Math 156, Introduction to Statistics, Section 5

Here is a shortcut to the course schedule/homework page.

Here is a link to the page of common
comments on graded assignments. *[See below for explanation.]*

Here is a shortcut to the summary table below of
components of the grades for this course. *[See below for explanation.]*

**Instructor:** Jonathan
Poritz
**Office:** GCB 314D
**E-mail:**
`jonathan@poritz.net`

**Phone:** 549-2044 (office — any time); 357-MATH
(personal; please use sparingly)

**Office Hours:** TW 10am-2pm or by appointment

**Textbook:** No (physical, commercial) book is required for this class.
If you have accidentally purchased the book which is required for another
section of Math 156, feel free to return it, sell it, or keep it for later
consultation (it's not a bad book, aside from the price), as you like.

Instead, there will be frequent, substantial, required readings for this
class, but they will always be freely available on the 'net — although,
of course, you may print out the readings if you prefer to study off of hard
copies. These readings will come from a variety of sources, including some
created just for this class and others which are widely used, open, electronic
resources. Exactly what is to be read, when, is detailed on the
HW/schedule page for this course.
In addition to readings, the HW/schedule page will
have many other materials you will be expected to access in a timely manner.
These will include video and audio files, perhaps online (or in person, for you
to do in the privacy of you own home) simulated experiments, *etc.* If
you cannot view or listen to one of these file types, contact your instructor
immediately and we can figure out what needs to be done.

**This course is online.** But nevertheless, it is a full version of
our Math 156 curriculum. You will therefore be expected to put in as much time
as you would for regular class which happens on campus — replacing
classroom seat time with time you will spend reading, watching videos, listening
to audio, writing more, *etc.* — including the additional time
students spend for homework and studying. Note the latter, non-classroom time
is expected to be be at least 2-3 hours per classroom hour, meaning that for
this three-credit class, you should budget at least 3-4 hours every other day.
Don't expect this to be a light-weight course, simply because it is online.
Instead, expect to do as much as you would in-class, with in fact an additional
requirement on your organization and tenacity due to the fact that you won't be
seeing me every other day to remind you to work.

Note, however, that if you put in the time and energy, and come to me in person or electronically whenever you are having problems, you will certainly learn statistics well and get the grade you need. This is useful, beautiful, and powerful material, and you can certainly master it.

**Prerequisites:** Satisfactory placement exam score or Math 099 or
equivalent.

**Postrequisites:** This course is one of the six classes which satisfy
the Quantitative Reasoning Skill of the General Education Requirement. It is
also required for the AIM major, the Biology major, the CM program, the
Nursing major, and the Mass Communication BS degree, is one required option
for the Chemistry major, the Liberal Studies program, and the Social Work
program, a prerequisite for MATH 362, MATH 550, and NSG 351, and is one
required option for several other classes. Actually, one could argue that a
course like this is a requirement for any educated person to understand the
modern world.

**Course Content/Objective:** The Catalog describes it as:

In practice, we tend not to get all the way to the $\chi^2$ (that's a Greek letter, written in English as "chi" and pronounced in English like a hard "k" sound followed by the English word "eye") test. A more precise list of what you will know about by the end of this class is:Introduction to data analysis. Binomial and normal models. Sample statistics, confidence intervals, hypothesis tests, linear regression and correlation, and chisquare tests.

- Describing data and distributions
- graphing
- measures of variation
- density curves
- Normal distributions, the 68-95-99.7 rule

- Relationships in data
- scatterplots
- correlation -- the least-squares line
- cautions: extrapolation, hidden variables, "correlation is not causation"

- producing data
- simple random samples ("independent, identically distributed")
- matched-pair and block designs
- the placebo effect, double-blind experiments
- experimental ethics

- probability
- outcome space, events, combining events, mutually exclusive events
- independent events
- the Law of Large Numbers
- distributions, cumulative distributions
- random variable
- the situation of repeated Bernoulli trials
- mean (expectation), variance, standard deviation
- sampling distributions
- the Central Limit Theorem

