## Colorado State University — Pueblo, Fall 2016 Math 156, Introduction to Statistics, Section 1 [In Physical Space] 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).

Below, we refer to the text Introduction to Statistics, hosted by Saylor Academy, as SIS. The book was originally written by Douglas S. Shafer and Zhiyi Zhang, both of the University of North Carolina, and is released under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported (CC BY-NC-SA 3.0 license. Here is an on-line version of this book, while here is a PDF of the full book (and here is a local copy) and here is a DOCx, either of which can be downloaded and saved, printed, or searched.

If you see the symbol below, it means that class was videoed and you can get a link by e-mailing 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.

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 e-mail (at jonathan@poritz.net) telling me:
2. Your e-mail address. (Please give me one that you actually check fairly frequently, since I may use it to contact you during the term.)
4. What you intend to do after CSUP, in so far as you have an idea.
5. Past math classes you've had.
6. The reason you are taking this course.
9. Anything else you think I should know (disabilities, employment or other things that take a lot of time, etc.).
10. [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 e-mail, 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 self-introductory e-mail with information as I would fill it out for myself.]
• Some content we discussed, terms defined:
• individuals, population, sample
• variables, measurements
• categorical [also called qualitative] and quantitative
• some big picture discussion of what the whole subject of statistics is about
• :
• Read SIS §1.1, SIS §1.2, SIS §1.3, SIS §2.1
• Some content we discussed, terms defined:
• parameter vs statistic
• data list and data frequency table
• graphs for categorical variables:
• bar charts
• pie charts
• graphs for a quantitative variables:
• a stem-and-leaf plot
• the main such graph: a histogram
• variants: frequency and relative frequency
• shape
• classes [or bins]
• Hand in BI1. This will be an unusual one: write down two or three things you were surprised about in the organization of this course. Be specific, mention types or numbers or formats of some assignments, etc.
• :
• Discussion of ASEs (see more below, next Monday). First is due soon!
• Some content we discussed, terms defined:
• the notation $\sum x$, or $\sum_{i=1}^n x_i$
• measure of central location [of some quantitative data]:
• [sample] mode
• sample mean $\overline{x}$ and population mean $\mu$
• Quiz 1 today
• Hand in HW1: SIS §1.1: 16, SIS §1.3: 4, SIS §2.1: 4, 8, 14 [in 14, add: What kind of graphical representation(s) of this data can you make? Sketch it (them)!]
• Hand in BI2 (on an idea from Wednesday's class or readings)
• Today [Friday] is the last day to add classes.

#### Week 4

• :
• Some content we discussed, terms defined:
• complement of a subset [event], notation $E^c$, translation into English: not
• Venn diagrams
• probability rule for complements
• intersection of sets [events], notation $A\cap B$, translation into English: and
• union of sets [events], notation $A\cup B$, translation into English: or
• Hand in BI9 (on an idea from Friday's class or readings)
• Hand in ASE3. See above, here and here, for the required parts of an ASE (the second of those explanations above also has a list of a few sites you could go to in order to find materials for an ASE, although of course something you are interested in yourself would probably be much more fun). Please look for something which mentions variability, standard deviation, and/or outliers.
• :
• Some content we discussed, terms defined:
• mutually exclusive events, notation $\emptyset$ for the empty set
• the book's Probability Rule for Mutually Exclusive Events is somewhat inaccurate: while it is true that if events $A$ and $B$ are mutually exclusive, then $P(A\cap B)=0$, it is not true that if $P(A\cap B)=0$ then $A$ and $B$ are necessarily mutually exclusive.
• the conditional probability $P(A\mid B)$ of event $A$ given event $B$
• Hand in BI10 (on an idea from Monday's class or readings)
• :
• Some content we discussed, terms defined:
• independent and dependent events
• random variables [RVs]
• discrete and continuous RVs
• Hand in BI11 (on an idea from Wednesday's class or readings)
• Quiz 4 today [on probability computations, including Venn diagrams, intersections, unions, complements, and conditional probabilities]
• Hand in HW4: SIS §3.1: 2, 6, 16, SIS §3.2: 4, 8, 16, and SIS §3.3: 6, 10

