Colorado State University — Pueblo, Fall 2016
Math 156, Introduction to Statistics, Section 5 [Online]
Course Schedule & Homework Assignments

Here is a link to the page of common comments on graded 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 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.

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 handed in at my office or emailed to me by 3pm. It's probably a good idea to do the BIs for a particular reading, video, or audio immediately after you consume that media. They are almost always on the schedule as due a day or two later, but if you wait to do them, the medium will not be fresh in your mind.

• :
  • A lot of bureaucracy and introductions:
    • Vid1: What is Statistics?
    • Vid2: Syllabus Walkthrough
  • Read the course syllabus and policy page.
  • Vid3: First Basic Terms, which were:
    • individuals, population, sample
    • variables, measurements
    • categorical [also called qualitative] and quantitative
  • 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.]
• :
  • Read SIS §1.1, SIS §1.2, SIS §1.3, SIS §2.1
  • Content:
    • data list and data frequency table
    • graphs for categorical variables, for which see the discussion from the top of page 14 to the top of page 19, in this reading.
      • bar charts
      • pie charts
    • You might be interested in this particular example of a bad bar chart [what's wrong with it?] or this general critique of 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 [sometimes also called bins]
  • Submit (electronically or on paper) BI1: a response to Vid1: What is Statistics? This will be hard to do with the precision most BIs will have in the rest of the course, but try anyway. You may also want to consult SIS §1.2.
  • Submit BI2. 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. Consult Vid2: Syllabus Walkthrough and the syllabus itself.
  • Submit BI3. This will be much more like BIs for the rest of the course: find a big idea in the material from Vid3: First Basic Terms, some of which is also in the reading for today (SIS §1.1), for which to give a very precise, general definition.
• :
  • Read the description, below, of an ASE — one is due on Monday!
  • Read SIS §2.2
  • Content to concentrate on first, from this reading:
    • 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 $\mu$
    • some comments on this material are in Vid4: Comments on Measures of Central Location.
  • Quiz 1 today — drop by my office any time today to take it, or else make other arrangements with me.
  • Submit BI4 on data lists and data frequency tables. Consult SIS §1.3.
  • Submit BI5 on bar and pie charts for categorical variables. Consult this reading and/or the bad example and general critiques mentioned above.
  • Submit BI6 on stem-and-leaf charts and/or histograms (how to make them, particularly being careful about bins/classes, etc.). consult SIS §2.1
  • Submit 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)!]
  • Today [Friday] is the last day to add classes.

• :
  • Reread SIS §2.2
  • Submit BI7 on measures of central location. Consult SIS §2.2 and Vid4: Comments on Measures of Central Location.
  • Submit 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 create 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!).
  • Last content from the current reading to concentrate on:
    • computing means from data and data frequency tables
    • means are very sensitive to outliers [not a phrase used in the book, but very important nonetheless]
    • [sample] median $\widetilde{x}$
    • shape of a histogram: symmetric, and skewed right or left — how to tell which direction is the skew; see Vid5: Mode, Skew, and Balance Points.
• :
  • Read SIS §2.3
  • Content:
    • the range
    • the sample variance $s^2$ and sample standard deviation $s$
    • the population variance $\sigma^2$ and population standard deviation $\sigma$
  • See Vid6: S2O of Range, Variance, StDev -- Variability for:
    • sensitivity to outliers of range, variance, and standard deviation
    • discussion of importance of variability in data; what it means for the variance (standard deviation) to be 0.
  • See Vid8: Computation of Variability Measures with Electronic Devices for an explanation of how to compute variances and standard deviations with electronic tools.
  • Many web pages describe how to use your favorite calculator to do statistical computations. If you have a TI-84, for example, this is a good reference for variance, standard deviation, and IQR. If you have another calculator, just use your favorite search engine to look for "compute standard deviation on a calculator name." You can also find many smartphone apps, some probably free, on your favorite app store. And finally, if you search for "online standard deviation calculator," you will find many web pages which will do these kinds of computations for you on whatever Internet-connected device you have.
  • Submit BI8 on further aspects of measures of central location, based on recent readings and videos.
• :
  • Read SIS §2.4
  • Content:
    • percentiles
    • quartiles $Q_1, Q_2, Q_3$
    • the five-number summary
    • a boxplot (also called box-and-whisker plot)
    • the interquartile range [IQR] — which is a measure of the variability of a dataset which is insensitive to outliers!
    • the $z$-score of a data value
  • See Vid7: inS2O of the IQR and Importance of z-Scores for:
    • how to compute and display these things with electronic tools
    • the insensitivity to outliers of the IQR
    • discussion of the role of $z$-scores
  • See Vid8: Computation of Variability Measures with Electronic Devices for an explanation (also; we've seen this video before) of how to compute IQRs with electronic tools.
  This page> (which we have seen before) explains how to compute IQRs on a TI-84, if that's your calculator. If you have a different calculator, just use your favorite search engine to look for "compute IQR on a calculator name" or "compute quartiles on a calculator name." You can also find many smartphone apps, some probably free, on your favorite app store. And finally, if you search for "online IQR calculator" or "online quartile calculator" you will find many web pages which will do these kinds of computations for you on whatever Internet-connected device you have.
  • Submit HW2: SIS §2.2: 10,12, 16, 26, SIS §2.3: 12, 16, 18
  • Submit BI9 on measures of variability, from recent readings and videos
  • Quiz 2 today — as usual, drop by my office any time today to take it, or else make other arrangements with me.