- confidence intervals (for means with known and unknown population
standard deviation)
- definitions
- confidence levels
- critical values on the Normal distribution
- dependence on sample size
- Student's
*T*-distribution

- hypothesis testing (tests of significance; for means with known and
unknown population standard deviation)
- null hypothesis, alternative hypothesis
- test statistic
*p*-values

**General Education Student Learning Outcomes:** This course satisfies
the general education mathematics requirement which has the following
learning outcomes:

*Critical Thinking*– Identify, analyze and evaluate arguments and sources of information to make informed and logical judgments, to arrive at reasoned and meaningful arguments and positions, and to formulate and apply ideas to new contexts.- Identify questions, problems, and arguments.
- Differentiate questions, problems, and arguments.
- Evaluate the appropriateness of various methods of reasoning and verification.
- State position or hypothesis, give reasons to support it and state its limitations.
- Identify stated and unstated assumptions.
- Assess stated and unstated assumptions.
- Critically compare different points of view
- Formulate questions and problems.
- Construct and develop cogent arguments.
- Articulate reasoned judgments.
- Discuss alternative and points of view.
- Defend or criticize a point of view in view of available evidence.
- Evaluate the quality of evidence and reasoning.
- Draw an appropriate conclusion.

*Quantitative Reasoning*– Apply numeric, symbolic and geometric skills to formulate and solve quantitative problems.- Select data that are relevant to solving a problem.
- Use several methods, such as algebraic, geometric and statistical reasoning to solve problems.
- Interpret and draw inferences from mathematical models such as formulas, graphs, and tables.
- Generalize from specific patterns and phenomena to more abstract principles and to proceed from abstract principles to specific applications.
- Represent mathematical information symbolically, graphically, numerically and verbally.
- Estimate and verify answers to mathematical problems to determine reasonableness, compare alternatives, and select optimal results.

**This course is also in gT Pathways.** This course is approved in the
State of Colorado gT Pathways curriculum as GT-MA1. According to the
Colorado Department of Higher Education website, "after starting on you
higher education pathway at any public college or university in Colorado,
and, upon acceptance to another, you can transfer up to 31 credits of
previously and successfully (C-or better) completed gT Pathways (general
education) coursework. These courses will automatically transfer with you
and continue to count toward your general education core or graduation
requirements for any liberal arts or science associate or bachelorâ€™s degree
program."

**Maximum number of Mathematics credits that are guaranteed to
transfer:** The total number of Mathematics credits guaranteed to transfer
in the gtPathways curriculum is three (3).

**Numerical computation:** There are a lot of numbers in statistics,
and often we want to do fairly elaborate arithmetic with them. We also like
to assemble these numbers into pretty pictures (graphs). Both of these
processes are made far simpler for the student (and the experienced
statistician alike) by using electronic computational devices. There is a
whole host of "scientific calculators" available for purchase which will do
all of this tedious work for you, and any one you might already have is
perfectly fine in this class so long as it has basic statistical functions
and graphs — show it to your instructor if you aren't sure.

In addition, feel free to use any computer programs you like which will perform these tasks on a laptop, desktop (when you're home or in a campus computer lab working on homework), or smartphone. There are also many websites and free online tools which will do just fine. Your instructor will post materials which show many such tools, and is happy to work with you to find a cheap (free!) one that you can use on whichever device to which you have convenient access.

Note that there will be no problem with getting used to some electronic tools and then not having them when you take quizzes and tests since you will be allowed to use whatever devices you like at all times.

The Mathematics Department does have a *TI-84 Plus* calculator rental
program, with a limited number of such calculators available on a first-come,
first-serve basis for a non-refundable fee of $20 per semester
payable at the Bursar's window in the Administration Building. For more
information, contact Tracey Blanco in the Math Learning Center (PM 132).

