Colorado State University, Pueblo; Fall 2015
Math 156 — Introduction to Statistics, Section 3
Course Schedule & Homework Assignments
Here is a link back to the course syllabus/policy page.
This schedule is will be changing very frequently, please check it at
least every class day, and before starting work on any assignment (in case the
content of the assignment has changed).
In the following all reading assignments, sections, and page numbers refer to
the required course textbook, The Basic Practice of Statistics,
7^{th} ed., by Moore, Notz, and Fligner, unless otherwise
specified.
If you see the symbol
below, it means that class was videoed and you can get a link by emailing me.
Note that if you know ahead of time that you will miss a class, you should
tell me and I will be sure to video that day for you.
When there is a reading assignment, please read the named section(s) before
that day.
Homework for a particular day is due that day, either in class or
handed in at my office by 3pm.
Week 1
 :
 A lot of bureaucracy and introductions.
 Read the course syllabus and policy page.
 HW0 Send me email (at
jonathan@poritz.net)
telling me:
 Your name.
 Your email address. (Please give me one that you actually check
fairly frequently, since I may use it to contact you during the
term.)
 Your year/program/major at CSUP.
 What you intend to do after CSUP, in so far as you have an idea.
 Past math classes you've had.
 The reason you are taking this course.
 Your favorite mathematical subject.
 Your favorite mathematical
result/theorem/technique/example/problem.
 Anything else you think I should know (disabilities, employment
or other things that take a lot of time, etc.).
 [Optional:] The name of a good book you have read
recently.
Please do this some time Monday. But as some direct incentive: I will
only enter your name into my gradebook and give you your Homework
Late Passes when I get this email, so you really need to
do this assignment as soon as possible. [By the way, just to be fair,
in case you are interested, here is a
version of such a selfintroductory email with information as I would
fill it out for myself.]
 Some content we discussed, terms defined:
 individuals
 variables, categorical and quantitative
 :
 Read Chapters 0 and 1
 Some content we discussed, terms defined:
 graphs for categorical variables:
 bar charts
 pie charts
 frequency
 relative frequency
 graphs for a quantitative variables:
 a stemandleaf plot
 the main such graph: a histogram
 shape
 left or rightskewed
 symmetric
 :
 [Re]read Chapter 1 and read Chapter 2
 Some content we discussed, terms defined:
 distribution
 center [="middle"]
 mean [="average"]
 median
 mode
 Quiz 1 today
 Hand in HW1: 1.{26, 34, 40}
 Today [Friday] is the last day to add classes.
Week 2
 :
 [Re]read Chapter 2
 Hand in ASE1: This first ASE is
quite simple and will likely be fairly short (1/2 a page?). Find
on a website, in a newspaper or magazine, or in a book (maybe a
textbook from another class) a passage (or graph) which uses one or
more of the terms we have worked with so far in this class (the
terms in bold above). What you are to hand in should have
the following parts:
 A statement of the source of your passage. This does
not have to be in any particular bibliographic format, but it
should have enough information so that I could find the passage
myself either in a library or on the Internet.
 Quote the passage or copy the graph. You might
want to cutandpaste into a word processor page, or print out or
copy the item and attach it to the rest of your ASE.
 Have an explanation of the quote or graph: identify what
are the variables, what type they are (categorical or quantitative),
methods (kind of graph; mean or skew or whatever) used.
 Give a critique of the method:
 Is an appropriate method being used (e.g., pie charts
only work for categorical variables where the total is 100% of
the data, etc.)?
 Are good rules used in display (correct terminology used,
graphs fully labelled, high enough resolution to show what is
interesting, etc.)?
 Do you have any concerns about the reliability of the data
— is there an explanation of where it came from, is it
reasonable to assume that it is accurate?
 etc.
Here is an example of the kind of thing we
are looking for. (The "critique" in this example is very friendly and
positive — which is actually unsurprising, since the source is a
famously careful and impartial research organization — while
yours may not be as positive (e.g., sometimes it is fun to find
a published statistic which is full of errors!).
 Some content we discussed, terms defined:
 uni, bi, or multimodal
 how to calculate the median
 mean vs median
 spread
 quartiles
 IQR
 variance and standard deviation
 fivenumber summary
 boxplot
 using a TI8x calculator to compute the fivenumber summary
 1.5IQR rule for outliers
 :
 Read Chapter 3
 Some content we discussed, terms defined:
 density curves
 mean, median, and standard deviation of a
density curve
 Normal distribution and its properties (location of the
mean and standard deviation; symmetry; long, thin tails)
 the standard Normal distribution
 689599.7 rule
 Hand in HW2: 2.{38, 40, 48(hint: compare boxplots,
explain)}
 :
 [Re]read Chapter 3
 Some content we discussed, terms defined:
 working with the Normal distribution:
 symmetry
 total area is 1 (=100%)
 standardizing a nonstandard Normal distribution
 discussion of when Normal distributions are likely to occur
 using the calculator and the book's Table A to find Normal and
inverse Normal values
 Hand in ASE2: Your second ASE should
be something about what we've been covering since the first one,
probably to do with mean, median, mode, spread, IQR, standard
deviation, outliers, etc. It should have the same parts as
the first ASE, as described above, including
 Source
 Quote/copy
 Explanation: identify the variables, what type they are,
methods
 Critique
Here is another example ASE.
