Math 360: Statistical Methods

Prof. Ross

Winter Semester 2013

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We believe that the RELATIONSHIPS we have and those we continue to develop will support us as we learn and grow together as a community.

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Basic Information

This version posted on: 2013-01-03

General Description

This course will pay particular attention to the need of future math teachers (math-secondary-education majors), as well as math minors and computer science majors. The K-12 Common Core State Standards (CCSS) require much more statistical thinking than previous standards have included.

This course alone will not be enough to prepare you to teach AP Statistics. From an MET draft document: "it is clear that extensive additional preparation in statistics is required to teach AP Statistics. Several graduate courses in statistics are desirable (chosen in individual consultation with faculty in a graduate statistics program). The minimum preparation would be a good lower-level introductory statistics course, based on the sort of textbooks mentioned above, followed by either a second undergraduate statistics course or a graduate statistics course designed for teachers (see the MET Professional Development website for details about such a course)."

Course Catalog Entry

A comprehensive overview of statistical methods and analysis with applications. Topics include descriptive statistics, probability theory, random variables and probability distributions, sampling distributions, estimation and testing hypotheses, correlation and regression, introduction to computer-assisted statistical analysis.


Math 120 (Calculus I)

Follow-up courses:

MATH 419W - Introduction to Stochastic Mathematical Modeling (Gen Ed Area I, W)
ECON 415 - Introduction to Econometrics
MATH 460/576 Applied Survey Sampling
MATH 461/575 Linear Regression Analysis
MATH 462/572 Design and Analysis of Experiments
MATH 468 - Introduction to Biostatistics
MATH 469 - Introduction to Categorical Data Analysis
MATH 474W/574 - Applied Statistics (Gen Ed Area I, W)

MATH 571 Mathematical Statistics I: Probability Theory
MATH 573 Statistical Data Analysis
MATH 577 Applied Multivariate Statistics
MATH 578 Nonparametric Statistics. 

Class Meetings

Section 0, CRN 21748: Tue/Thu 11:00-12:15 in Pray-Harrold 520 
Section 1, CRN 25043: Tue/Thu  2:00- 3:15 in Pray-Harrold 520 

Brief schedule overview: 3 credit hours.

Class meetings will be mostly interactive lectures, with some time to work on problems in class, and perhaps some time to go over problems from the homework.

I expect that you will work on Math 360 for 6 to 10 hours per week outside of class.

Instructor information

Professor Andrew Ross
Pray-Harrold 515m
(734) 487-1658, but I strongly prefer e-mail instead of phone contact.
Math department main office: Pray-Harrold 515, (734) 487-1444

Office Hours and other help

Here is my complete schedule.
	10:00-11:00 office hour
	11:00-12:15 Math 360 Pray-Harrold 520
	12:15- 2:00 office hours and lunch
	2:00- 3:15 Math 360 Pray-Harrold 520
	3:30- 4:45 Math 419W/519 Pray-Harrold 520
	no schedule--I'm usually on campus, though.
	I have various meetings to go to.
	Send e-mail to make an appointment.

I am also happy to make appointments if you cannot come to the general office hours. Please send me e-mail to arrange an appointment. However, I am not available when I am teaching other classes:

The Mathematics Student Services Center (or "Math Lab") is also here to help you, in Pray-Harrold 411 Their hours are posted here. Please give them a call at 734-487-0983 or just drop by.

Another resource on campus is the Holman Success Center, formerly the Holman Learning Center.

Some assignments in this course will be in the form of papers, which I want to be well written. Please consult with The Writing Center for help in tuning up your writing.

Teaching philosophy, interests

I am a very applied mathematician. Applied, applied, applied. Not pure. Impure. I try to focus on real-world problems, rather than artificial drill problems (though I do recognize the need for some drill). My classes spend much more time on formulating problems (going from the real world to math notation and back) than on proving theorems. If you want the theoretical basis for anything we are discussing, please ask!

My general math interests are in Industrial Engineering and Operations Research (IEOR). In particular, I do research in applied probability and queueing theory, the mathematics of predicting how long it takes to wait in line for service. You can learn more about this in Math 319 and 419 when I teach them. I also enjoy teaching about cost-minimizing/profit-maximizing methods called Non-Linear Programming (NLP) in Math 560, Optimization Theory.

Required materials

Textbook: Introduction to Statistics & Data Analysis, 4th edition, by Peck, Olsen, and Devore amazon link.

This textbook is not calculus-based, but our course is a calculus-based course. So, I will be writing a calculus-based supplement to the textbook.

A lot of our work will be done on computers. If you had been waiting for a good reason to buy a laptop, this is it.

Course Web Pages

I will post data files, homework assignment files, etc. on my home page.

We will use on-line homework submission and gradebook via EMU-Online to keep track of grades. You are expected to keep an eye on your scores using the system, and get extra help if your scores indicate the need.

Supplementary Materials

Electronic data sets from the textbook. You probably want the Excel version, near the top.

Course Content

Course Goals

The objective of this course is to give students an elementary overview of sampling and data analysis using graphical methods, basic probability theory, discrete and continuous random variables, sampling distribution, point and interval estimation, and hypothesis testing. Exposure to computer software, for example, SAS, R or Excel is recommended for statistical analysis purposes.


