Math 218, Mathematical Statistics
Spring 2009 D Joyce BP 322, 793-7421. Department of Mathematics and Computer Science Clark University |

[This course page is obsolete. I'll make another when I teach the course again.]General information

**Office hours. Semester schedule****Course Hours:**MWF 11, BP 316**Description of this course:**The emphasis of this course is to develop the fundamental statistical concepts of inference and hypothesis testing from a classical perspective using the tools of probability theory. Topics investigated include sampling and sample distributions, graphical data analysis, point and interval estimation, hypothesis testing and an introduction to Bayesian inference.**Prerequisite:**Math 217, Econ 260, or permission.See also Clark's

*Academic Catalog***Textbook:***Statistics and Data Analysis*by Ajit C. Tamhane and Dorothy D. Dunlop, Prentice-Hall, 2000. ISBN 0-13-744426-5. Prentice-Hall's web site for the book.**Course goals.**- To provide students with a good understanding of the theory of statistics as described in the syllabus.
- To show how statistical methods depend on the theoretical principles of probability.
- To illustrate the use of statistics in science, both physical and social science
- To examine the assumptions of statistical methods.
- To make connections between statistics and other branches of mathematics, and to see some of the history of statistics.

**Syllabus****Assignments, quizzes, tests, final:**There will be numerous short assignments, mostly from the text, occasional quizzes, two tests during the semester, and a two-hour final exam during finals week.Practice problems will be assigned daily from the text to help you master the concepts discussed in class. Periodically, problems will be assigned to be turned in and graded. Although not all practice problems will be submitted for a grade, it is expected that you will keep up to date on the problems. Collected homework is due in class on the assigned day. No late assignments will be accepted.

Tests are closed notebook, but you may bring one sheet of notes and a calculator. In the event that an emergency arises, you are responsible to contact me before the regularly scheduled exam to make alternative arrangements.

- The course grade will be determined as follows:
2/9 assignments and quizzes,
2/9 each of the two midterms, and
1/3 for the final exam.
- Math 217 class notes from Fall 2007

Math 218 class notes from Spring 2008

(This part of the course page will be constantly updated.)

- Monday, Jan. 12. Welcome! Discussion of statistics (Chapter 1).

Summary of basic probability theory, part 1. - Wednesday, Jan. 14. We'll review some high points of probability
theory (Chapter 2). The purpose of this review is just to explain what
I assume you already know. We'll start the summary today and continue
it later.

Summary of basic probability theory, part 2. - Friday, Jan. 16. Notes.

Begin a discussion of collecting data: types of statistical studies, control groups in a comparative study, sample surveys, prospective and retrospective studies, basic sampling designs, simple and other kinds of random sampling. (Chapter 3) - Monday, Jan. 19. No class. Martin Luther King day.
- Wednesday, Jan. 21.

Common probability distributions and a summary table for them. See also the Gallery of distributions at http://www.itl.nist.gov/div898/handbook/eda/section3/eda366.htm. - Friday, Jan. 23. Notes.

Experimental studies.

Exercises due from page 101, exercises 1, 3, 4, 7, 8, 9, 12, 13, 15. - Monday, Jan. 26. Notes.

Survey of the chapter on summarizing and exploring data.

Normal probablility plot

Exercises due from page 105, exercises 19, 20. - Wednesday, Jan. 28. Notes.

Distribution of the sample mean, central limit theorem, approximation of the binomial distribution by a normal distribution. - Friday, Jan. 30. Notes.

Sample variance, the chi^{2}distribution, the gamma function. - Monday, Feb. 2. Notes.

Exercises due: From chap. 5, p. 189, exercises 4, 5, 8, 14. - Wednesday, Feb. 4.
Student's
*t*distribution and Snedecor-Fisher's*F*distribution.

Due: From chap. 5, p. 191, exercises 16, 17, 23. - Friday, Feb. 6. Notes.

Inferences about parameters based on data from a sample. - Monday, Feb. 9. Notes.

Maximum likelihood estimators for discrete distributions.

Exercises due: From page 229, exercises 1, 2ab, 5, 7. - Wednesday, Feb. 11.
Maximum likelihood estimators for continuous distributions.

Introduce confidence intervals. Notes.

Exercises due: From page 658, exercises 1, 3. - Friday, Feb. 13.
Notes.

More on confidence intervals. - Monday, Feb. 16.
Introduce hypothesis tests.

Exercises due: From page 230: 11, 13a, 14, 15ab. - Wednesday, Feb.18. Notes.

More on hypothesis tests.

Review. - Friday, Feb. 20. First test up through Chapter 5.
- Monday, Feb. 23. Notes.

Normal sample with known variance, any large sample:*z*-confidence intervals and hypothesis tests, hypothesis tests for the mean. - Wednesday, Feb. 25. Notes.

Small normal sample:*t*-distribution.

Due: From chap. 6, p. 231, exercises 17-20, 22. - Friday, Feb. 27. Notes.

Inferences on variances. Chi^{2}-intervals and tests.

Spring break.

- Monday, Mar 9. Notes.

Inferences for two samples.

Due: From chap. 7, p. 262, exercises 1, 2, 9, 11, 12. - Wednesday, Mar. 11. Notes.

Inferences with matched pairs design.

Summary of basic probability theory, part 3.

Vardeman's directions for creating a normal plot in Excel - Friday, Mar. 13. Notes.

Inferences for proportions and count data.

Due: From chap. 7, p. 265, exercises 17, 18, 19. - Monday, Mar. 16. Notes.

Inferences for comparing two proportions. Introduction to the method of least squares.

Due: From chap. 8, p. 290, exercises 1, 2, 3, 9. - Wednesday, Mar. 18. Notes.

The model for simple linear regression and its analysis. - Friday, Mar. 20. Notes.

Estimating the error variance σ^{2}of the model. Statistical inferences based on the model.

Due: From chapter 8, exercise 14, and from Chapter 9, exercises 1--3, 6. - Monday, Mar. 23. Review.
- Wednesday, Mar. 25. Second test on chapters 6—9. Answers.
- Friday, Mar. 27.
Notes.

Confidence and prediction intervals for simple linear regression, regression diagnostics. - Monday, Mar. 30.

Student presentations from chapter 10. - Wednesday, Apr. 1.
Notes.

Introduction to multiple linear regression. - Friday, Apr. 3.

Vectors and matrices. The multiple linear regression model in the notation of linear algebra. - Monday, Apr. 6. Class cancelled.
- Wednesday, Apr. 8.

Student presentations from chapter 10. - Friday, Apr. 10.

More on multiple linear regression, intervals and hypothesis tests. - Monday, Apr. 13. Notes.

Introduction to Bayesian statistics, the Bernoulli process. - Wednesday, Apr. 15. Notes.

Student presentations on exercises from chapter 11.

Bayes' pool table example. Conjugate prior families of distributions - Friday, Apr. 17.

Student presentations on exercises from chapter 11.

Bayesian point estimators and probability intervals. - Monday, Apr. 20. Notes.

Bayesian statistics for the Poisson process. - Wednesday, Apr. 22. Notes.

Bayesian statistics for normal distributions with known variances. - Friday, Apr. 24. Notes.

Bayesian statistics for normal distributions with unknown variances. - Take home final exam

This page is located on the web at

http://aleph0.clarku.edu/~djoyce/ma218/