MATH 376 -- Spring 2012

Holy Cross Mathematics and Computer Science

Mathematics 376 -- Mathematical Statistics

Syllabus Spring 2012

Professor: John Little
Office: Swords 331
Office Phone: 793-2274
Office Hours: MF 10 - 12 pm, TR 1 - 2 pm, W 3 - 5 pm, and by appointment
Email: little@mathcs.holycross.edu, or jlittle@holycross.edu
Course Homepage: http://mathcs.holycross.edu/~little/ProbStat1112/PS2.html

Course Description

Statistics is the branch of the mathematical sciences that deals with the collection, analysis, and interpretation of data. A typical statistical task is to try to make some inference about a quantity for a whole population based on the data from a random sample where the individual data points are subject to some variability, or randomness. Statistics is used very widely today in the physical, life, social, and management sciences for making decisions and predictions in the presence of uncertainty. Some typical examples are:

Demonstrating evidence for an empirical relationship between different quantities in a physics experiment, where measurement errors or fundamental elements of randomness (e.g. quantum physical effects) may be present,
Analyzing the results of treating patients with a new drug in a clinical trial, where the reaction of an individual patient depends on too many different types of factors to be predictable,
Predicting the outcome of an election by sampling voter preferences (see below for a fuller discussion of this case),
Estimating how to price an insurance policy based on likely risks to the persons covered. (This is a large part of what actuaries do in insurance companies.)

Indeed statistical reasoning is probably the most common use of mathematics in real world applications at present.

This course is a continuation of Probability Theory from the fall semester. This term, we will apply almost all of the concepts from probability that we learned last fall to study

statistical models describing the distributions of characteristics in a population,
estimators for population parameters,
statistical inference -- the process of deriving conclusions about a population from the information contained in a random sample,
procedures for for identifying models describing the population.

The course will be organized as follows:

Unit I: Sampling Distributions -- The Theoretical Basis of Statistics (from Chapter 7 of WMS, about 5 class days)
Unit II: Estimating Population Parameters -- Point Estimators, Interval Estimators and Confidence Intervals (Chapter 8 of WMS, about 11 class days)
Unit III: Properties of Estimators -- efficiency, consistency, sufficiency; Deriving Estimators -- Method of Moments and Method of Maximum Likelihood (Chapter 9 of WMS, about 5 class days)
Unit IV: Hypothesis Testing -- The Rationale and Design of Statistical Tests (Chapter 10 of WMS, about 6 class days)
Unit V: Linear Models and Regression for Parameter Estimation, Basics of Design of Experiments (Chapters 11, 12 of WMS, about 10 class days)

The remaining 2 class days will be devoted to 2 midterm exams (see below for dates). A more detailed day-by-day schedule will be maintained on the course homepage for you to consult as needed.

Course Objectives

The major objectives of the course will be:

To introduce you to the basic topics of sampling distributions, estimation, hypothesis testing, linear models and regression, and some basics of experimental design.
To develop applications of these statistical techniques drawn from various areas of the physical and social sciences.
To look at the implementation of some of these techniques in the R statistical package.
To further develop your problem-solving and proof-writing skills.

Texts

We will continue to use both of the texts from the fall:

Mathematical Statistics with Applications, 7th ed. by D. Wackerly, W. Mendenhall, and R. Scheaffer. We will cover most of the material in Chapters 7-12 this semester, with a few detours back to Chapter 6 as needed.
Introductory Statistics with R, 2nd ed. by P. Dalgaard. We will use this as a reference and a source of examples on the use of the R statistical software package.

Course Assignments and Grading

The assignments for the course will consist of:

Two in-class midterm exams, together worth 40% of the course grade. Tentative dates: Friday, March 16 and Friday, April 27. If the class agrees, these may be given the previous Thursday evening to remove the element of time pressure.
Final examination, worth 25% of the course grade.
Problem sets, worth 20% of the course grade. Notes:
- I will put complete solutions of all assigned problems on reserve in the Science Library after class on the date the assignment is due. You may consult these and photocopy them for your own use at any time if you wish.
- Because of the availability of these complete solutions, because every effort will be made to return your graded problem sets in a timely fashion, and for reasons of fairness, no problem sets will be accepted for credit after the announced due date, except in the case of a verified medical excuse. If you are authorized to hand in a problem set late, I will ask you sign a statement that you have not consulted the reserve solutions in preparing your work.
Group Projects -- Several during the semester we will meet in the HA 136 PC Lab to work in small groups on projects related to the topics we have discussed recently in the course. Each project will lead to a group writeup, together worth 15% of the course grade.