• :
  • Yes, we will continue with statistics 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.
  • Reread SIS §2.4 and this [the first 14 pages, in particular] as well
  • Content:
    • the $z$-score of a data value
    • the $1.5\times{}IQR$ rule for outliers
  • Submit ASE2: Your second ASE should be something about what we've been covering since the first one, probably to do with .... 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."]
  • Submit BI10 on something with percentiles and/or quartiles
  • Submit BI11 on something with the five-number summary and/or boxplots
  • Today [Monday] is the last day to drop classes without a grade being recorded.
• :
  • Read SIS §2.5 and start SIS §3.1
  • Content:
    • the empirical rule — also known as the 68-95-99.7 rule
    • the idea of randomness
    • sample spaces, outcomes, events
  • Submit BI12 on $z$-scores
  • Submit BI13 on the $1.5\times{}IQR$ rule
• :
  • Continue reading SIS §3.1
  • Content:
    • the idea of probability
    • fair coins and dice
  • Submit BI14 on the empirical rule
  • Submit BI15 on some of the basic ideas and terms of probability
  • Submit HW3: SIS §2.4: 12, 14, 26, 32, and a supplemental problem which we will call 2.4.S1 which is Are there any outliers in the data for problem 32?, and SIS §2.5: 8, 24
  • Quiz 3 today [on quartiles, the five-number summary, boxplots, the IQR, z-scores, the 1.5IQR rule for outliers, and the empirical rule — also known as the 68-95-99.7 rule] — as usual, drop by my office any time today to take it, or else make other arrangements with me.

• :
  • Read SIS §3.2
  • Content:
    • 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
  • Submit BI16 on some more ideas and terms of probability
  • Submit 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.
• :
  • Reread SIS §3.2 and read SIS §3.3
  • Content:
    • 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.
    • additive rule of probability
    • the conditional probability $P(A\mid B)$ of event $A$ given event $B$
  • Submit BI17 on conditional probability
• :
  • Reread SIS §3.3 and read SIS §4.1
  • Content:
    • independent and dependent events
    • random variables [RVs]
    • discrete and continuous RVs
  • Quiz 4 today [on probability computations, including Venn diagrams, intersections, unions, complements, and conditional
  • Submit BI18 on [in]dependent events
  • Submit BI19 random variables and discrete/continuous for RVs
  • Submit HW4: SIS §3.1: 2, 6, 16, SIS §3.2: 4, 8, 16, and SIS §3.3: 6, 10