Why Study Statistics
The Nature and Role of Variability
Statistics and the Data Analysis Process
Types of Data and Some Simple Graphical Displays
Statistical Studies: Observation and Experimentation
Simple Comparative Experiments
More on Experimental Design
More on Observational Studies: Designing Surveys (Optional)
Interpreting and Communicating the Results of Statistical Analyses
Displaying Categorical Data: Comparative Bar Charts and Pie Charts
Displaying Numerical Data: Stem-and-Leaf Displays
Displaying Numerical Data: Frequency Distributions and Histograms
Displaying Bivariate Numerical Data
Interpreting and Communicating the Results of Statistical Analyses
Describing the Center of a Data Set
Describing Variability in a Data Set
Summarizing a Data Set: Boxplots
Interpreting Center and Variability: Chebyshev's Rule, the Empirical Rule, and z Scores
Interpreting and Communicating the Results of Statistical Analyses
Linear Regression: Fitting a Line to Bivariate Data
Assessing the Fit of a Line
Nonlinear Relationships and Transformations
Logistic Regression (Optional)
Interpreting and Communicating the Results of Statistical Analyses
Chance Experiments and Events
Definition of Probability
Basic Properties of Probability
Conditional Probability
Some General Probability Rules
Estimating Probabilities Empirically Using Simulation
Random Variables
Probability Distributions for Discrete Random Variables
Probability Distributions for Continuous Random Variables
Mean and Standard Deviation of a Random Variable
Binomial and Geometric Distributions
Normal Distributions
Checking for Normality and Normalizing Transformations
Using the Normal Distribution to Approximate a Discrete Distribution
[ Calculus supplement: x versus X, CDF/PDF and integrals/derivatives,
 moments, Exponential distribution, misc other distributions,
 Poisson process]
Statistics and Sampling Variability
The Sampling Distribution of a Sample Mean (incl Central Limit Thm)
The Sampling Distribution of a Sample Proportion
Point Estimation
Large-Sample Confidence Interval for a Population Proportion
Confidence Interval for a Population Mean
Interpreting and Communicating the Results of Statistical Analyses
Hypotheses and Test Procedures
Errors in Hypotheses Testing
Large-Sample Hypothesis Tests for a Population Proportion
Hypotheses Tests for a Population Mean
Power and Probability of Type II Error
Interpreting and Communicating the Results of Statistical Analyses
Inferences Concerning the Difference Between Two Population or Treatment Means Using Independent Samples
Inferences Concerning the Difference Between Two Population or Treatment Means Using Paired Samples
Large Sample Inferences Concerning a Difference Between Two Population or Treatment Proportions
Interpreting and Communicating the Results of Statistical Analyses
Chi-Square Tests for Univariate Data
Tests for Homogeneity and Independence in a Two-way Table
Interpreting and Communicating the Results of Statistical Analyses
Simple Linear Regression Model
Inferences About the Slope of the Population Regression Line
Checking Model Adequacy
Inferences Based on the Estimated Regression Line (Optional)
Inferences About the Population Correlation Coefficient (Optional)
Interpreting and Communicating the Results of Statistical Analyses
The following chapters are parts of the book that we will not have time for:

Multiple Regression Models
Fitting a Model and Assessing Its Utility
Inferences Based on an Estimated Model (online)
Other Issues in Multiple Regression (online)
Interpreting and Communicating the Results of Statistical Analyses (online)
Activity 14.1: Exploring the Relationship Between Number of Predictors and Sample Size
Single-Factor ANOVA and the F Test
Multiple Comparisons
The F Test for a Randomized Block Experiment (online)
Two-Factor ANOVA (online)
Interpreting and Communicating the Results of Statistical Analyses (online)
Distribution-Free Procedures for Inferences About a Difference Between Two Population or Treatment Means Using Independent Samples (Optional)
Distribution-Free Procedures for Inferences About a Difference Between Two Population or Treatment Means Using Paired Samples
Distribution-Free ANOVA

Some variations in this outline are to be expected.

Grading Policies


Regular attendance is strongly recommended. There will be material presented in class that is not in the textbook, yet will be very useful. Similarly, there are things in the textbook that are might not be covered in class, but are still very useful. If you must miss a class, arrange to get a copy of the notes from someone, and arrange for someone to ask your questions for you.

My lectures and discussions mostly use the whiteboard, along with demonstrations in Excel and other mathematical software. I do not usually have PowerPoint-like presentations, and thus cannot hand out copies of slides.


Homework will be assigned about twice per week. All homework should be typed and submitted via the EMU-Online Dropbox. The policy is: if it isn't in the Dropbox, it doesn't exist.


There will be a midterm exam and a final exam. Quizzes might also occur, announced or not, during the semester.


You will do a project where you create a question, decide how to study it, design a data collection method, collect data, and analyze it. You will write a project proposal so I can be sure you are on the right track, and a final report, which is usually about 5 to 10 pages long. The grade breakdown for the project is:

On average, students should spend a total of about 30 minutes in office hours discussing the project. Plan for this in advance!