#### Week 5

• :
• Some content we discussed, terms defined:
• the [probability] distribution of a discrete RV
• mean or expectation of an RV
• Hand in BI12 (on an idea from Friday's class or readings)
• Hand in ASE4. Please try to find something which mentions probability, maybe even conditional probability, and/or independence [for events], if possible.
• :
• Read SIS §5.1 and SIS §5.2
• Some content we discussed, terms defined:
• the [probability] distribution of a continuous RV
• how to computer probabilities from the distribution of a continuous RV
• the Normal Distribution with mean $\mu$ and standard devision $\sigma$
• the standard Normal RV
• tools [tables] to compute probabilities on the standard Normal distribution
• Hand in BI13 (on an idea from Monday's class or readings)
• :
• Some content we discussed, terms defined:
• computing probabilities for general [non-standard] Normal RVs, algebraically and then with a standard Normal table or tool
• computing probabilities for general [non-standard] Normal RVs, directly with calculators and computers
• Hand in BI14 (on an idea from Wednesday's class or readings)
• Quiz 5 today [on independence, RVs, distribution of RVs, Normal distributions and probabilities]
• Hand in HW5: SIS §3.3: 2, 4, 8, SIS §4.1: 4, SIS §4.2: 2, 10, 12 a&b, SIS §5.1: 4, and SIS §5.2: 2 a, b, d, & e

#### Week 6

• :
• Some content we discussed, terms defined:
• areas of tails of the standard Normal distribution
• finding cut-offs for tails of the standard Normal distribution with specified areas
• the above for non-standard Normal distributions
• Hand in BI15 (on an idea from Friday's class or readings)
• Hand in ASE5. It would be nice to find something which uses one of our recent terms, such as normally distributed, or expectation [in probability].
• :
• :
• Test I in class today. Make sure you are comfortable with the material outlined on this review sheet. Don't forget your calculator, or other favorite electronic device!

#### Week 7

• :
• There was a delay with grading midterm I -- sorry! As a consequence, it's best to start new material today and come back to the midterm on Wednesday. So:
• Skim the following background, examples of ethically questionable experiments:
1. Nazi doctors experimented on human subjects during the Holocaust. It is very hard to read about this horror. But — despite the denials of some deranged quacks even today — it really did happen, and We Must Never Forget, as is said. If you want to look into this, search a bit on the Internet, or read a few articles in Wikipedia on the subject.
2. The Tuskegee syphilis experiment, particularly the background sections on History, Study termination, and Aftermath, as well as the section Ethical implications, important for our class
3. Philip Zimbardo's Stanford Prison Experiment, particular the sections on Goals and methods and Ethical issues
4. Stanley Milgram's experiment on obedience to authority figures, particularly the sections The experiment and Ethics
• Some content we discussed, terms defined: Ethical experimental design is now a major subject of study. Major organizations have made statements of principles in this area, for which you might look at this Wikipedia page or other articles to which it refers. In this large, nuanced field, we will take as basic at least the following four required components of ethical experimentation on human subjects:
1. Informed Consent: Note that true informed consent is more difficult than it might seem at first. In particular, economic or other constraints on potential experimental subjects might make it very hard for them to refuse. Also, being truly informed does mean that subjects are aware of all possible consequences and outcomes, good and bad, of the experimentation.
2. "Do No Harm": This, also, can be tricky. Some inconvenience to a subject might be considered small harm contrasted with a potentially large benefit from running the experiment through to its conclusion. But the principle insists that we confront this issue and always err, to the extent we can, on conservative views of what might harm the experimental subjects. This principle is related, therefore, to the Hippocratic Oath taken by physicians, which contains the requirement First do no harm.
Note also that paying attention to this issue sometimes requires that an experiment be interrupted early, if preliminary data show that one treatment or another in the experiment is doing harm to some of the subjects.
3. Anonymity/Confidentiality: This again is based on respect for the autonomy of experimental subjects, that they should be able to control the release of information about themselves. The default, therefore, is that subjects' identities must be kept confidential when the experimental results are announced. The easiest way to do this, although often not the way it is actually done, is for the subjects actually to remain anonymous during the entire experiment.
4. Institutional Review Board [IRB] (or FDA) oversight: The IRB is an external board which checks that the principles of ethical experimental design are being followed in each case. The IRB must be approached, in advance, regarding any experimentation that has human subjects, for approval when the organization (university, company, research lab, etc.) gets any US Federal support. Failure to do so can result in all future such funding being cut to that organization. See this Wikipedia article.
In the US, the Food and Drug Administration (FDA) has oversight of medical products and drugs, some of which includes detailed control of the clinical experiments done to validate them.
• :
• Test I post-mortem.
• Hand in BI17 on basics of experimental ethics.
• :
• Skim The Belmont Report (or even this Wikipedia summary), a famous and important report giving Ethical Principles and Guidelines for the Protection of Human Subjects of Research, as its subtitle says.
• Hand in BI18. This is a special one: please write a paragraph about how you think Test I went for you. Are you perfectly content with how it turned out? If not, what do you think was the cause of the trouble? And what can you do next time to make things better?
• Hand in Test I revisions, if you like.
• Quiz 6 today [on experimental ethics]