If you are looking for a good source of possible statistics in the
wild to analyze on an ASE, you could try:
 any material used in one of your other classes
 any online version of a newspaper, such as
 a specifically datadriven organization, such as one of the
following [descriptions below, when in quotation marks and
italics are taken from the respective site's
selfdescription]

FiveThirtyEight
[FiveThirtyEight is an online journalism site which applies
careful research and thoughtful statistical modeling to
current stories in politics, economics, science, "life", and
sports. It was founded by Nate Silver, who has done
statistical analysis for sports betting and also predicted
statebystate the outcomes in the last several presidential
elections with incredible accuracy.]

The Pew Research
Center ["Pew Research Center is a nonpartisan fact
tank that informs the public about the issues, attitudes and
trends shaping America and the world. It conducts public
opinion polling, demographic research, media content analysis
and other empirical social science research. Pew Research
does not take policy positions."]

The Gapminder
Foundation ["Gapminder is a nonprofit venture –
a modern 'museum' on the Internet – promoting
sustainable global development and achievement of the United
Nations Millennium Development Goals."]

the Gallup polling
organization ["Gallup delivers forwardthinking
research, analytics, and advice to help leaders solve their
most pressing problems. Combining more than 75 years of
experience with its global reach, Gallup knows more about the
attitudes and behaviors of the world's constituents,
employees, and customers than any other organization."]
 Quiz 2 today ... which became a takehome quiz. Please
take this seriously: no consultation with others (including your
textbook and the Internet), sit down and work on it at one go —
do not work for a while, get up, do other things, come back and do more,
etc.
Week 3
 :
 Yes, we do have class today, even though it is the federal
holiday celebrating the achievements of workers and the labor movement
— if you like the 40 hour work week, now is the time to give
thanks.
 Quiz 2 is due at the beginning of class.
 [Re]read Chapter 3 and Read Chapter 4
 Some content we discussed, terms defined:
 a bit more of calculating things with the Normal distribution
(e.g., inverse normal)
 making a scatterplot; explanatory and response
variables
 How to do scatterplots on the calculator.
 Today [Monday] is the last day to drop classes without a grade
being recorded.
 :
 [Re]read Chapter 4
 Some content we discussed, terms defined:
 qualitative descriptions of scatterplots:
 the correlation coefficient $r$ and its relationship to
direction, strength, and form in a scatterplot
 How to compute the correlation coefficient $r$ on the calculator.
 the somewhat different idea of outliers in the context of
scatterplots (...influential observations)
 correlation doesn't care which is explanatory, which is response
 correlation is unchanged when units change
 Hand in HW3: 3.{30, 32, 36}, 4.4 (the problem mentions an
applet which we do not have — just use your calculator or do it
by hand)
 :
Week 4
 :
 [Re]read Chapter 5
 Some content we discussed, terms defined:
 meaning of the LSRL: minimize the sum of the squares of the
residuals
 interpretation of the square of the correlation coefficient $r^2$.
 cautions about regression:
 sensitivity to outliers
 ecological correlation
 lurking variables
 correlation is not causation
 interpretation of the slope of the regression line
 Hand in HW4: 4.{24, 26, 30, 36}
 :
 [Re]read Chapter 5
 Some content we discussed, terms defined:
 finishing regression:
 patterns in residuals
 using the regression line to make predictions
 but beware of extrapolation
 but, the Challenger disaster story...
 residuals
 Hand in ASE4. Good topics would be something with correlation,
which mentioned $r^2$, or which talked about (linear) regression,
etc.
 Starting review for Test I
 :
 More review for Test I. See this review
sheet
 Quiz 4 today
 Hand in HW5: 5.{34, 36, 40, 42}
Week 5
 :
 :
 :
 Read Chapter 8.
 Some content we discussed, terms defined:
 sample vs population
 simple random sample [SRS]
 bias
 voluntary sample bias
 Hand in Test I revisions, if you like.
Week 6
 :
 [Re]Read Chapter 8.
 Some content we discussed, terms defined:
 stratified random sample
 undercoverage
 nonresponse
 response bias and wording effects
 Hand in ASE5 — please try to find one which mentions
sampling, [non]response rates, wording effects, bias, or such things
(or at least describes completely the sampling method).
