Math 207: Introduction to Probability and Statistics – Fall Term, 2009

Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write.

— H.G. Wells (1866 – 1946)

Course Goals

In general, a statistics course teaches you to both descriptively and inferentially explain the variation that occurs in real data. Upon completion of this course, you should know how to (among other things)

· Graphically, numerically, and verbally describe single variables and relationships between variables

· Model single variable distributions (via the binomial, hypergeometric, Poisson, or normal distributions) and model linear relationships between quantitative variables (via regression)

· Collect data appropriate for your research question and with no (or limited) bias

· Understand and apply the rules and definitions of probability, and use counting rules to determine probabilities

· Understand and work with the sampling distributions of common statistics

· Use sampling distributions of appropriate statistics to make inference about population values (via significance testing and confidence intervals)

• Understand the general concept of inference, as well as its limitations
• Effectively communicate the method and results of any statistical analysis
• Realize that statistical analysis is important, applicable, rich, interesting (and fun!)

Professor Contact Information

Joy Jordan, Associate Professor of Statistics, 410 Briggs Hall

PHONE: 832-6894, EMAIL: joy.jordan@lawrence.edu, WEB: www.lawrence.edu/fast/jordanj/

Please note the URL for my homepage. On this page is a link to the Math 207 web page, where I will post homework assignments, solutions, handouts, etc. (bookmark the Math 207 class page, as you will visit it often). I check email regularly (2-3 times a day), but not obsessively. If you need to contact me urgently (e.g., you have a family emergency, you want to make an appointment as soon as possible), then please call me.

Required Textbook

Introduction to Probability and Statistics, 12^th Edition, Mendenhall, Beaver, and Beaver, 2006, Brooks/Cole

There is a new (13^th) edition of this textbook, but in an effort to keep costs down for you, we are using the 12^th edition of the book (that is, used copies should be easy to find). Also, a copy of the textbook is on 2-hour reserve at the library.

Office Hours

Monday: 3:00 – 4:30, Tuesday: 1:30 –2:30, Wednesday: 8:30 – 9:30, Thursday: 1:30 – 3:00

If these times do not work with your particular class schedule, I am happy to make individual appointments for other times. (You need not make an appointment during regular office hours—just come in.) Please ask if you need help, and I will do all I can to assist you. That said, I expect you to come to office hours prepared (e.g., having done the reading, knowing the definitions) and not simply looking for easy answers. Besides office hours, anytime my door is open, feel free to come in and ask questions. If my door is closed, I am either out of the office, or I’m working and prefer not to be disturbed.

Homework

Homework assignments will be given most weeks and due on Fridays (see attached course schedule). No late homework assignments will be accepted (unless you have cleared things with me in advance). After the due date, I will provide written solutions to all of the problems (they will be posted on the course web page). My homework solutions should be thought of as required reading for the course, since certain (small) topics may be illustrated through homework problems rather than lecture. Your homework assignments will be graded on both content and exposition. More explicit homework expectations will be given with the first assignment.

Quizzes

An announced quiz will be given on some Wednesdays (see attached course schedule). This will be an in-class quiz (given at the beginning of class) that will take about 20 minutes to finish. The quizzes are designed to regularly gauge your understanding and to serve as a motivational study aid. Quizzes will cover the major topics of the week, and will include questions requiring both problem solving and explanation. There will be no make-up quizzes, except for excused absences.

Computer Lab (Briggs 421)

The weekly computer lab should be thought of as an extension of the lecture, and new material will sometimes be presented in lab. The lab session will be used to investigate and interpret real data (using statistical software). A lab syllabus will be given on the first day of lab (9/22 or 9/24, depending on your section).

Exams

There will be two in-class exams during the term and a final exam. The first exam will be Wednesday, October 14 and the second exam will be Monday, November 9. The cumulative final exam will be Tuesday, November 24 at 1:30 p.m.

Study Tips

Before starting a homework assignment, it’s vitally important you first understand the concepts and definitions. Read the textbook and class notes carefully before starting an assignment (and ask me if you have questions). Also, students often say they understand individual concepts, yet they get easily confused when reading a new problem and deciding which method to apply. In preparation for an exam, you should obviously do many practice problems. To make these problems more like exam problems (where you’re not sure what section they’re from), you can do end-of-chapter problems and/or you can create your own practice test by retyping homework, lecture, and quiz problems into Word, and then randomly arranging the problems. Furthermore, be sure you can carefully explain each step of your answer—this ensures you understand the whole solution process (rather than simply memorizing specific situations).

