MATH 322 Syllabus (Spring 2025)

Course Overview

Mathematical Statistics II continues the story of statistics from a more-mathematical standpoint than received in introductory statistics. In that course, you performed statistical analyses. In this course, you better understand why we did what we did in that course.

Course Catalog Description

This course provides a rigorous study of the theory of statistics with attention to its applications. Major topics include point and interval estimation, hypothesis testing, regression and correlation, goodness-of-fit testing, and analysis of variance (ANOVA).

• The prerequisite is a successful completion of Mathematical Statistics I (MATH 321)
• This, in turn, currently requires both Multivariate Integral Calculus and Linear Algebra; MATH 205 and MATH 185, or equivalent, respectively.

Course Overview

The major purpose of this course is to solidify two things in your minds: the probabilistic nature of the world and the mathematics behind our statistical estimators. The first major goal extends the probability theory you learned in MATH 321 to include many other probability distributions and why they matter.

The second major goal extends the inferential statistics you learned in STAT 200. In that class, you learned some recipes for performing statistical analysis. Here, you will see why (and when) those recipes work. To accomplish this goal, we will use our probability theory and mathematics to obtain some elementary results, and we will use Monte Carlo simulation to obtain some more complicated results.

Required Materials

Textbook:

Kandethody M. Ramachandran and Chris P. Tsokos. Mathematical Statistics with Applications in R. Cambridge, MA: Academic Press.

The third edition is pictured to the right. I use the second edition as a reference. However, there are two other versions of the book available. Here are links to the second and third editions at Amazon.

• Edition 2
• Edition 3

The calendar provides equivalent sections for the first and second editions. In other words, feel free to use any of the three editions. But, get a book and use it.

Software:

As aspects of this course focus on applied statistics, you will also need to use a computer to perform important statistical calculations. For many reasons, including flexibility, cost, ubiquity, and pedagogy, we will use the R statistical environment.

In addition to the statistical software, you will also need to use a typesetting program called LaTeX. This is the standard program for writing mathematics because of how easily it produces and presents mathematical work. You may want to download an entire LaTeX distribution (MiKTeX, for instance).

However, because downloading this program may take more than an hour, there is a free online “version” available. I assume everyone will use this online version. It is called Overleaf. We will have an entire class period dedicated to LaTeX and Overleaf.

Course Objectives

By the end of this course, you should

1. use Monte Carlo simulation to examine a statistic;
2. understand what is meant by a “good” estimator;
3. prove unbiasedness and efficiency for statistics;
4. illustrate bias and efficiency for other statistics;
5. evaluate several statistical methods and select (and perform) the most appropriate; and
6. use the R statistical environment to perform analyses.

Behavioral Expectations

If your question is “What will it take to succeed in this course?” then the answer is “Being a good student.” In my experience, your ability as a student is the greatest predictor of success in courses such as this. Being a good student means that you

• get a full night’s sleep every night;
• read and outline the readings before class;
• make sure your notes make sense to you;
• summarize your notes using diagrams and figures;
• ask questions about the readings during class;
• are an active participant in your learning;
• begin homework as soon as it is assigned;
• are aware of course deadlines;
• spend enough time on the material to learn it;
• study for mastery (not for the grade);
• are observant;
• use learning techniques you developed in previous courses; and
• recognize your limitations and work to strengthen them.

You are responsible for all material covered during the class period and all material in the readings and activities. Feel pressured to ask questions during the class regarding the material, since the material covered during the classes may or may not cover everything that is in the text. Asking questions signals to me that you are engaged. Those who do not ask questions tend to be lost.

As with most 300-level courses at Knox, you should be willing to spend 15 hours per week on the coursework for this class. That includes time in class and the time outside class. Since you spend 4 hours in class each week, you should be willing to spend 11 hours outside class in preparing for class, working on homework, reviewing notes, and anything else associated with the course.

However, since you have determined that this course directly supports and builds your life from this point forward, you should be spending as much time as needed. Also, for the same reason, you should be working hard to make your presentation (how your assignments look) as close to perfect as you can.

Key to Success: When you come to class, review your notes from the previous class and from the chapter you just read. This will help you do better in the class because you will know what to expect in the class —giving you important context.

