STAT 342 - Introduction to Probability and Statistical Inference II


  • [June 5] For those of you graduating this year, and thinking of getting rid of old textbooks: see this link for one way you can do it.
  • [June 5] I will be in my office (PDL B-220) tomorrow morning from 11am- noon, to answer any last minute questions you may have!
  • [June 4] Fascinating research.
  • [May 31] There will be no *morning* office hours on Monday, June 4th. See below for extra office hours for the final.
  • [May 29] Here is the info on our final.
  • [May 19] The solution to the data analysis problem on Assignment 4 has just been posted.

    Course Description:

    This course is a continuation of STAT 341, where you first began studying mathematical statistics: the mathematical theory behind the basic statistical techniques used today. Time permitting, we will look at estimation, confidence intervals, hypothesis testing, and regression. Roughly, this equates to Chapters 5-9 and 11 of the textbook.

    The official prerequisite of this course is STAT 341, and I will assume that you are familiar and comfortable with the material covered in that course. We will also make use of quite a bit of calculus and matrix algebra.

    Contact Info:

    Instructor: Hanna Jankowski

    E-mail: hanna[at]
    Please include "[342]" (using square brackets) in the subjects of your e-mails; this'll help me separate if from my other, mostly junk, mail. Also, please send only plain text messages, no html.

    Office Hours with HJ: Every Monday and Friday, in Padelford B-220, from 10-11am. Office hours will begin Friday, March 30th.
    If you cannot make it to my office hours, please schedule an appointment. All appointments will take place in my office, Padelford B-220.

    TA: The teaching assistant for this course is Roopesh Ranjan. His email address is roopesh.ranjan[at], and office phone 206-543-8471.

    Office hours with RR: Tuesdays 3-4pm in Padelford B-314, and Thursdays 1-3 pm in library of McCarty Hall (where the Stats Help Centre is). The office hours begin the second week of classes.

    Lectures will be held in THO 134/135, as scheduled.

    Tutorials will take place every Wednesday in THO 134, from 11:30 to 12:20. The tutorials will start April 4th. On March 28th you will have a regular lecture.

    Tutor & Study Centre Some of RR's office hours will take place in the Statistics Tutor & Study Centre (see above for dates/times). However, you are welcome to take advantage of the resource on your own as well. Click here for more info.

    Text/Reference Material:

    The main reference for this course will be the lectures, and the text: An Introduction to Mathematical Statistics and Its Applications, by Larsen and Marx, 4th Edition.

    There is a copy of this text available (soon) for short-term loan from the Mathematics Research Library in Padelford Hall C-306. I have also requested that Mathematical Statistics and Data Analysis by John Rice be placed on reserve. The book offers nice explanations of the material we will be covering.

    Message Board:

    I have created a message board for this course. It is available here. Information on how to use the message board can be found here.

    The idea of the message board is for you to be able to communicate with HJ/RR/other students quickly and easily, regarding any topic related to the course. For example, if you're stuck on a question and need a hint, you could post your question here. Both HJ and RR will check the message board regularly. Please, do not post complete solutions to any question here!

    The natural disclaimer is that I have not used this technology in a course yet, and I expect that some ironing out of wrinkles will be necessary before we are all comfortable with how to use the message board. Hopefully it will be a success.

    Grading Scheme and Assignments:

    There will be roughly 6 assignments, one mid-term test and a final in this course. The assignments will be posted below, and will be worth 30% of your final grade.

    Note: all assignments are due at the beginning of each lecture on the day that they are assigned. There are no exceptions. I do not accept late assignments.

    Assignment 1. Due: Friday, April 6th.

    Assignment 2. Due: Wednesday, April 18th.

    Assignment 3. Due: Monday, April 30th.

    Assignment 4, with problem and data set. Due: Friday, May 18th.

    Here is the solution to Q1 on Assignment 4.

    Assignment 5 with data. Due: Wednesday, May 30th.

    Bonus Assignment Due: see details.

    Solutions to your assignments are available here.

    Midterm: Friday, May 4th, 30%

    Final: June 6th, 2:30-4:20pm 40%

    Course Policies etc.