Grading

Your final grade is based on a weighting of quizzes (10%), homework (10%), and exams (first exam – 25%, second exam – 20%, final exam – 35%). The letter grades will be assigned as follows, corresponding to Lawrence’s GPA system (note: the cutoff is the lowest percentage that receives that letter grade):

Cutoff	Grade
93.75	A
90.00	A-
86.25	B+
83.75	B
80.00	B-
76.25	C+
73.75	C
70.00	C-
66.25	D+
63.75	D
60.00	D-

Class Atmosphere and Life Balance

Even though this is a large class, I strongly encourage questions from students, responses to my queries, and lively discussion. You are warmly welcome to participate in class, regardless of whether you have the “right” answer. Please join the conversation.

Because I love statistics so much, I will encourage you to work hard to learn the material. But please realize that your self-worth is not associated with your letter grade on a particular quiz or exam (or even with your final course grade). You are all good people, regardless of your official class performance on tasks.

Furthermore, I think as a society in general, and at Lawrence in particular, we are over-scheduled and allow precious little downtime and quiet reflection. I encourage you to think carefully about the intensity and number of courses, activities, and obligations in your life, and to seek balance as much as possible. (I’m happy to talk with you more about this—that is, we can discuss life as well as statistics.)

Tentative Course Schedule (with corresponding textbook reading and notice of supplementary material)

Date	General Material	Corresponding Reading
M 9/14	Introduction to the course and topics	Introduction, Chapters 1 and 2
W 9/16	One-variable analysis – graphs, interpretation, numerical summaries, relative standing (working in groups on problems)	Chapters 1 and 2
F 9/18	Discuss problems from Wednesday and start scatterplots	Chapters 1, 2, and 3
M 9/21	Two-variable analysis – scatterplots, correlation, regression analysis (supplementary material presented in lecture)	Chapter 3
W 9/23	Quiz 1, and regression analysis and diagnostics (supplementary material presented in lecture)	Chapter 3
F 9/25	Probability definitions axioms, propositions, and proofs (supplementary material presented in lecture); HW 1 due	Sections 4.1 – 4.3, 4.5
M 9/28	Finish proofs and start counting rules	Section 4.4
W 9/30	Quiz 2 and counting rules	Section 4.4
F 10/2	Counting rules, conditional probability, and independence; HW 2 Due	Section 4.6
M 10/5	Conditional probability and Bayes’ rule (using tree diagrams)	Sections 4.6 – 4.7
W 10/7	Quiz 3, general discrete distributions, and expected value	Section 4.8
F 10/9	Binomial, hypergeometric, and Poisson distributions; HW 3 Due	Chapter 5
M 10/12	Catch-up and exam review
W 10/14	Exam 1 (Chapters 1 – 5)	Reread Chapters 1 – 5
F 10/16	Normal distribution and general sampling distributions (Sections 7.1 – 7.2 covered in lab this week)	Sections 6.1 – 6.3, 7.1 – 7.3
M 10/19	General sampling distributions and sampling distributions of an average and total	Sections 7.3 – 7.5
W 10/21	Quiz 4 and sampling distributions of an average and total	Sections 7.4 – 7.5
F 10/23	No class – Reading Period
M 10/26	Sampling distributions of averages and totals in the binomial setting (normal approximation in the binomial setting)	Sections 6.4, 7.6
W 10/28	Confidence interval for a population mean	Sections 8.1 – 8.5
F 10/30	Confidence interval for a population proportion, difference in means, and difference in proportions; HW 4 Due	Sections 8.5 – 8.7
M 11/2	Sample-size determination and significance test for a population mean	Sections 8.9, 9.1 – 9.3
W 11/4	Quiz 5 and significance test for a population mean (Power of a statistical test covered in lab this week)	Sections 9.1 – 9.3
F 11/6	Significance test for a population mean, power, and review; HW 5 Due	Sections 9.1 – 9.3
M 11/9	Exam 2 (Chapters 6 – 9.3)	Reread Chapters 6 – 9.3
W 11/11	Significance test for a difference in population means (and relationship to confidence intervals), practical significance, significance test for a difference in proportions	Sections 9.4, 9.6, 9.7
F 11/13	T-distribution and small sample inference (one-sample); HW 6 Due	Sections 10.1 – 10.3
M 11/16	Small sample inference (paired and two-sample)	Sections 10.4 – 10.5
T 11/24	Exam 3 (Chapters 1—10) – 1:30pm	Reread Chapters 1 – 10