Academic Integrity ( honor )

Knox College is committed to the maintenance of the highest standards of academic integrity, including ethical conduct, of its citizens. Personally, I strive to maintain this level of ethical behavior and integrity in this course because it encourages you to understand how to advance humanity at the local level.

Should I discover that you participated in a behavior that violates academic integrity (e.g., unauthorized collaboration, plagiarism, cheating on examinations, fabricating information (lying), helping another person cheat, unauthorized advance access to examinations, altering or destroying the work of others, or fraudulently altering academic records), I will sanction you because your actions undercut the value of Knox College and what it offers to its students (you), its alumni (future you), and the world (all of you). Please read through the Knox College Honor System to familiarize yourself with what constitutes a violation. When in doubt, please check with me. I am here to help.

Ultimately, this all has little to do with cheating. It has everything to do with understanding what it actually means to learn and to represent yourself academically. In college, your personal value has not increased because of your grades; it has increased because of your learning. To cheat is to claim two things about yourself and your skills: I am not able to do this; and I am only focused on today and not the future.

Specifically, to be clear, for this class:

Again, please, if you are looking to take a shortcut, then chat with me. This desire often arises from what I call “life crash,” where things are just happening faster than you planned. Again, let’s chat to see how to fix this before you cheat.

I’ve taught for 30 years. I have some experience. Communication is key.

Office of Disability Support Services ( odss )

Knox College abides by Section 504 of the Rehabilitation Act of 1973 which stipulates that no student shall be denied the benefits of an education “solely by reason of a handicap.” Disabilities covered by law include, but are not limited to, learning disabilities, psychological disabilities, health impairments, hearing, and sight or mobility impairments.

If you have a disability that may have some impact on your work in class and for which you may require accommodations, please contact the awesome Stephanie Grimes at the Office of Disability Support Services (ODSS information; office: SMC E-115; email: disabilityservices@knox.edu) so that such accommodations may be arranged. Note that the accommodations are not retroactive; I cannot make adjustments until ODSS contacts me to let me know what I can do. Furthermore, accommodations need to be reinstated at the start of each term.

Red Room Tutoring ( ctl )

Needing— and asking for help in college is a positive sign that you are engaging your learning and coursework. I really like to hear questions! By the way: The Center for Teaching and Learning (CTL) wants to help you! The CTL is responsible for the academic support needs of all Knox students. Here is some information provided about the CTL tutors this term:

Writing Tutors. If you want help on a paper, no matter the course, you can find writing tutors in Red Room, Seymour Library, Monday thru Friday, from 10:30 to 4:00pm, and again in Red Room on Tuesday, Wednesday, and Thursday nights, from 7:00 to 9:00pm. You can also schedule appointments to meet with a writing tutor by visiting the Center for Teaching and Learning website.

There are two Red Room Study Tables: “Red Room” and “Red Room SMC.” Red Room SMC is intended to support those classes taught in SMC and is located in SMC A-201, while Red Room is for most other courses and is located in the Red Room on the second floor of Seymour Library. Both study areas are free and open on a walk-in basis from 7:00pm to 9:00pm, on Tuesday, Wednesday, and Thursday nights.

Specifically, for this class:

• There are no subject-matter CTL tutors for MATH/STAT 322. Make friends in class.

Flunk Day

This is the Spring at Knox. Thus, we will celebrate Flunk Day some time during the term. I do not know when it will be. I will be as surprised as you when it happens. Be aware that there will probably be at least one “false alarm” during the term (a Flunk Day Ruse). Because this will be my eighth Flunk Day, I have created some guidelines to help you avoid bothering me on that most holy of days.

• If Flunk Day is held on Tuesday, I will cancel class on Wednesday.
• If Flunk Day happens on an exam day, the examination will be postponed as such: a Monday test changed to Wednesday; Tuesday to Thursday; Wednesday to Friday; Thursday to Monday; and Friday to Monday. If Flunk Day is the day before an examination, the exam will be postponed one class day.
• If an assignment is due on Flunk Day, the due date will be extended as such: a Monday due date changed to Wednesday; Tuesday to Thursday; Wednesday to Friday; Thursday to Monday; and Friday to Monday.
• If you fall for a Flunk Day Ruse and miss class because of it, it will not be an excused absence. Also, I will laugh at you.