• #### 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 3rd 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.)
• Some content we discussed, terms defined:
• observational studies vs experiments
• bias
• control groups
• randomization [to prevent bias]
• The Placebo Effect
• blinding and particularly double-blind experiments
• RCTs
• Hand in BI19 (on an idea from Friday's class or readings)
• Hand in ASE6, which is a special one: read this article and any other sources you find on the same subject which are useful (such as the research report in the Proceedings of the National Academy of Sciences to which there is a link in that first article), and then do as detailed an ASE as you can on this topic, containing all the usual parts. 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 the readings from last week. As a consequence, this ASE will probably be a fair bit longer than usual.
• :
• Some content we discussed, terms defined:
• the sampling distribution of a statistic
• the probability distribution of the sample mean, particularly its mean and standard deviation
• Hand in BI20 (on an idea from Monday's class or readings)
• :
• Some content we discussed, terms defined:
• The Central Limit Theorem [CLT]
• volunteer sample bias
• block designs for experiments
• Quiz 7 today [on experimental design, basics of the sampling distribution of the mean, and SRSs]
• Hand in BI21 (on an idea from Wednesday's class or readings)
• Hand in HW7:
1. Suppose I am curious if people learn as well when they read books on a screen (such as a phone, computer, or e-reader) as they do when they read the same book on paper. Describe in a sentence or two (or three...) an observational study I might do on this topic, and then, separately, an experiment.
2. For the observational study, think of a lurking variable which might be confounded with the variable of the study you proposed.
3. People who eat lots of fresh fruits and veg have lower rates of colon cancer than people who don't eat those things. One ideas is that certain vitamins in these foods have a preventative effect for cancer. To test this, a researcher got 1000 people who were at risk of colon cancer and divided them into a group which got a vitamin supplement every day and another group which got a placebo. The experiment was performed double-blind.
After four years of this study, it was found that there was almost no difference in colon cancer rates.
1. Was that an observational study or an experiment?
2. Explain very concretely how the experiment was (should have been) done: groups chosen, pills given, results processed, etc.
4. The experimental result in the previous problem was surprising because it is really a fact that people who eat the fruit and veg which have those vitamins do have lower rates of colon cancer. Suggest some lurking variables which might explain this observation. Since the experiment found no difference in colon cancer rates, one of the lurking variables you suggest might be the real cause of the beneficial effect of eating fruits and veg, rather than just the vitamins, as our disappointed experimenter above was hoping.
5. SIS §6.1 problem 4

#### Week 9

• :
• Some content we discussed, terms defined:
• the idea of a confidence interval, particularly the meaning of its confidence level [very important!]
• the large-sample confidence for the population mean
• the margin of error of a confidence interval
• the critical values used in the formulæ for confidence intervals
• Hand in BI22 (on an idea from Friday's class or readings)
• Hand in ASE7. See if you can find a source which describes its experimental design, mentioning a few of the terms we have used in our discussions of this topic. Then do a usual ASE which talks about individuals, populations, variables, methods, etc., and then also includes a critique of the stated experimental design.
• :
• Some content we discussed, terms defined:
• the small-sample confidence for the population mean
• Student's $t$-distribution
• Hand in BI23 (on an idea from Monday's class or readings)
• :
• Some content we discussed, terms defined:
• the large-sample confidence interval for the population proportion
• Hand in BI24 (on an idea from Wednesday's class or readings)
• Quiz 8 today [on confidence intervals for the population mean]
• Hand in HW8: SIS §6.2: 2, 10; SIS §7.1: 2, 8; SIS §7.2 6, 8
• Today [Friday] is the last day to withdraw (with a W) from classes.

