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/SE 16 (for Windows, Mac, or Linux) - Stata Corporation. Tufts has an Enterprise license for Stata, so you can download and install Stata for free. More details about Stata including features and how to access the software can be found on the Stata product page on AccessTufts. Choose the version of Stata that is right for your operating system and follow the installation instructions on the page.

The Stata software package is also on many of the machines in the public-access computer labs on campus. In addition, you can access STATA through the Tufts Virtual Lab (instructions below).

To access STATA anytime/anywhere using the Tufts Virtual lab:
• Go to: https://access.tufts.edu/software/tts-virtual-lab-vdi
• Click on the orange Open box to access Tufts Virtual Lab.
• Click on HTML on the right to open this virtual desktop in your browser.
• Login with your credentials and then double click TTS Virtual Lab.
• This will make your screen look like you are sitting at a lab computer. (If you use a Mac, this will make your computer look like a PC.)
• When you first get into the lab computer, be sure to log in to Box. You'll be prompted to do that. You can then save your work to your Box folder.
• To access STATA, open the list of programs from the bottom right and find STATA/IC 16.
• To access the course website from the virtual lab, open any web browser platform.
• You can also select to Install VMWare Horizon Client to your desktop. This will give you a virtual lab icon you can click whenever you want to access the virtual lab. If you do this, enter “vdi.it.tufts.edu” as the server when asked.
• When saving your files in the virtual lab, you must save them to your storage account on Box, which you can access here: https://access.tufts.edu/box

Graded Work:
1. Two term exams, each worth 22.5% of the grade. The first term exam will be given on October 14 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 18 and will cover the material on the next four sections of the reading list (through Chapter 7 in the text).

2. There will be weekly problem sets worth 15% of the grade. The due dates for the problem sets will be indicated on each problem set, with the first problem set due on September 16. The problem sets will involve both assigned problems and computer exercises.

All problem sets are available in the Assignments area of Canvas. All problem sets must be submitted online through Canvas. No late problem sets will be accepted and all problem sets must be submitted online in Canvas.  Adobe Scan and Microsoft Lens (for Android) are good options for scanning your problem sets, but feel free to use whatever app is easiest for you.

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 Friday, December 18 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.

Academic Integrity: Tufts holds its students strictly accountable for adherence to academic integrity. The consequences for violations can be severe. It is critical that you understand the requirements of ethical behavior and academic work as described in Tufts’ Academic Integrity handbook. If you ever have a question about the expectations concerning a particular assignment or project in this course, be sure to ask me for clarification. The Faculty of the School of Arts and Sciences and the School of Engineering are required to report suspected cases of academic integrity violations to the Dean of Student Affairs Office. If I suspect that you have cheated or plagiarized in this class, I must report the situation to the dean.

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.

Academic Support at the StAAR Center: The StAAR Center (formerly the Academic Resource Center and Student Accessibility Services) offers a variety of resources to all students (both undergraduate and graduate) in the Schools of Arts and Sciences, and Engineering, the SMFA, and The Fletcher School; services are free to all enrolled students. Students may make an appointment to work on any writing-related project or assignment, attend subject tutoring in a variety of disciplines, or meet with an academic coach to hone fundamental academic skills like time management or overcoming procrastination. Students can make an appointment for any of these services by visiting go.tufts.edu/TutorFinder, or by visiting go.tufts.edu/StAARCenter.

Policy on sharing. This course is designed for everyone to feel comfortable participating in discussion, asking questions, learning, and facilitating the learning of others. In order for that atmosphere to be maintained, the recordings of our conversations will only be shared with the enrolled students in the class (not posted publicly), and it is prohibited for any of us who have access to the video to share it outside the course. Similarly, I have specifically designed the syllabus, exams, handouts, and lectures for the people who are enrolled in the course this term and those may not be shared outside this course. It is against Tufts policy for anyone to share any content made available in this course including course syllabi, reading materials, problems sets, videos, handouts, and exams with anyone outside of the course without the express permission of the instructor. This especially includes any posting or sharing of videos or other recordings on publicly accessible websites or forums. Any such sharing or posting could violate copyright law or law that protects the privacy of student educational records.

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 virtually on Zoom. I will begin the synchronous classes at 10:45 am, but the Zoom sessions will start at 10:30 am. You can access the Zoom sessions from the appropriate Module or from the Zoom page in Canvas. The passcode for each class is Enter13.

The recitation sessions will also meet virtually on Zoom, and the sessions can be accessed via the Zoom page on Canvas. The passcode for the recitations is 090920. Recitations will either be Stata lab sessions or problem sessions.   I will announce (in class and by e-mail) if the week's recitation sessions is a Stata lab session or a problem session. The first recitation sessions are Stata lab session and will be on Thursday, September 10 and Friday, September 11.

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

I. Introduction
September 9 - Chapter 1

II. Descriptive Statistics
September 9 - Secs. 3.1 - 3.4
September 14 - Secs. 3.5, 3.6, 2.2, 2.4
September 16- Sec. 2.3
September 21 - Secs. 2.5, 3.7, 12.1 - 12.3

III. Basics of Probability: Axioms of Probability, Counting, and Bayes' Theorem
September 23 - Secs. 4.1, 4.2
September 28 - Sec. 4.3
September 30 - Secs. 4.4, 4.7
October 5 - Sec. 4.5
October 7 - Sec. 4.6

October 14 - FIRST TERM EXAM

IV. Random Variables
October 12 - Secs. 5.1, 5.2, pp. 233-235 and Conditional Probability Distributions from Lectures on Probability, Statistics, and Econometrics
October 19 - Secs. 5.3 and Conditional Expectation from Lectures on Probability, Statistics, and Econometrics
October 21 - Secs. 5.4, 5.5.1, and Independent random variables from Lectures on Probability, Statistics, and Econometrics

V. Special Discrete Distributions
October 26 - Sec. 5.6
October 28 - Secs. 5.7, 5.8

VI. Continuous Distributions
November 2 - Secs. 6.1, 6.2
November 4 - Secs. 6.3 - 6.7

VIII. The Central Limit Theorem and Distributions of Statistics
November 9 - Secs. 7.1 - 7.4
November 10 - Secs. 7.5 - 7.6

November 18 - SECOND TERM EXAM

IX. Estimation
November 16 - Secs. 8.1 - 8.4, 12.3 and  Point Estimation from Lectures on Probability, Statistics, and Econometrics
November 23 - Secs. 8.5 - 8.7
November 30 - Secs. 10.4, 12.3

X. Hypothesis Testing
December 2 - Secs. 9.1 - 9.3
December 7 - Secs. 9.4, 9.5
December 9 - Secs. 10.1 - 10.4, 12.4 - 12.5

December 18 - FINAL EXAM