• :
  • Read SIS §4.2
  • Content:
    • the [probability] distribution of a discrete RV
    • mean or expectation of an RV
  • Submit BI20 on what is the distribution of an RV.
  • Submit BI21 on the mean/expectation of an RV.
  • Submit 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
  • Content:
    • 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
  • Submit BI22 on computing probability from the distribution of a continuous RV.
  • Submit BI23 on the Normal distribution
• :
  • Read SIS §5.3
  • Content:
    • 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
  • Submit BI24 on computing probabilities from Normal distributions
  • Quiz 5 today [on independence, RVs, distribution of RVs, Normal distributions and probabilities]
  • Submit 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

• :
  • Read SIS §5.4
  • Content:
    • 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
  • Submit BI25 on converting between Normal distributions with different means and standard deviations, such as from or to a standard Normal distribution.
  • Submit BI26 on cut-offs for areas of tails of Normal distributions
  • Submit ASE5. It would be nice to find something which uses one of our recent terms, such as normally distributed, or expectation [in probability].
• :
  • Use this time to review for Test I. See this review sheet.
  • Submit BI27 on anything from this first unit of the course which you have not yet BIed about
  • Submit HW6: SIS §5.3: 2, 16, SIS §5.4: 2, 18, 22
• :
  • Test I today. You may take this test at my office, GCB 314, any time today you like, but please inform me in advance of when that will be. Make sure you are comfortable with the material outlined on this review sheet Don't forget your calculator, or other favorite electronic device!

• :
  • 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
  • Here are two videos which introduce our experimental ethics unit are:
    • Part 1 and
    • Part 2
  • Content: 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.

• :
  • Yes, we will continue statistics 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 this page which discusses some basics of experimental design.
  • Content:
    • observational studies vs experiments
    • bias
    • control groups
    • randomization [to prevent bias]
    • The Placebo Effect
    • blinding and particularly double-blind experiments
    • RCTs
  • Submit BI30 on something further to do with experimental ethics (e.g., you could go deeper into detail on some of the fundamental precepts of experimental ethics, or you could mention something from the Belmont Report which new to you)
  • Submit 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.
• :
  • Read SIS §6.1 and this page.
  • Content:
    • the sampling distribution of a statistic
    • the probability distribution of the sample mean, particularly its mean and standard deviation
    • simple random samples [SRSs]
  • Submit BI31 on experimental design.
• :
  • Read SIS §6.2 and this page.
  • Content:
    • The Central Limit Theorem [CLT]
    • lurking and confounding variables
    • volunteer sample bias
    • block designs for experiments
  • Quiz 7 today [on experimental design, basics of the sampling distribution of the mean, and SRSs]
  • Submit BI32 on the mean and standard deviation of the sampling distribution of the sample mean
  • Submit BI33 on the idea of an SRS
  • Submit 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

• :
  • Read SIS §7.1 and the first part of this page.
  • Content:
    • 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
  • Submit BI34 on the CLT
  • Submit BI35 on explanatory and response variables
  • Submit BI36 on lurking and confounding
  • Submit BI37 on voluntary samples
  • Submit 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.
• :
  • Read SIS §7.2 and the rest of this page.
  • Content:
    • the small-sample confidence for the population mean
    • Student's $t$-distribution
  • Submit BI38 on formulæ for large-sample CIs for the population mean; maybe margin of error.
  • Submit BI39 on the idea of a confidence level of a CI
• :
  • Read SIS §7.3 and this page.
  • Content:
    • the large-sample confidence interval for the population proportion
  • Submit BI40 on formulæ for small-sample CIs for the population mean
  • Submit BI41 on Student's $t$-distribution
  • Quiz 9 today [on confidence intervals for the population mean]
  • Submit 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.