**Homework:** Mathematics at this level is a kind of practical (although
purely mental) **skill**, not unlike a musical or sports skill — and,
like for those other skills, one must **practice** to build the skill. In
short, *doing problems is the only way truly to master this material* (in
fact, it is *the only way to pass this course*).

There will be frequent homework sets assigned and collected. Here are some details:

- Homework is due to me, either by e-mail or at my office,
**no later than 3pm**. - Homework is due as
*sets*, but will be graded by problem. Each problem will be worth**5 points**. - Note that none of us is actually at all interested in the specific
*answers*to these problems: homework is about learning*how to do these kinds of problems*; everyone knows that quote about giving someone a fish versus teaching them how to fish. In short, "Showing your work" is not something extra that you can add to a homework assignment —**it**.*is*the homework assignment - If we have agreed that homework — and this is true of every thing
else you hand in, including quizzes, tests, and ASEs — is a form of
communication between student and instructor about what
*thought process*the student is following, then some things are important to make that communication as clear as it can be. For example:- Always define all variables, clearly and completely and with units (if relevant).
- Always explain all steps of every calculation you do — this
could be something like
- $s=17$
*(from calculator's*`STD DEV`) or - $s=17$
*(used eqn 3.14 from such-and-such a reading)*or - $s=17$
*(used def $s=\sqrt{\frac{1}{n-1}\sum_i^n(x_i-\bar{x})^2}$ from class)*.

- $s=17$
**Exception:**you can skip explaining a step which amounts to $2+2=4$, or even one where you compute a very basic object from this class after we have been doing it for weeks.*E.g.,*towards the end of semester, you don't need to quote a formula or book equation every time you compute a sample mean $\bar{x}$.**Exception to the exception:***on tests*, every concept you learned in this class should be defined with a formula the first time you use it.

- Experience shows that this issue of explaining your work is often
quite difficult for students, at least at first — it is so very
different from what you have been doing in math classes for years,
probably, and it is hard to break old (bad) habits. But once you get
into new (good) habits, they will make this part easy. And this is
very important in using and talking about statistics outside of a
math classroom. Furthermore, since most quizzes and tests will be
open-book, there really is very little point in merely checking
whether you can plug numbers into a formula: what matters is whether
you
*understand*what you are doing, and what it means. **Always label all axes of graphs and parts of diagrams.**

- Homework assignments appear on the schedule/homework web page on a regular basis. Please get used to going to that page frequently — at least every other day, and certainly before starting your work on a homework set.
- Late homework will count, but at a reduced value — generally,
the score will be reduced by 20% for each day late, unless you use
a
*Homework Late Pass*[see below].**Exception:**Late homework will count as**zero**, even even if you try to use a*Homework Late Pass*, when handed in after the next major test (the next hour exam during the semester, and the final for the end of the course).**Exception to the exception:**revisions of graded homework [see below] can always be handed in two days after the graded work was returned (or on Monday, if the work was returned on Friday), even if that is after the midterm ending a unit of the class.

- After you complete
**HW0**, you will receive a sheet of 10which may be used to hand in homework late but without penalty, subject to the restrictions mentioned above. It is your responsibility to keep track of these passes — don't loose them, they are valuable! Any unused passes may be turned in at the end of the term for general course extra credit.*Homework Late Passes* - Your seven lowest scores (on individual homework problems) will be dropped.
- Please label your homework clearly (make sure you name is there!). If you are handing in HW on paper (as opposed to sending it electronically) and don't staple the pages together, that's fine — just make sure each page then has your name and the assignment title on it. Please cut of the ragged edges of paper which come if you tear your HW out of a spiral-bound notebook.

**Big Ideas:** Part of the *Critical Thinking* mentioned above is
an idea of assimilating material, understanding its assumptions and
hypotheses and being able then to articulate them. In order to help you
practice this skill, and to help keep you concentrated and in synch on the
various learning materials such as readings and videos, you will be expected
to write up (and get to me) a *Big Idea [BI]* for essentially all
materials. The content and due dates for all *BIs* will be detailed on
the HW/schedule page.