 :
 :
 [Re]Read Chapter 9.
 Some content we discussed, terms defined:
 publication bias
 confounded variables, again
 experimental design
 statistically significant ... is not the same thing as
significant in regular speech
 block designs
 matchedpairs designs
 Hand in ASE6 — please try to find one which mentions
experimental design, controls, placebos, etc. Remember from
now on, ASEs should always include in their critiques a
discussion of issues of sampling design, possible sources of bias,
issues like wording effects, doubleblindness, voluntary sample bias,
etc.
 Quiz 5 today.
Week 7
 :
 Read Chapter 10.
 Some content we discussed, terms defined:
 confidentiality and anonymity
 institutional review board (or FDA, etc.)
 informed consent
 do no harm
 Hand in HW7: 9.{22, 38, 50}
 :
 Read Chapter 12.
 Some content we discussed, terms defined:
 probability
 sample space
 outcomes vs events
 probability model
 disjoint
 addition rule for disjoint events
 complementary event
 fair coin/die
 Hand in ASE7, which is a special one: read
this article and any other sources you find on the same subject which are
useful, and then do as detailed an ASE as you can on this
topic, containing all the usual parts (as usual since last week,
critique also sampling design and discuss possible sources of bias).
Also include a section in this ASE discussing the
ethics of this study. Use the ethical criteria we
discussed in class and which are in Chapter 10 of our textbook.
[This ASE may be handed in on Friday, if you prefer ‐ but
it is probably a good idea at least to get started now, since there is
also a homework set due on Friday.]
 :
 [Re]Read Chapter 12.
 Some content we discussed, terms defined:
 finite probability model
 random variable [RV]
 discrete and continuous RVs
 distribution of an RV
 density curve of a continuous RV
 Quiz 6 was handed out today, it is due on Monday
 Hand in HW8: 10.{10, 12, 18}, 12.32
Week 8
 :
 Yes, we do have class today, even though it is the federal
holiday celebrating the arrival of Christopher Columbus in the New
World. (Not so clear why we celebrate him: his idea of how big the
world is was wildly off the mark (unlike the quite accurate estimate
produced by Eratosthenes in the 3^{rd} century BCE); he never
actually made it to the North American continent; he brought back from
his very first trip some of the indigenous people he met as slaves;
etc., etc.)
 Read Chapter 13
 Some content we discussed, terms defined:
 the conditional probability of event $A$ given event $B$,
written $P(A\mid B)$
 independent events
 multiplication rule for independent events
 Venn diagrams
 Hand in Quiz 6
 Hand in ASE8 — again please try to find one which
mentions experimental design... maybe controls, placebos,
or the like. Again, critique sampling, look for possible sources of
biases  also ethics, if it is at all possible.
 :
 [Re]Read Chapter 13
 Some content we discussed, terms defined:
 two addition rules for probabilities: the general case and
the case of disjoint events
 two multiplication rules for probabilities: the general
case and the case of independence events
 relationship between "disjoint" and "independent"
(almost none!)
 tree diagrams to simplify conditional probability
computations
 the Monty Hall Problem
 :
 Review for Test II. See this review sheet.
 Hand in HW9: 12.{42, 44, 48}, 13.{30, 32, 38}
 Quiz 7 today.
Week 9
 :
 :
 :
 Read Chapter 15
 Some content we discussed, terms defined:
 parameter vs statistic
 the Law of Large Numbers
 population distribution vs
sampling distribution
 the sample mean $\overline{x}$ as a statistic for the
population mean $\mu$: it is an unbiased statistic
 Hand in Test II revisions, if you like.
 no quiz today
 Today [Friday] is the last day to withdraw (with a W) from
classes.
Week 10
 :
 [Re]Read Chapter 15
 Some content we discussed, terms defined:
 standard deviation of the statistic $\overline{x}$ is
$\sigma/\sqrt{n}$ for SRSes of size $n$
 if samples are SRSes taken from a Normally distributed population
then $\overline{x}$ is also Normally distributed
 The Central Limit Theorem: as $n$ gets large, the
distribution of $\overline{x}$, if the samples are SRSes, gets
closer and closer to $N(\mu,\sigma/\sqrt{n})$
 Hand in ASE9, which is another special one: Please find some
discussion of probability (might be called "chance" or
"likelihood") in a book, article, or website. This should be
fairly complete discussion of the probability of something, maybe with
a conclusion to be drawn from that probability (e.g., "Don't
take statistics in college, there's an 87% chance you'll end up loving
it so much you will switch majors to math"). On this ASE (and
only on this ASE), then, skip the usual parts, but instead
have:
 a complete reference to the source you are analyzing
 a complete description of the probability calculation they are
using: what is the sample space, probability model, any
assumptions about independence,
conditional probability (maybe not called exactly that, but
there anyway), etc.
 a critique of the model: is it a reasonable description of the
realworld phenomenon under discussion, and is it put together in
a mathematically reasonable way (e.g., can you suggest any
corrections/improvements...)