I will be keeping your course average in numerical form throughout the semester, and only converting to a letter for the final course grade. The course grade will be assigned according to the following conversion table (also see Note below):

A -- 94 and above
A- -- 90 - 93
B+ -- 87 - 89
B -- 84 - 86
B- -- 80 - 83
C+ -- 77 - 79
C -- 74 - 76
C- -- 70 - 73
D+ -- 67 -- 69
D -- 60 - 66
F -- 59 and below.

Note: Depending on how the class as a whole is doing, some downward adjustments of the above letter grade boundaries may be made. No upward adjustments will be made, however. (This means, for instance, that an 85 course average would never convert to a letter grade of B- or below. But a 79 course average might convert to a letter grade of B- depending on the distribution of averages across the whole class.)

If you ever have a question about the grading policy, or about your standing in the course, please feel free to consult with me.

Departmental Statement on Academic Integrity

Why is academic integrity important?

All education is a cooperative enterprise between teachers and students. This cooperation works well only when there is trust and mutual respect between everyone involved. One of our main aims as a department is to help students become knowledgeable and sophisticated learners, able to think and work both independently and in concert with their peers. Representing another person's work as your own in any form (plagiarism or ``cheating''), and providing or receiving unauthorized assistance on assignments (collusion) are lapses of academic integrity because they subvert the learning process and show a fundamental lack of respect for the educational enterprise.

How does this apply to our courses?

You will encounter a variety of types of assignments and examination formats in mathematics and computer science courses. For instance, many problem sets in mathematics classes and laboratory assignments in computer science courses are individual assignments. While some faculty members may allow or even encourage discussion among students during work on problem sets, it is the expectation that the solutions submitted by each student will be that student's own work, written up in that student's own words. When consultation with other students or sources other than the textbook occurs, students should identify their co-workers, and/or cite their sources as they would for other writing assignments. Some courses also make use of collaborative assignments; part of the evaluation in that case may be a rating of each individual's contribution to the group effort. Some advanced classes may use take-home examinations, in which case the ground rules will usually allow no collaboration or consultation. In many computer science classes, programming projects are strictly individual assignments; the ground rules do not allow any collaboration or consultation here either.

What are the responsibilities of faculty?

It is the responsibility of faculty in the department to lay out the guidelines to be followed for specific assignments in their classes as clearly and fully as possible, and to offer clarification and advice concerning those guidelines as needed as students work on those assignments. The Department of Mathematics and Computer Science upholds the College's policy on academic honesty. We advise all students taking mathematics or computer science courses to read the statement in the current College catalog carefully and to familiarize themselves with the procedures which may be applied when infractions are determined to have occurred.

What are the responsibilities of students?

A student's main responsibility is to follow the guidelines laid down by the instructor of the course. If there is some point about the expectations for an assignment that is not clear, the student is responsible for seeking clarification. If such clarification is not immediately available, students should err on the side of caution and follow the strictest possible interpretation of the guidelines they have been given. It is also a student's responsibility to protect his/her own work to prevent unauthorized use of exam papers, problem solutions, computer accounts and files, scratch paper, and any other materials used in carrying out an assignment. We expect students to have the integrity to say ``no'' to requests for assistance from other students when offering that assistance would violate the guidelines for an assignment.

Specific Guidelines for this Course

For this course, examinations will be given in class, and the other assignments will be weekly individual problem sets and group projects. As was the case last semester, I will let you bring formula notecards/sheets to the exams. No unauthorized access to information other than what is contained in these sheets, sharing of information of any form with other students, copying of others' work, etc. will be permitted during exams. On the problem sets, discussion of the questions with other students in the class, and with me during office hours is allowed, even encouraged. If you do take advantage of these options, you will be required to state that fact in a "footnote" accompanying the problem solution. Failure to follow this rule will be treated as a violation of the College's Academic Integrity policy. The group projects are entirely collaborative assignments and close consultation with your group is expected.