Math 360: Statistical Methods

Prof. Ross

Winter Semester 2012

Eastern Michigan University Creed

We believe the INTEGRITY of our work and the RESPECT we show for our fellow students, faculty, alumni and staff are an integral part of our ongoing EDUCATION.

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.

INTEGRITY adds value to our educational experience.

RESPECT promotes unity and understanding through individual differences within our community.

EDUCATION allows us to develop socially, intellectually, and emotionally.

RELATIONSHIPS are the foundation of our growth.

Basic Information

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 21928: Mon/Wed 9:30-10:45 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 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.
     9:30-10:45 Math 360, Pray-Harrold 520
    10:45-11:30 office hours
     1:00- 2:00 office hours
     2:00- 3:15 Math 110 Pray-Harrold 418
     3:15- 4:00 office hours
     1:00- 2:00 office hours
     2:00- 3:15 Math 110 Pray-Harrold 323
     3:15- 4:00 office hours
  No official office hours, but I'm often on campus.
  E-mail me to make an appointment, or drop by.

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: Probability & Statistics for Engineers & Scientists by Walpole, Myers, Myers, and Ye, 9th edition

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 an on-line 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

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.


Unit One: Introduction to Statistics and Data Analysis Topics include an elementary overview of statistical inference, samples, populations, probability, sampling procedure, data collection procedures (observational study, designed experiment), measures of center and dispersion, classification of data, various graphs and charts.

Unit Two: Probability Topics include sample space, events, and probability rules.

Unit Three: Random Variables and Probability Distributions Topics cover discrete, continuous and joint probability distributions (discrete case only).

Unit Four: Mathematical Expectation Key concepts in this unit include mean, variance and covariance of random variables, mean and variance of linear combinations of random variables.

Unit Five: Discrete and Continuous Probability Distributions Topics include probability distributions of various discrete random variables (uniform, binomial, multinomial, hypergeometric, negative Binomial, geometric, and Poisson) and various continuous random variables (Normal distribution and its application, exponential, gamma and chi-squared distributions).

Unit Six: Sampling Distributions Topics cover sample mean and sample standard deviation, sampling distribution of sample mean.

Unit Seven: One- and Two-Sample Estimation Problems This unit covers point and interval estimations of mean, proportion and variance based on a single sample, point and interval estimation of differences between two means, proportions and ratio of two variances based on two samples.

Unit Eight: One- and Two-Sample Tests of Hypotheses Topics include one-and two-sample tests of hypotheses concerning means, proportions and variances.

Some variations in this outline are to be expected.

An example outline from Walpole, Myers, Myers, and Ye would be

CH 2
Sample space
Counting sample points  
Probability of an event
Additive Rules
Conditional probability
Multiplicative rules
Bayes' rule (sensitivity, specificity, positive predictive value, etc)

CH 3
Concept of a random variable  
Discrete probability distributions
Continuous probability distributions

CH 4
Mean of random variables
Variance of random variables

CH 5
Discrete uniform distribution
Binomial distribution
Poisson distribution

CH 6
Continuous uniform distribution 
Normal distribution
Exponential distribution 

CH 8
Random sampling
Sampling distributions of means  
The Central Limit Theorem (statement)
Sampling distributions of variances
Student's t distribution

Ch 9
Statistical inference  
Estimating the mean  
Standard error
Estimating the difference of means  
Paired observations
Estimating single sample proportion  
Estimating difference of proportions
Estimating the variance  

Ch 10
Statistical hypothesis
Type 1 and type 2 errors  
Tests for the mean  (standard deviation known and unknown)
Goodness of Fit test
Categorical Tests of Independence/Homogeneity

Ch 11
Introduction to linear regression
The simple linear regression model
Least squares and the fitted model
Choice of a regression model

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 chalkboard, 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 once or twice per week. It will sometimes be a small problem set designed to help you understand the behavior of math models. Other times, it will involve writing up a little paper on an assigned topic.

Homework 01: Chapter 1.3 Measures of Center, plus the GEICO simulation, Bloom's Taxonomy, and 8 Standards for Mathematical Practice
Homework 02: Chapter 1.4 (#1.7 through #1.12)
Homework 03: Types of Data; Stem-and-Leaf
Homework 04: Effects of Shifting and Scaling (on-line multiple-choice quiz)
Homework 05: Histograms (based on a scan from another textbook, Watkins/Schaeffer/Cobb)
Homework 06: Chapter 2.1 & 2.2, 2.3: Sets, Combinatorics
Homework 07: Combinatorics, divided for teachers/nonteachers.
Homework 08: Chapter 2.5 - 2.7: Conditional probability, Bayes' Rule
Homework 09: Chapter 3.1-3.4: PDFs, CDFs, calculus-based problems
Homework 10: Chapter 4: expected value, calculus-based problems
Homework 11: Chapter 5: binomial, geometric distribution
Homework 12: Chapter 6: normal approximation to binomial (skip continuity correction)
Homework 13: Chapter 8: sampling distributions
Homework 14: Chapter 9: part 1
Homework 15: Chapter 9: part 2, confidence intervals
Homework 16: Chapter 10: hypothesis tests
Homework 17: Chapter 10.11: Goodness-of-Fit test
Homework 18: emu-online version of photocopied hypothesis-test concept test
Homework 19: Chapter 10.12 Workshop Statistics stapled photocopies from class
Homework 20: Chapter 10.12/13 homework for all
Homework 21: Chapter 10.12/13 for teachers
Homework 22: Chapter 10.12/13 for nonteachers
Homework 23: Chapter 11 part 1 for all
Homework 24: Chapter 11 part 1 for teachers
Homework 25: Chapter 11 part 1 for nonteachers
Homework 26: Chapter 11 part 2 for all
Homework 27: Chapter 11 part 2 for teachers
Homework 28: Chapter 11 part 2 for nonteachers


There will be 3 exams plus a final exam.


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 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:

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:

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.