• :
  • Read SIS §7.4
  • Content:
    • 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)
  • Submit BI42 on formulæ for large-sample CIs for the population proportion
  • Submit 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"
  • Content:
    • 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
  • Submit BI43 on the sample size needed for a particular margin of error in a CI for a population mean
  • Submit BI44 on the sample size needed for a particular margin of error in a CI for a population proportion
• :
  • 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.
  • Content:
    • 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
  • Submit BI45 on the basic structure of hypothesis testing
  • Submit BI46 on Type I and II errors in hypothesis testing
  • 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]
  • Submit 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

• :
  • 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.
  • Content:
    • 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".
  • Submit BI47 on the test statistic in hypothesis testing for a population mean with known population standard deviation $\sigma$
  • Submit BI48 on the meaning and how to compute the $p$-value in a hypothesis test for a population mean
  • Submit 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
  • Content:
    • 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
  • Submit BI49 on the test statistic in hypothesis testing for a population mean with unknown population standard deviation
• :
  • Use this time to review for Test II. See this review sheet.
  • Submit BI50 on hypothesis testing for a population proportion
  • 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]
  • Submit 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.

• :
  • Test II today. You may take this test at my office, GCB 314, any time today you like, but please inform me in advance of when that will be. Make sure you are comfortable with the material outlined on this review sheet Don't forget your calculator, or other favorite electronic device!
• :
  • Test II post-mortem videos here:
    • Problem 1
    • Problem 2
    • Problem 3
    • Problem 4
    • Problem 5
    • Problem 6
    • Problem 7
    • Problem 8
• :
  • Yes, we will continue statistics today, even though it is the federal holiday honoring veterans of the United State Armed Forces.
  • Read SIS §10.1 and SIS §10.2
  • Content:
    • independent and dependent variables
    • scatterplots
    • shape, strength, and direction of a relationship visible in a scatterplot
    • [linear] correlation coefficient, some properties
  • Submit BI51. This is another special one: think about the previous special BI29. 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?
  • Submit Test II revisions, if you like.

• :
  • Skim SIS §10.3 and read SIS §10.4
  • Content:
    • 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:
      • calculators — see this page about the TI-84+C Silver Edition or just search for "your calculator name scatterplot correltation coefficient linear regression"
      • websites — see this page about desmos.com or search similar keywords
  • Submit BI52 on scatterplots, and the shape, strength, and direction of the relationships they may show.
  • Submit BI53 on the correlation coefficient and some of its properties
  • Submit 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].
• :
  • Reread SIS §10.4 and this page
  • Content:
    • 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
  • Submit BI54 on the LSRL
  • Submit HW11: SIS §10.1: 4, 8, 12; SIS §10.2: 6, 12; and SIS §10.4: 4, 12.
• :
  • Since this material is important and this page was not posted until recently, now is a good time to consolidate your understanding of this last unit of the course and to read that page.
  • 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.

• :
  • Use this time to review for Test III. See this review sheet.
  • Here is a video with some specific suggestions about reviewing for this Test III; it is not all that much more than is in the review sheet and the other page on this material written specifically for this class, but if you like to hear the suggestions spoken out loud, by all means watch the video.
  • Submit BI55 on interpolation and extrapolation
  • Submit BI56 on the meaning of $r^2$
• :
  • Test III today. You may take this test at my office, GCB 314, any time today you like, but please inform me in advance of when that will be. 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 submit any late work, even with Homework Late Passes.
• :
  • Test III post-mortem videos will be sent to you in individual emails.
  • Use this time to review for final exam. See this review sheet and watch this video.
  • Submit BI57, 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!
  • Make sure you drop by GCB314 at some point to pick up any graded work for which you may be waiting.

• Exam week!
• You must take your comprehensive FINAL EXAM in person at the Math Learning Center (MLC) on the ground floor of the Physics/Math Building on any day this week except Friday — so, on Monday, Tuesday, Wednesday, or Thursday — and at a time of your choosing — but be aware that you have 2 hours and 20 minutes for the final and the MLC is open 8:30am to 5pm Monday to Thursday, which means that on the day you choose to take your final, you must start your final after 8:30am and before 2:30pm.
  Don't forget to bring your calculator, smartphone, laptop, or other favorite electronic device. You may also bring other materials to consult during the test (such as notes, graded HW, etc.). See the final review sheet for other information about the final.
• Submit Test III revisions, if you like, at GCB314 before the end of the day on Thursday.