    Material Covered and Practice Problems:

    In this section I will keep an ongoing list of the material we have covered, and the suggested practice questions attached to each lecture. It is imperative that you work through these on a timely basis.

    NB. In square brackets I am also putting reference chapters for you. LM stands for the course textbook, and R for the Rice reference available in the library.

    We have covered the following sections/topics:

    Week 1 :

  • Introduction. Review of likelihood, MOM, MLE, bias, efficiency [ML 5.2, 5.4].
  • Cramer-Rao lower bound, sufficiency, consistency [ML 5.5, 5.6, 5.7].
  • Lectures 1 and 2 applied to uniform example. Confidence intervals [ML 5.3], normal distribution theory [ML 4.3, 7.3, 7.A.2, 7.A.3, R 5.3, 6].

    Week 2 :

  • Continuation of Normal distribution theory: mle for \mu and \sigma^2 in the normal case, confidence intervals for the two quantities [ML 7.2, 7.3, 7.4, 7.5].
  • Hypothesis testing: a review of the normal test for the mean, including p-value, Type II error and power [ML 6.2, 6.4].

    Week 3:

  • Likelihood Ratio Test [R 9.3]
  • Generalized LRT [ML 6.5, R 9.5] and Binomial tests [ML 6.3]

    Week 4:

  • Duality between CI's and hypothesis testings [R 9.4]; Hypothesis testing in the news.
  • Hypothesis test for mean and variance of normal data, variance unkown. [ML 7.4,7.5] p-values in physics. Review (based on flow chart).

    Week 5:
    The two-sample t-test and associated CI [ML 9.2,9.5; R 11.2]
    Two sample t-test con't. Test for equal variance [ML 9.3]; Test for two bernoulli parameters and CI [ML 9.4, 9.5]

    Week 6:
    Review and Midterm!

    Week 7:
    Paired t-test & Wilcoxon Signed Rank test [ML 13.3, 14.3, R 11.3]
    Wilcoxon Signed Rank test con't. Intro to Regression (LSE) [ML 11, R 13]

    Week 8:
    Jen's visit. Regression con't. (mean, var, covar of LSE)
    More on regression: normal assumption, testing the betas, R^2, interpreting computer output, assessing fit (perhaps not in that order)

    Week 9:
    Finishing up Regression (MLEs, "centering").
    Start Anova (Boxplots, Anova table, Tukey's multiple comaprisons) [ML 12.1-12.3, R 12.1, 12.2]

    Week 10:
    Finish up Anova: Tukey and Bonferroni multiple comparisons [R 12.2]
    Review and summary.

    Practice (non-credit - do not hand these in) problems:

    Week 1:
    5.2.3, 5.2.4, 5.2.11, 5.2.19
    5.4.6, 5.4.11, 5.4.19
    5.7.2, 5.7.3a, 5.7.4
    5.3.9, 5.3.21

    Week 2:
    7.3.2, 7.3.4, 7.3.5
    7.4.15, 7.4.9a
    7.5.9 (but you can do variance, not
    6.2.1, 6.2.2, 6.4.3, 6.2.8

    Week 3:
    6.5.1, 6.5.2, 6.3.1

    Week 4:
    7.4.17, 7.5.8, 7.5.13

    Week 5:
    9.2.1, 9.2.5; for each question though, calculate the p-value; you could also try doing side-by-side boxplots.
    9.5.1, 9.5.2
    9.3.3, 9.3.5
    9.4.1, 9.4.3

    Week 6:

    Week 7:
    13.3.1, 13.3.3
    14.3.3, 14.3.5 (Wilcoxon only) NB. You should use the Wilcoxon tables here, and not the normal approximation. Hence, your answers won't match those of the text.
    11.2.4, 11.2.5, 11.2.6, 11.2.9, 11.2.12

    Week 8:
    11.2.27, 11.3.12, 11.3.8, 11.3.2
    More practice problems, with plot 1 and plot 2.

    Week 9/10:
    12.2.2, 12.2.3 (for each question, draw side-by-side boxplots, and find the p-value, regardless of what the question asks)
    12.2.12, 12.3.4, 12.3.6
    Repeat the above Tukey problems, but use the Bonferroni method instead. Is the answer the same or different?
    More practice problems, with plots, plots, and data, data.