#### Week 10

• :
• Some content we discussed, terms defined:
• the sample size needed for a particular margin of error in a CI for a population mean
• the sample size needed for a particular margin of error in a CI for a population proportion
• the most conservative estimate (of that sample size for proportions)
• Hand in BI25 (on an idea from Friday's class or readings)
• Hand in ASE8. Try to find one about a confidence interval for a population mean or average (same thing). It can help to look for the phrase "margin of error." Be careful not to get a source which is about a confidence interval for a percentage (like election data often is, for example), since that is not a CI for a mean (means are not percentages).
• :
• Read SIS §8.1 but skip the sections called The Rejection Region and Standardizing the Test Statistic; in the section Two Types of Errors, only read the definition of the two types, skip the "level of significance of the test"
• Some content we discussed, terms defined:
• the null hypothesis $H_0$ and alternative $H_a$ of a test of hypotheses ... also called a test of significance and hypothesis test
• our null hypotheses $H_0$ are (always!) of the form $H_0$: parameter = value
• our alternative hypotheses $H_a$ can have the form
• $H_a$: parameter ≠ value, called a two-tailed test; or
• either
• $H_a$: parameter < value or
• $H_a$: parameter > value
both called one-tailed tests
• conclusions we make: "reject $H_0$" or "fail to reject $H_0$"
• what could go wrong? there are two types of errors we could make:
• a Type I error, when we reject the $H_0$ even though it is true, and
• a Type II error, when we fail to reject the $H_0$ even though it is false
• Hand in BI26 (on an idea from Monday's class or readings)
• :
• Read SIS §8.2 looking mostly for the definition of the test statistic and the examples; read this page for details of how we will do the tests in this class.
• Some content we discussed, terms defined:
• test statistic or $z$-statistic
• $p$-value of a test [this is very important, and you will be expected to understand and to be able to explain this concept]
• significance level
• Hand in BI27 (on an idea from Wednesday's class or readings)
• Quiz 9 today [on confidence intervals for the population proportion, finding the sample size needed for a given margin of error, and/or some basic ideas/terms from hypothesis testing]
• Hand in HW9: SIS §7.3: 6, 20 [hint: "point estimate" here is another way of saying "sample proportion"]; SIS §7.4: 2, 4, 16; SIS §8.1: 2.

#### Week 11

• :
• Read, if you like, SIS §8.3 — that is the book's description of the material we've already seen on this page. New material to read for today is SIS §8.4, or this page for our version of this.
• Some content we discussed, terms defined:
• Always start a hypothesis test by stating the population, RV, parameter of interest, and null and alternative hypotheses $H_0$ and $H_a$
• formulæ for the test statistic in a hypothesis for a population mean $\mu$ in the case of
• known population standard deviation $\sigma$: the test statistic is a $z$-statistic, with formula $z=\frac{\overline{X}-\mu_0}{\sigma/\sqrt{n}}$; you compute the $p$-value with the standard Normal table (based upon what kind of alternative hypothesis you have); this whole test is then called a "$Z$-Test".
• unknown population standard deviation: the test statistic is a $t$-statistic, with formula $t=\frac{\overline{X}-\mu_0}{s/\sqrt{n}}$, where $s$ is the sample standard deviation; you compute the $p$-value with the appropriate part of a table of Student's $t$-Distribution depending upon the degrees of freedom $df=n-1$ and in the direction determined by the kind of alternative hypothesis you have); this whole test is then called a "$T$-Test".
• Hand in BI28 (on an idea from Friday's class or readings)
• Hand in ASE9. Try to find one about a confidence interval for a population proportion -- there should be tons of these in coverage of the presidential election. It can help to look (again) for the phrase "margin of error." Be careful not to get a source which is about a confidence interval for a population mean; proportions will often be expressed as percentages, remember.
• :
• Read SIS §8.5 or our version of this material
• Some content we discussed, terms defined:
• the test statistic for a hypothesis test of the population proportion: $z=\frac{\widehat{p}-p_0}{\sqrt{p_0(1-p_0)/n}}$
• the process for a hypothesis tests for the population proportion, which is just like the $Z$-Test using this new version of the $z$-statistic
• Hand in BI29 (on an idea from Monday's class or readings)
• :
• Review for Test II. See this review sheet.
• Hand in BI30 (on an idea from Wednesday's class or readings)
• Quiz 10 today [on confidence intervals for the population mean with known and/or unknown population standard deviation and/or for the population proportion; particular attention on the logic and structure of hypothesis test and the meanings of $p$-values]
• Hand in HW10: In these problems, always use the $p$-value approach of the descriptions in the web pages for our class: one, two, three, and four. Problems to do are SIS §8.2: 8, 14; SIS §8.4: 12, 18; and SIS §8.5: 12, 14.

