Math 156, Introduction to Statistics, Section 3

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**Lectures:** MWF 12-12:50pm in PM 106
**Office Hours:** M1-1:50pm and T$\Theta$ 12-1:50pm, or by appointment

**Instructor:** Jonathan
Poritz
**Office:** PM 248
**E-mail:**
`jonathan.poritz@gmail.com`

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

**Text:** *The Basic Practice of Statistics, 6 ^{th} ed.,*
by Moore, Notz, and Fligner.

**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 $\chi^2$ 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

- 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

**Calculator:** A calculator is necessary throughout this course, often
in class and when doing homework, always on quizzes and during tests. The
calculator you use must be capable of performing basic scientific computations
(including logarithms, exponentials and factorials), doing simple plots, and
computing standard simple statistical functions of small data sets.
Essentially any *Texas Instruments* calculator from the *TI-83* up
will suffice; the instructor will use a *TI-84 Plus*.

The Mathematics Department does have a *TI-84 Plus* calculator rental
program, with rental of a limited number of 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 Prof. Tammy Watkins in the Math Learning Center (PM 132).

**Attendance and workload:** Regular attendance in class is a key to
success — don't skip class, don't be late. But more than merely
attending, you are also expected to be *engaged* with the material in
the class. In order for this to be possible, it is necessary to be current
with required outside activities such as reading textbook sections and doing
homework problems: you are expected to spend 2-3 hours per hour of class on
this outside work. This is not an exaggeration (or a joke!), but if you put
in the time and generally approach the class with some seriousness you will
get quite a bit out of it (certainly including the grade you need).

If you absolutely have to miss a class, please inform me in advance and I will
video the class and post the video on the 'net. You should e-mail me no earlier
than a few hours after class (to allow for upload time) asking for the link to
that video, and you can then watch the class you missed in the comfort of you
home and (hopefully) not fall behind. Classes I have videoed will have the icon
next to that day's entry on the
schedule/homework page to remind you of the
available video. Even if you are not the one who originally requested the
video, you may want to watch it (as part of reviewing for a test, maybe) —
but you have to e-mail me for the links as the videos cannot simply be found
by a search on **YouTube**.

**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 roughly weekly homework sets assigned and collected. Here are some details:

- Homework is due either in class or at my office,
**no later than 2pm**. - 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`) - $s=17$
*(used eqn 3.14 in the book)* - $s=17$
*(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.

- Always label all axes of graphs and parts of diagrams.

- Homework assignments appear on the homework web page on a regular basis. Please get used to going to that page frequently — at least every class day (for special announcements), 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*, if 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 at the next class meeting after the graded work was returned, 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.
- 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 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 worthextra credit at the end of the term.*Green Points*

**Quizzes:** Most Fridays, during weeks in which there is no hour
exam, there will be a short (10-15 minute) quiz at the end of class. These
may or may not be open book or notes, but calculators will (usually) be
allowed. The quizzes are intended to encourage reading the textbook and
classroom discussion about the "real meaning" of some technique we have
learned. Quizzes are each graded out of 10 points, and your lowest quiz
score will be dropped.

**Applied Statistical Exegeses [ASEs]:** You will write six or seven
1-2 page explanations of statistical results whose description you find 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). Our **final exam** is
scheduled for **Tuesday, April 28 ^{th} 10:30am-12:50pm in our
usual classroom**.

**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, 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 at the very next
class meeting. The percentage you can earn back is given in the "revision %"
column of the table below.

**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, **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 | 7 probs | 75% | 18% |

Quizzes: | 10 | ≈10 | 1 | 50% | 13% |

ASEs: | 10 | ≈7 | 0 | 50% | 11% |

Midterms: | >100 | 3 | 0 | 33.33% | 40% |

Final Exam: | >200 | 1 | 0 | 0% | 18% |

**Contact outside class:** Over the years I have been teaching, I have
noticed that the students who come to see me outside class 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, PM 248, during official office hours. If you want to talk to me
privately and/or cannot make those times, please mention it to me in class or
by e-mail, and we can find another time. Please feel free to contact me for
help also by e-mail at
`jonathan.poritz@gmail.com`, 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 before the
next class, or even talk on the telephone (in which case, include in your
e-mail a number where I can reach you).

**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
or number in the subject line of all messages to me**. Also, if you are
writing me for help on a particular problem, please do not assume I have my
book, it is often not available to me when I am answering e-mail; therefore,
you should give me enough information about the problem so that I can
actually help you solve it (*i.e.,* "How do you do problem number
*n* on page *p*" is often not a question I will be able to answer).

**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.
Please do not use a cell phone during class. You may not use a cell phone or
share a calculator with another student during a test.

** Nota bene:** Most rules on due dates, admissibility of make-up
work, etc., will be interpreted with great flexibility for students who are
otherwise in good standing (

**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 in class on this requirement during
the term, so that it does not come as a surprise during tests.

**Tutoring Help:** ** The Math Learning Center** offers
registered CSU-Pueblo students

The PROPEL Center @ CSU-P offers FREE walk-in, one-on-one and online tutoring in addition to mentoring, supplemental instruction sessions, study groups and Summer Academic Forgiveness Education (SAFE) courses with the aim of addressing the individual needs of students pursuing a STEM degree and/or taking STEM courses (Biology, Chemistry, Engineering, Physics, Civil Engineering Technology). The PROPEL Center (Life Science Room 122; 719-549-2652) is open Monday-Friday 9am-4pm.

**Students with disabilities:** 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)*

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 scapel is a surgeon.

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