what you do not understand.
• Please be willing (or, even better, eager!) to ask questions and contribute answers and work on problems (when I ask you to) during class.

I also expect you to devote 8-12 hours per week, outside of class time, to your work for this course. I anticipate that this work will be divided among:

• reading the textbook
• reviewing your class notes
• working on assignments
• preparing for exams

Naturally, you should expect me to prepare for class and to devote substantial time to the course outside of class as well.

Grading Policies: Your course grade will be determined by the following components, with relative weights as indicated:

• homework assignments (30%)
• two midterm exams (20% each)
• final exam (30%)

Assignments: Homework assignments will be made roughly weekly. You are encouraged to discuss homework problems with each other, but your solutions must be written up individually in your own words. I urge you to ask questions about these problems (ahead of time!) inside and outside of class. Many of the homework problems will be taken from the text. Be aware that answers to many odd-numbered questions appear in the back of the book, but of course you will be graded on your method of solution and clarity of explanation. Assignments are due at 4pm on the indicated day. Late assignments will not be accepted, except that you may have one 24-hour extension on a due date.

The purposes of these homework and investigation assignments are:

• to give you the practice with proof and problem-solving techniques in order to learn, understand, and apply the course material,
• to provide you with feedback regarding your understanding of the material,
• to further your discovery and exploration of course material,
• to improve your abilities to communicate well and to use computing, and
• to prepare you for the kinds of questions that will be on the exams.

Exams: You will received detailed guidelines regarding the exams a week or so in advance. They will be open-book and open-notes, and they will involve both in-class and take-home components. The final exam will focus on more recent material but will also have a cumulative component. You may make up an exam only with a written medical excuse.

Advice: With apologies to David Letterman, I offer the following "Top Ten" suggestions to improve your learning in this course:

• Come to class.
• Participate in class.
• Invest time outside of class.
• Read carefully.
• Ask questions.
• Use office hours.
• Start the assignments early.
• Work together.
• Write well.
• Think!

A common theme emerges from this list: You are responsible for your own learning. As your instructor, I view my role as providing you with contexts and opportunities that facilitate the learning process. Please call on me to help you with this learning in whatever ways I can.

Tentative Schedule: The following is always subject to change but should give you a sense for what topics we will cover and when:

Week	Dates	Topics	Sections from Text
1	March 27-30	Testing Simple Hypotheses, Uniformly Most Powerful Tests	8.2, 8.3
2	April 3-6	Two-Sided Alternatives, t-Tests	8.4, 8.5
3	April 10-13	Comparing Means of Two Normal Distributions, F-Distribution	8.6, 8.7
4	April 17-20	Exam, Goodness-of-Fit Tests	9.1, 9.2
5	April 24-27	Contingency Tables, Tests of Homogeneity	9.3, 9.4
6	May 1-4	Simpson’s Paradox, Kolmogorov-Smirnov Tests	9.5, 9.6
7	May 8-11	Sign and Rank Tests, Exam	9.8
8	May 15-18	Randomization and Permutation Tests, Bootstrapping	Notes
9	May 22-25	Decision Theory	Notes
10	May 30 – June 1	Expected Value of Sample Information	Notes
	Thursday, June 8, 10:10-1:00	Final Exam

Disclaimer: All of these details are subject to change as the course develops. I welcome and value your input.