A good *Big Idea* is a short but complete explanation of a new idea,
piece of terminology, formula, or algorithm but **is not just an example**.
Make sure you describe the context and define all variables used in a *BI*.
For example, if one reading discussed the Pythagorean Theorem, then a good
*BI* to hand in for that would be

In contrast, the following would beBig Idea:ThePythagorean Theoremtells us that if a triangle has sides of lengths $a$, $b$, and $c$, and if the angle between the sides of lengths $a$ and $b$ is $90^\circ$, then $a^2+b^2=c^2$.

- "$a^2+b^2=c^2$."
*[Missing all the set-up, including defining variables and stating the hypothesis that it's a right triangle.]* - "In a right triangle, $a^2+b^2=c^2$."
*[Forgot to define the variables.]* - "In a right triangle with legs of length 3 and 4, the hypotenuse has
length 5."
*[This is an example, not a general idea.]*

*BIs* are not part of the *Late Homework Pass* system, but they can
be corrected and resubmitted for full credit. They are graded out of 2 points,
as follows:

*BI*not handed in or having no clear idea at all (*e.g.,*if it is an example rather than an idea);*BI*present and mostly on track, but missing an important piece like a crucial hypothesis or variable definition; and*BI*present and complete.

**Quizzes:** Most Fridays, during weeks in which there is no hour exam,
there will be a short (10-15 minute) quiz. This should be taken in person, on
campus, at a time convenient for you (contact me if it not be possible for you
to be on campus at all, physically, on quiz days). These will
usually be "open book and notes," and calculators will (usually) be allowed.
The quizzes will often be quite similar to a homework problem from that week;
if you have been keeping on track with all class assignments, you should have
no trouble with the quiz. Quizzes are each graded out of 10 points, and your
lowest quiz score will be dropped.

**Applied Statistical Exegeses [ASEs]:** Roughly once a week you will
write a 1-2 page explanation of a statistical result whose description you
found on a website, in an article you read for pleasure or for your studies,
in a textbook from another class, or other source you find on your own (after
consultation with your instructor). The idea for these write-ups will be to
take information of a statistical nature you find elsewhere and to explain it
in detail using the terminology and methods of this class — and then to
think about it critically and to see if you can offer suggestions for how it
might be improved. More information about these ASEs will follow soon.

**Exams:** We will have three midterm exams on dates to be determined
(and announced at least a week in advance). You will take these exams in
person and on campus, but at a mutally agreed time which is convenient for
you (unless this is an extraordinary hardship for you: contact me if you will
not be able to make it to campus physically for midterms). Our **final
exam** will be arranged for a two hour and twenty minute time slot that
works for you (in person on campus) during exam week (which runs from Monday,
December 5^{th} to Friday, December 9^{th}).

**Revision of work on homework, quizzes, ASEs, and tests:** A great
learning opportunity is often missed by students who get back a piece of work
graded by their instructor and simply shrug their shoulders and move on
— often depositing their graded work in a trash can without even
looking at it! In fact, painful though it may be, looking over the mistakes
on those returned papers is often the best way to figure out exactly
where *you* tend to make mistakes. If you correct that work, taking the
time to make sure you really understand completely what was missing or
incorrect, you will often truly master the technique in question, and never
again make any similar mistake.

In order to encourage students to go through this learning experience, I will
allow students to hand in revised solutions to all homeworks, *BIs*,
quizzes, ASEs, and midterms. There will be an expectation of slightly higher
quality of exposition (more clear and complete explanations, all details
shown,
*etc.*) but you will be able to earn a percentage of the points you
originally lost, so long as you hand in the revised work no more than two days
after something was returned with missing points (or on the next Monday, if
the work was returned on Friday). The percentage you can earn back is given
in the "revision %" column of the table below. It is
often quite substantial, since I am hoping students will very frequently take
advantage of this possiblity for revision.