 :
 Read Chapter 16
 Some content we discussed, terms defined:
 confidence interval, its confidence level
 formulæ for the confidence interval for a population mean
when the population standard deviation $\sigma$ is known
 the critical value $z^*$
 Hand in HW10: 15.{24, 26, 28, 30}
 :
 [Re]Read Chapter 16
 Some content we discussed, terms defined:
 being able to explain the meaning of the confidence level
of a confidence interval which, oddly, tells us nothing about the
particular interval reported but instead about the method used to
create those kinds of intervals
 the margine of error [MoE] of a confidence interval
 response of the MoE to changing the confidence level, population
standard deviation, or sample size
 Quiz 8 today.
Week 11
 :
 Read Chapter 17
 Some content we discussed, terms defined:
 test of significance (also called a hypothesis test)
 null and alternative hypothesis, $H_0$ and $H_a$
 test statistic (also called the $z$statistic)
 the logic of a test of significance: the idea of a
pvalue (be able to explain!)
 formulæ for the pvalue in a test about the mean
of a population when the population standard deviation $\sigma$ is
known
 Hand in HW11: 16.{8, 10, 20, 22}
 :
 [Re]Read Chapter 17
 Some content we discussed, terms defined:
 one and twosided tests; different formulæ
for the pvalue (always assuming the population standard
deviation $\sigma$ is known)
 again, the logic of the pvalue
 a test valid (or statistically significant) at some
significance level $\alpha$
 Hand in ASE10 — please try to find one which mentions
confidence intervals, margin of error (sometimes called
"sampling error" in the press). This is back to the usual
style of ASEs which needs all parts laid out completely
(source, explanation including
individuals/variables/methods/etc., critique...).
 :
Week 12
 :
 [Re]Read Chapter 18
 Some content we discussed, terms defined:
 confidence intervals for means or tests of significance using
the $z$statistic are very sensitive to outliers, so always make
a histogram to see if the data is wellbehaved before using these
methods
 a formula for how big a sample size you need to have in order to
get a specific MoE for a confidence interval
 Type I (rejecting a true $H_0$) and Type II
(failing to reject $H_0$ when $H_a$ is true) — these are
related to, but "false positive" and "false negative" but
not the same, because "negative" and "positive" can change
meaning depending upon the precise wording of the hypotheses
 Hand in ASE11 — please try to find one which mentions
tests of significance, hypothesis testing (pvalue
would be great) ... look for any of the terms from tests of significance
particularly "[alternate/null] hypothesis". Do a complete
usual ASE, also laying out what the hypotheses were, the type
of test statistic used, the pvalue found (if given), or the
significance level used (also if given).
 :
 Yes, we do have class today, even though it is the federal
holiday honoring verterans of the United State Armed Forces.
 Review for Test III. See
this review sheet.
 Hand in HW13: 18.{12, 18, 20, 34}
 :
 Test III in class today. Don't forget your calculator!
Week 13
 :
 :
 Read Chapter 20
 Some content we discussed, terms defined:
 using the $t$distribution table (or function in the calculator):
degrees of freedom
 standard error
 confidence intervals using the $t$distribution, for the
population mean when the population standard deviation is unknown
 Hand in Test III revisions, if you like.
 :
 Read Chapter 20
 Some content we discussed, terms defined:
 tests of significance for the population mean when the population
standard deviation is unknown: the $t$test, which uses
the $t$statistic
 doing confidence intervals or tests of significance in
matched pairs experimental designs
Week 14
 Thanksgiving Break! No classes, of course.
Week 15
 :
 Read Chapter 22
 Some content we discussed, terms defined:
 sample proportion is usually denoted $\hat{p}$
 when $n$ is large and the samples are SRSes, $\hat{p}$ is
approximately $N\left(p,\sqrt{p(1p)/n}\right)$
 confidence intervals for the population proportion
 Hand in HW14: 20.{24, 26, 28, 40, 44} [you may hand this
homework in on Tuesday this week, in case you didn't finish it over
Thanksgiving Break, and it will not count as late ... but don't
delay more than that, there is more material coming up!]
 :
 Read Chapter 22
 Some content we discussed, terms defined:
 how big a sample to take to achieve confidence interval for
the population proportion with some desired MoE
 the test statistic for tests of significance about the
population proportion
 the plus four confidence interval
 Hand in ASE12 — subject of your choice (but be careful
and complete)!
 :
 Review for final exam. See
this review sheet.
 Hand in HW15: 22.{8, 26, 38, 44}
 Today is the last day to hand in any late work, even with
Homework Late Passes.
Please also hand in any unused Homework Late Passes you have left,
for course extra credit.
Week 16