Overall Grades

No scores will be dropped, unless a valid medical excuse with evidence is given. In the unfortunate event of a medical need, the appropriate grade or grades might (at the instructor's discretion) be dropped entirely, rather than giving a make-up. You are highly encouraged to still complete the relevant assignments and consult with me during office hours to ensure you know the material.

Your final score will be computed as follows: The usual 90-80-70 scale will be applied for final letter grades, with the caveat that if needed, a curve will be applied.

General Caveat

The instructor reserves the right to make changes to this syllabus throughout the semester. Notification will be given in class or by e-mail or both. If you miss class, it is your responsibility to find out about syllabus and schedule changes, especially the due dates and times of projects, assignments, or presentations.

Advice from My Other Students

In past years, I've asked my upper-level students to give advice to you, future students, based on their experiences in my courses. Here are some of the highlights:

University Writing Center

The University Writing Center (115 Halle Library; 487-0694) offers one-to-one writing consulting for both undergraduate and graduate students. Students can make appointments or drop in between the hours of 10 a.m. and 6 p.m. Mondays through Thursdays and from 11 a.m. to 4 p.m. on Fridays. Students should bring a draft of what they're working on and their assignment sheet. The UWC opens for the Winter 2013 semester on Monday, January 14 and will close on Friday, April 19.

The UWC also offers small group workshops on various topics related to writing (e.g., Organizing Your Writing; Incorporating Evidence; Revising Your Writing; Conquering Commas; Finding and Fixing Errors). Workshops are offered at different times in the UWC. Visit the UWC page ( ) to see our workshop calendar. To register for a workshop, click the link from the UWC page for the type of workshop you wish to attend.

The UWC also has several satellite sites across campus. These satellites provide writing support to students within the various colleges. For more information about our satellite locations and hours, visit the UWC web site: .

The Academic Projects Center (116 Halle Library) also offers one-to-one writing consulting for students, in addition to consulting on research and technology-related issues. The APC is open 11 a.m. to 5 p.m. Mondays through Thursdays for drop-in consultations . Additional information about the APC can be found at . Students visiting the Academic Projects Center or any of the satellites of the University Writing Center should also bring with them a draft of what they're working on and their assignment sheet.

Standard University Policies

Religious Holy Days

Current University policy recognizes the rights of students to observe religious holidays without penalty to the student. Students will provide advance notice to the instructor in order to make up work, including examinations, they miss as a result of their absence from class due to observance of religious holidays. If satisfactory arrangements cannot be made with the instructor, the student may appeal to the school director or head(s) of department(s) in which the course(s) is / are offered.

Academic Honesty

Academic dishonesty, including all forms of cheating, falsification, and/or plagiarism, will not be tolerated in this course. Penalties for an act of academic dishonesty may range from receiving a failing grade for a particular assignment to receiving a failing grade for the entire course. In addition, you may be referred to the Office of Student Conduct and Community Standards for discipline that can result in either a suspension or permanent dismissal. The Student Conduct Code contains detailed definitions of what constitutes academic dishonesty but if you are not sure about whether something you are doing would be considered academic dishonesty, consult with the course instructor. You may access the Code online at:

Classroom Behavior

Students are expected to abide by the Student Conduct Code and assist in creating an environment that is conducive to learning and protects the rights of all members of the University Community. Incivility and disruptive behavior will not be tolerated and may result in a request to leave class and referral to the Office of Student Conduct and Community Standards (SJS) for discipline. Examples of inappropriate classroom conduct include repeatedly arriving late to class, using a mobile/cellular phone while in the class session, or talking while others are speaking. You may access the Code online at

When we aren't in a computer lab, if ever, those who use laptops during class should sit in the back row if possible, to avoid distracting others with what is on their screens.

Special Needs Accomodations

If you wish to be accommodated for your disability, EMU Board of Regents Policy 8.3 requires that you first register with the Disability Resource Center (DRC) in 240K EMU Student Center. You may contact DRC by telephone (734.487.2470). Students with disabilities are encouraged to register with the DRC promptly as you will only be accommodated from the date you register with them forward. No retroactive accommodations are possible.

Student and Exchange VISitors (SEVIS)

The Student Exchange Visitor Information System (SEVIS) requires F and J students to report the following to the Office of International Students 244 EMU Student Center within ten (10) days of the event: Prior permission from OIS is needed for the following: Failure to report may result in the termination of your SEVIS record and even arrest and deportation. If you have questions or concerns, contact the Office of International Students at 734.487.3116, not the course instructor.

The Family Educational Rights and Privacy Act (FERPA)

The Family Educational Rights and Privacy Act (FERPA) is a Federal law designated to protect the privacy of a student's education records and academic work. The law applies to all schools and universities which receive funds under an applicable program of the U.S. Department of Education and is applicable to students at EMU. All files, records, and academic work completed within this course are considered educational records and are protected under FERPA. It is your right, as a student in this course, to expect that any materials you submit in this course, as well as your name and other identifying information, will not be viewable by guests or other individuals permitted access to the course. The exception will be only when you have given explicit, written, signed consent. Verbal consent or email is insufficient.