Since often a number of students have similar issues that could be revised in
their work, there will be a web page where comments are available for all
students to see. That way, any student who sees a notation of the form
"C:*n*" will know to go to the comment web page and look for comment
number *n* associated to that HW problem number (or quiz or BI or
*etc.*) to read the comment. It might also be interesting for other
students just to see the kinds of things that their colleagues sometimes have
trouble with, to avoid such similar troubles themselves. This common comments
page can be found here.

**Green points:** I am trying to reduce the carbon footprint of my
classes. So I ask that you reuse paper whenever possible, by taking any
pages you can find that are blank on one side (handouts from other classes,
drafts of your work for this or other classes, *etc.*), putting a big
"X" over the previously used side, and doing your HW, ASEs, revisions,
*etc.*, for this class on the blank side. To encourage this, I will keep
track of how many such reused pages you hand in and they will be worth
*Green Points* extra credit at the end of the term.

Note that submitting work electronically is an even more eco-friendly
approach. So if you submit any work by e-mail, you will get a *Green
Point* for each page you saved in that way. It will probably be most
convenient for you in this online course to "hand in" most things by sending
them as e-mail. If you are comfortable using your favorite word processor to
make HWs, *BIs*, revisions, *etc.*, look good, which you can attach
to e-mails, then go right ahead. If you are having difficulties with images,
drawings, or equations in these electronic submissions, contact me and I
might be able to help out.

**Grades:** On quiz or exam days, attendance is required — if you
miss a quiz or exam, you will get a **zero** as score; you will be able to
replace that zero only if you are regularly attending class and have informed
me [*e.g.,* by e-mail],
**in advance**, of your valid reason for missing that day.

In each grading category, the lowest *n* scores of that type will be
dropped, where *n* is the value in the "# dropped" column. The total
remaining points will be multiplied by a normalizing factor so as to make the
maximum possible be 100. Then the different categories will be combined,
each weighted by the "course %" from the following table, to compute your
total course points out of 100. Your letter grade will then be computed in a
manner not more strict than the traditional "90-100% is an **A**, 80-90%
a **B**, *etc.*" method. *[Note that the math department does not
give "+"s or "-"s.]*

pts each | # of such | # dropped | revision % | course % | |
---|---|---|---|---|---|

Homework: | 5/prob | ≈75 probs | 5 probs | 75% | 14% |

Big Ideas: | 2 | ≈117 | 5 | 100% | 10% |

Quizzes: | 10 | ≈10 | 1 | 75% | 12% |

ASEs: | 12 | ≈12 | 2 | 75% | 12% |

Midterms: | >100 | 3 | 0 | 50% | 36% |

Final Exam: | >200 | 1 | 0 | 0% | 16% |

Green Points: | 1/page | ≤200 ? | 0 | 0% | XC |

**Please come see me in person!** Over the years I have been teaching,
I have noticed that the students who come to see me at my office are very
often the ones who do well in my classes. Now correlation is not causation,
but why not put yourself in the right statistical group and drop in sometime?
I am always in my office, GCB 314D, during official office hours. If you
want to talk to me privately and/or cannot make those times, please mention
drop me an e-mail, and we can find another time. Feel free to contact me for
help also by e-mail at
`jonathan@poritz.net`, to
which I will try to respond quite quickly (usually within the day, often much
more quickly); be aware, however, that it is hard to do complex mathematics
by e-mail, so if the issue you raise in an e-mail is too hard for me to
answer in that form, it may well be better if we meet in person, or even talk
on the telephone (in which case, include in your e-mail a number where I can
reach you).

In addition, for this online course, I will set up some "working group" times that students can come to work with each other on HW and ASEs, get help from me, and generally get to know each other. This will take place in the 314 suite on the third floor of the GCB (best view on campus!). At the moment, the best time seems to be between 10 and 2 on Wednesdays, but if some students cannot make any of that and want to come, we will reschedule for a better time.