I also enjoy Flunk Day. I will (most likely) start the day in my office because I will not know it is Flunk Day until I get there. Then, I will probably return home and enjoy the day in my yard (or in my Lay-Z-Boy watching TV if the weather is not nice).

Homework Assignments ( assn )

The usual assignments are designed to test a small sliver of what we covered in the course — or to quiz your understanding. These may be from the book or from my own mind. The submission may be something hand-written (if done in class), something typed, and/or something presented orally in class.

When submissions need to be typed, they must be typeset using LaTeX (not doing this means a zero). There are some great online sites that do not require downloading the LaTeX program. Here is one that has been used in the past for this course and for STAT 225: Overleaf.

I do encourage, however, you to download the LaTeX environment to your computer. This should make things easier for you in the long-run, especially as LaTeX is the typesetting language of mathematics.

Statistical Computing Activities ( sca )

To help you learn to explore statistics, I provide several computing activities throughout the term. These are designed to get you to experience randomness and its effect on our statistical estimators. The SCAs also give you skills for checking the importance of the assumptions of the theorems we cover. These also raise the question of practical difference, which is frequently more important than statistical significance.

The are worth 20 points each and must be typeset in LaTeX (not doing this means a zero). If you are not happy with your grade on a given assignment, then you have one week from when it was originally due to fix your responses to achieve acceptance.

Key to Success: Take these activities seriously. While practice always helps, it is more important to think deeply about the consequences of the SCAs. Think about what the activity is teaching, not what it is having you do. Anyone can follow the steps. A good student will think about why those steps exist.

Term Project ( proj )

There will be a single project in this course worth 100 points. It will cover a much larger swath of the material than any single homework assignment. It will concern a full statistical analysis of a test of Normality.

More information on the term project will be released later.

Quizzes and Other Things

Infrequently, I will give a quiz at the start of the class. These quizzes are designed to encourage you to properly prepare for the class. This means you read through the slide decks before class. Thus, I tend to have quizzes more frequently in the beginning of the term. This is the time you are forming habits for the term.

• If you arrive to class after I hand out the quizzes, you will not receive one. Be on time; it shows that you care about your learning.

My definition of “quiz” is very broad. If I give a small assignment that fits nowhere else in the grading scheme, it will be counted as a quiz.

These “quizzes” are worth three to five points each.

Examinations

There is a 100-point examination following the theory part of this course, and a 100-point cumulative final examination during the finals period.

Key to Success: You are prepared for an examination when you can do any problem without having to think through the process. An analogy is that you are ready to go to kindergarten when you can tie your shoes without thinking about it. Reflex indicates mastery. Attack the problem!

To encourage you to properly study, I will have no review sessions. When you show up for the examination, you should have already determined what will be on it.

To that end, I encourage all of you to meet up and hold weekly study sessions. While past courses have frequently formed these based on the major field of study, some of the more successful ones have been formed by those with an opening in their Tuesday schedule.

Late Assignments

The last day to turn in any assignment is the end of classes, May 29, 2025. I accept no late assignments without an excuse that I find acceptable. Such excuses include varsity sports, deaths, dismemberments, and zombie apocalypses (apocalypsi?).

Key to Success: To be early is to be on time. Plan ahead. As emergencies can (and do) come up, you should aim to have all major assignments completed at least 48 hours before they are due. Such a safety margin allows you to focus on the emergency when it happens, thus reducing the stress in your life.

Note that college is an easy on-ramp to professional adulthood. Mistakes can be made here without you necessarily being fired (given an F). Missing two days of classes will hurt your grade, but you will still have a job. In your profession, many deadlines are sacrosanct. Start treating them as such; it will make the transition much easier.

Attendance

I expect you to attend every single class period. If I’m there, you should be there. If you are not there, I expect you to accept the consequences for that decision. To make things more complicated, if you are sick (cold, flu, etc.), then you are morally responsible for those who get sick because of you. If you are sick, I hope you stay home, get well,… and not make others sick. I am serious about this.

