TUFTS UNIVERSITY

Description:
This course is intended to introduce you to some basic statistical concepts that are useful in business, in economics, and in the other social sciences. The course develops statistical and mathematical techniques for analyzing random phenomena that arise in economics and business. Specific topics will include probability theory, sampling theory, estimation, hypothesis testing, and linear regression.

Prerequisites: Economics 5 or its equivalent; Mathematics 32 or its equivalent.

Textbook (required):
Sheldon M. Ross, Introductory Statistics, 4th Edition (Burlington, MA: Elsevier Academic Press, 2017) - all readings listed below are in the text.

The text is available at the bookstore; just click the Purchase Course materials link in Canvas.

Several times in the semester, we will supplement the material from the textbook with material from the on line resource Lectures on Probability, Statistics, and Econometrics .  Links to the relevant material are provided in the syllabus.

Statistical Package (optional):
Stata/IC 16 (for Windows, Mac, or Linux) - Stata Corporation. You can order Stata/IC 16 with a sixth-month or a one-year license and a copy of the Getting Started at http://www.stata.com/order/new/edu/gradplans/student-pricing/. You will be sent an e-mail letting you know when the software is available for you to pick up.

The Stata software package is also on many of the machines in the public-access computer labs on campus. You do not need to buy the Stata/IC package; doing so may make completing some of the problem sets easier.

Graded Work:
1. Two term exams, each worth 22.5% of the grade. The first term exam will be given on October 15 and will cover the material on the first three sections of the reading list (through Chapter 4 in the text). The second term exam will be given on November 25 and will cover the material on the next four sections of the reading list (through Chapter 7 in the text).

2. Nine problem sets worth 15% of the grade. The due dates for the problem sets will be indicated on each problem set and will be announced in class. The problem sets will involve both assigned problems and computer exercises. No late problem sets will be accepted.  You are strongly encouraged to collaborate in planning and thinking through solutions, but you must write up your own solutions without checking over your written solutions with another student.  Do not pass solutions to problem sets nor accept them from another student.  If you are ever in doubt, ask for clarification on what is and is not appropriate.

3. Final exam on Tuesday, December 17 at 3:30 PM worth 40%. The final exam will cover all of the material in the course, with emphasis on the material after the second midterm.

Accommodations for Students with Disabilities: Tufts University values the diversity of our students, staff, and faculty, recognizing the important contribution each student makes to our unique community.  Tufts is committed to providing equal access and support to all qualified students through the provision of reasonable accommodations so that each student may fully participate in the Tufts experience. If you have a disability that requires reasonable accommodations, please contact the Student Accessibility Services office at Accessibility@tufts.edu or 617-627-4539 to make an appointment with an SAS representative to determine appropriate accommodations. Please be aware that accommodations cannot be enacted retroactively, making timeliness a critical aspect for their provision.

General comment: The only way to learn statistics is to work problems. Simply completing the problems on the problem sets is not enough. The problem sets include none of the exercises in the text. Solutions for the even-numbered exercises are in the back of the text. You should work as many of these exercises as you can. You should also work as many of the odd-numbered problems as you can. The solutions manual for the text is available in my office; it contains solutions for all of the problems (both even and odd). If you want to check an answer or if you are not sure how to solve a particular unassigned problem, please feel free to ask about the relevant problem during my office hours.

Class meetings: All of the class sessions will meet in Braker 1. The recitation sessions will meet both in their regularly scheduled classroom (Braker 113, Braker 118, Braker 223, or Braker 225) and in the computer lab in Eaton 208. The computer lab in Eaton 208 is at directly across the hall from the main lab in Eaton.  I will announce (in class on Monday and by e-mail) if the week's recitation sessions are in the classroom or the computer lab. The first recitation sessions in the computer lab will be on Thursday, September 12 and Friday, September 13.

Course Outline and Assignments:
The schedule is tentative. Any adjustments to the schedule will be announced in class.

I. Introduction
September 4 - Chapter 1

II. Descriptive Statistics
September 4 - Secs. 3.1 - 3.4
September 9 - Secs. 3.5, 3.6, 2.2, 2.4
September 11- Sec. 2.3
September 16 - Secs. 2.5, 3.7, 12.1 - 12.3

III. Basics of Probability: Axioms of Probability, Counting, and Bayes' Theorem
September 18 - Secs. 4.1, 4.2
September 23 - Sec. 4.3
September 25 - Secs. 4.4, 4.7
September 30 - Sec. 4.5
October 2 - Sec. 4.6

October 15 - FIRST TERM EXAM

IV. Random Variables
October 7 - Secs. 5.1, 5.2, pp. 233-235 and Conditional Probability Distributions from Lectures on Probability, Statistics, and Econometrics
October 9 - Secs. 5.3 and Conditional Expectation from Lectures on Probability, Statistics, and Econometrics
October 16 - Secs. 5.4, 5.5.1, and Independent random variables from Lectures on Probability, Statistics, and Econometrics

V. Special Discrete Distributions
October 21 - Sec. 5.6
October 23 - Secs. 5.7, 5.8

VI. Continuous Distributions
October 28 - Secs. 6.1, 6.2
October 30 - Secs. 6.3 - 6.7

VIII. The Central Limit Theorem and Distributions of Statistics
November 4 - Secs. 7.1 - 7.4
November 6 - Sec. 7.5, 7.6

November 25 - SECOND TERM EXAM

IX. Estimation
November 13 - Secs. 8.1 - 8.4, 12.3 and  Point Estimation from Lectures on Probability, Statistics, and Econometrics
November 18 - Secs. 8.5 - 8.7
November 20 - Secs. 10.4, 12.3

X. Hypothesis Testing
December 2 - Secs. 9.1 - 9.3
December 4 - Secs. 9.4, 9.5
December 9 - Secs. 10.1 - 10.4, 12.4 - 12.5

December 17 - FINAL EXAM