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 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.

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.

• :
  • A lot of bureaucracy and introductions.
  • Read the course syllabus and policy page.
  • HW0 Send me e-mail (at jonathan@poritz.net) telling me:
    1. Your name.
    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.)
    3. Your year/program/major at CSUP.
    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.
    7. Your favorite mathematical subject.
    8. Your favorite mathematical result/theorem/technique/example/problem.
    9. Anything else you think I should know (disabilities, employment or other things that take a lot of time, etc.).
    17. [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
    • 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 stem-and-leaf plot
      • the main such graph: a histogram
        • shape
        • left- or right-skewed
        • 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.

• :
  • [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:
    1. 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.
    2. Quote the passage or copy the graph. You might want to cut-and-paste into a word processor page, or print out or copy the item and attach it to the rest of your ASE.
    3. 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.
    4. 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
    • five-number summary
    • boxplot
    • using a TI-8x calculator to compute the five-number 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
    • 68-95-99.7 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 non-standard 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
    1. Source
    2. Quote/copy
    3. Explanation: identify the variables, what type they are, methods
    4. 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
      • The Pueblo Chieftain
      • The Denver Post
      • The New York Times
      • many, many others...
    • a specifically data-driven organization, such as one of the following [descriptions below, when in quotation marks and italics are taken from the respective site's self-description]
      • FiveThirtyEight [FiveThirtyEight is an on-line 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 state-by-state 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 non-profit 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 forward-thinking 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 take-home 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.

• :
  • 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:
      • direction
      • form
      • strength
    • 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)
• :
  • Read Chapter 5
  • Some content we discussed, terms defined:
    • review of equations of lines in the plane: $y=a+bx$
    • The least squares regression line
    • How to compute the least squares regression line on the calculator.
  • Quiz 3 today
  • 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).
    This ASE should please talk about something being "Normally distributed" (or even "bell-shaped curve," as long as there then is a lot of numerical detail which uses this Normal distribution) or should have a scatterplot and/or mention correlation coefficient.

• :
  • [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}

• :
  • Test I in class today. Make sure you are comfortable with the material outlines on this review sheet. Don't forget your calculator!
• :
  • Test I post-mortem.
• :
  • 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.

• :
  • [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).
• :
  • Read Chapter 9
  • Some content we discussed, terms defined:
    • observational studies vs experiments
    • subjects
    • treatment
    • factors
    • randomization and controls
    • double-blind
    • placebo, placebo effect — see the wonderful videos by Ben Goldacre, such as:
      1. A TED talk on "Battling Bad Science"
      2. a short one called The placebo effect
      3. or Ben at Nerdstock
  • Hand in HW6: 8.{30, 38, 46, 48}
• :
  • [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
    • matched-pairs 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, double-blindness, voluntary sample bias, etc.
  • Quiz 5 today.

• :
  • 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

• :
  • 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.

• :
  • Test II in class today. Make sure you are comfortable with the material outlines on this review sheet. Don't forget your calculator!
• :
  • Test II post-mortem.
• :
  • 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.

• :
  • 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 p-value (be able to explain!)
    • formulæ for the p-value 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 two-sided tests; different formulæ for the p-value (always assuming the population standard deviation $\sigma$ is known)
    • again, the logic of the p-value
    • 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...).
• :
  • Read Chapter 18
  • Some content we discussed, terms defined:
    • confidence intervals and tests of significance are only valid if the sample data is from an SRS
    • don't give too much importance to the p-value (it leaves you open to "p-hacking") [see this amusing post]
    • MoEs and p-values only account for variation due to the randomness of the sample choice, not for any effects due to poor survey or experiment design
    • careful how you state your conclusions: you can never use statistical evidence to prove or disprove your hypotheses
  • Quiz 9 today.
  • Hand in HW12: 17.{6, 10, 14, 32}

• :
  • [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 well-behaved 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 (p-value 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 p-value 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!

• :
  • Test III post-mortem.
• :
  • 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

• :
  • 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 $N\left(p,\sqrt{p(1-p)/n}\right)$
    • 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.

• Exam week, no classes.
• :
  • Extra office hours today, most of the day. If you want to be sure to find your professor at a particular time, make an appointment -- but drop by even if you don't have an appointment but want to talk about statistics.
• :
  • [comprehensive] FINAL EXAM in our usual classroom today from 8-10:20am. Don't forget to bring your calculator and page of formulæ — see the final review sheet for other information about the final.