Key to Success: Do not wait to study for the examinations. You should be studying for them throughout the term. Every class night, review your notes from that day and check that they make sense. Every weekend, review your notes from that week and check that they all make sense. At the start of every class, look over your notes to see what I will be talking about in class. (Get off your phone!) In all cases, look for patterns and connections. If you do this, then there will be no need for cramming, because you will have actually learned the material.

Overall Course Grade

I calculate your percent in the course by adding all of the points you earned during the semester and dividing by the total number of points that you could have earned. This percentage is then used to determine your final letter grade for the course. I do not round.

Should you ask me what your grade is, or what you need on the final to get a _________ (whichever the grade), I will suggest you calculate it for yourself. You have the mathematical skills to do so; they are a prerequisite for the course.

By the way: If you have the highest score in the course, and if your score is greater than 97%, then I will award you an A+.

Bloom’s Taxonomy

Remember college is not high school. Strive for a deeper understanding (this is what you are paying for — an understanding of your interests). Bloom’s Taxonomy is helpful here. You may not appreciate it until you do poorly on an examination, but you should be very familiar with it.

Look through it to check the level you were expected to achieve in high school. In college, you need to hit all levels. The higher you get, the better you have mastered the material. For many of you, this is your only chance to master the elementary levels of statistics. Take advantage of me for your edification.

Humankind cannot gain anything without first giving something in return. To obtain, something of equal value must be lost. That is […] the first law of Equivalent Exchange.

Here is a list of the verbs associated with each level. Use them to ensure that you are operating at the college level.

Source: Fractus Learning

Finally, there is an old adage that one never knows more than when teaching. That means you will never understand the material better than when you can teach it to others. You will want to achieve that level. It takes a lot of time, but the activities and labs push you to achieve the higher levels of mastery. Take advantage of them; you are paying for them.

Life tests you first, then gives you the lesson.

The Three Videos

Here are three videos that will help you better understand what it means to be a successful adult (college student). They encourage you to think about thinking. “Blowing these off” shows either that you do not care about mastery or that you think I do not know what I am doing.

• Scientifically Proven Best Ways to Study. What is it makes learning more effective? This video looks at some scientifically-proven methods. Some methods are obvious (exercise and avoiding cramming) others may be surprising (testing and sleeping).
  
  Link: Scientifically Proven Best Ways to Study
  [5:38]
• Marty Lobdell. If you spend hours and hours of studying, without improving your grades, or information retention, then learn how to study smart by Marty Lobdell. Lobdell taught Psychology at Pierce College in Washington State for 40 years. During Lobdell’s career, he has taught tens of thousands of students and he wants students to succeed. After watching students cram for eight hours or more for a test without any improvement, Lobdell has developed a studying technique that helps the brain retain the information that you are studying in this video.
  
  Link: Study Less, Study Smart
  [59:56]
• Matt Walker. Sleep is your life-support system and Mother Nature’s best effort yet at immortality, says sleep scientist Matt Walker. In this deep dive into the science of slumber, Walker shares the wonderfully good things that happen when you get sleep — and the alarmingly bad things that happen when you don’t, for both your brain and body. Learn more about sleep’s impact on your learning, memory, immune system and even your genetic code — as well as some helpful tips for getting some shut-eye.
  
  Link: Sleep is Your Superpower
  [19:09]
• Lera Boroditsky. There are about 7,000 languages spoken around the world — and they all have different sounds, vocabularies and structures. But do they shape the way we think? Cognitive scientist Lera Boroditsky shares examples of language — from an Aboriginal community in Australia that uses cardinal directions instead of left and right to the multiple words for blue in Russian — that suggest the answer is a resounding yes. “The beauty of linguistic diversity is that it reveals to us just how ingenious and how flexible the human mind is,” Boroditsky says. “Human minds have invented not one cognitive universe, but 7,000.”
  
  Link: How Language Shapes the Way We Think
  [14:03]

By the way… One of the most important things you can do to ensure your success in a course is to read — and understand — the entire syllabus. To help encourage you to gain proper habits in college, I will give five points of extra credit for those who email me a meme that makes me smile. Since I am easily amused, this should be an easy five points for you. I like cats and dogs and beavers and clever wordplay. This must be done by the end of the first Sunday of class (March 30, 2025).