#### Week 12

• :
• :
• Test II post-mortem.
• :
• Yes, we do have class today, even though it is the federal holiday honoring veterans of the United State Armed Forces.
• Read SIS §10.1 and SIS §10.2
• Some content we discussed, terms defined:
• independent and dependent variables
• scatterplots
• shape, strength, and direction of a relationship visible in a scatterplot
• [linear] correlation coefficient, some properties
• Hand in BI31. This is another special one: think about the previous special BI18. Did the same thing happen? Did you manage to make the change you contemplated? Did it have the desired effect? What do you think you could do next time?
• Hand in Test II revisions, if you like.

#### Week 13

• :
• Skim SIS §10.3 and read SIS §10.4
• Some content we discussed, terms defined:
• review of equations of lines:
• slope
• $y$-intercept
• equation: $y=mx+b$
• the idea of the least squares regression line [LSRL]
• how to compute the LSRL
• electronic tools to compute correlation coefficients and LSRLs:
• Hand in BI32 (on an idea from Friday's class or readings)
• Hand in ASE10: this is a "free-range" ASE: pick a topic that interests you, a nice article or webpage or whatever, which has a clear bit of statistical content, and write up an ASE as we've been doing all semester. [So be sure to clearly talk about the population, variable[s], parameter[s], sample, methods, etc.] If you want to do one which has a scatterplot and/or mentions correlation, that would be great [but is not required, since we've just started talking about this material].
• :
• Some content we discussed, terms defined:
• using the LSRL to guess missing values of a linear relationship [interpolation]
• potential issues with the LSRL:
• correlation is not causation — but it sure is a hint
• sensitivity to outliers — but what are outliers on scatterplots?
• extrapolation — but sometimes it's the best you can do
• the meaning of $r^2$, the square of the correlation coefficient
• time permitting, discussion of using LSRLs when the relationship is not linear
• Hand in BI33 (on an idea from Monday's class or readings)
• Hand in HW11: SIS §10.1: 4, 8, 12; SIS §10.2: 6, 12; and SIS §10.4: 4, 12.
• :
• Some content we discussed, terms defined:
• Hand in BI34 (on an idea from Wednesday's class or readings)
• No quiz today because this material [on scatterplots, the correlation coefficient, and least squares regression lines] will be tested in the [fairly short] midterm following our Thanksgiving Break.

#### Week 14

• Thanksgiving Break! No classes, of course.

#### Week 15

• :
• :
• Test III in class today. Make sure you are comfortable with the material outlined on this review sheet. Don't forget your calculator, or other favorite electronic device!
• Today is the last day to hand in any late work for credit, even with Homework Late Passes.
Please also hand in any unused Homework Late Passes you have left, for course extra credit.
• :
• Test III post-mortem will be sent by email! If you do not get an email with links to videos explaining how to do the Test III problems, inquire further (by email) about it. But there will be no in-person class.
• Make sure you drop by GCB314 at some point to pick up any graded work for which you may be waiting.
• Review for final exam by looking over this review sheet and watching this video.
• Hand in BI35, a special one: what do you intend to do for the next few days to enable you to do the best you possibly can on the final exam for this class? Be specific!