**A request about e-mail:** E-mail is a great way to keep in touch
with me, but since I tell all my students that, I get *a lot* of e-mail.
So to help me stay organized, please put **your full name and the course name
"Math 156-5" (or "Stat OL") in the subject line of all messages to me**.

**Early alert:** This course is part of CSU-Pueblo's general education
program, and participates in the Early Alert program. Early in the semester,
information about student performance in this class will be communicated to
Student Academic Services. This information is then relayed to faculty
academic advisors and to advisors in the first year program. Your advisor
may then ask to meet with you to discuss your progress. The program is
designed to promote success among our students through proactive advising,
and through referral to appropriate student support centers. The effort
continues throughout the semester, and instructor concerns can be posted to
the Early Alert system at any time.

**Academic integrity:** Mathematics is more effectively and easily
learned — and more fun — when you work in groups.
However, all work you turn in must be your own, and any form of cheating
is grounds for an immediate **F** in the course for all involved parties.
For details of what constitutes academic dishonesty, the processes that are
started when it is violated, and your rights in such proceedings, see
The Student Code of Conduct. In
any case, it is always a good idea to ask your instructor if you want to do
something which you are concerned might be, or even might appear to be, an act
of academic dishonesty.

** Nota bene:** Most rules on due dates, admissibility of make-up
work,

**Words:** One warning up front: I believe strongly that students
should learn to *think* in the way of a subject they are learning, not
merely that they become sophisticated calculators who can follow recipes.
Therefore I will **require** you to explain all your work on HWs and
tests and on the final. This doesn't mean that you have to write essay
answers to purely computational questions, but it does mean that you have
to tell me a word of two about what you are thinking as you do the
calculations. In particular, you could hand in an answer to some problem
with just a few numbers, all of which were correct — and get a **0**;
you could also hand in an answer with a few words explaining your numbers and
get full credit, even if all of the numbers were actually wrong. I will
try to give you feedback on HWs and other assignments on this requirement
during the term, so that it does not come as a surprise during tests.

**Tutoring Help:** ** The Math Learning Center** is open all
semester, except for Thanksgiving week, through the last day of finals
(December 9

**Accommodations:** The University abides by the
**Americans with Disabilities Act** and **Section 504** of the
**Rehabilitation Act of 1973**, which stipulate that no student shall be
denied the benefits of education "solely by reason of a handicap." If you
have a documented disability that may impact your work in this class for
which you may require accommodations, please see the Disability Resource
Coordinator as soon as possible to arrange accommodations. In order to
receive accommodations, you must be registered with and provide documentation
of your disability to the Disability Resource Office, which is located in
the Library and Academic Resources Center, Suite 169.

It is easy to lie with statistics, but it is easier to lie without them.

*Frederick Mosteller (1916 - 2006 )*

The plural of anecdote is not data.

*Roger Brinner*

Forecasting is very difficult, especially about the future.

*Edgar R. Fiedler (1929 - 2003)
(or maybe the Danish politician Karl Kristian Steincke; a version
is often attributed to the Nobel Laureate Niels Bohr, which is
probably based on another variant which is said to be a "Danish proverb")*

Statistical thinking will one day be as necessary for efficient citizenship
as the ability to read and write!

*Samuel S. Wilks (1906 - 1964),
paraphrasing Herbert G. Wells (1866 - 1946)*

Luck is probability taken personally. It is the excitement of bad math.

*Penn F. Jillette (1955 - )*

The only statistics you can trust are those you falsified yourself.

*Sir Winston Churchill (1874 - 1965)
(Attribution to Churchill is ironically falsified)*

Thirty years ago I was diagnosed with motor neurone disease, and given two
and a half years to live.

I have always wondered how they could be so precise about the half.

*Stephen Hawking (1942 - )*

It is commonly believed that anyone who tabulates numbers is a statistician.

This is like believing that anyone who owns a scalpel is a surgeon.

*Robert Hooke (1918 - ? .. not the Hooke who was a friend of Newton's!)*