STAT 205

Introduction to Mathematical Statistics

Author
Affiliation

Dr. Irene Vrbik

University of British Columbia Okanagan

Welcome!

This is the official course website for STAT 205. Here, you’ll find:

All other course material (e.g. assignments and grades) can also be accessed through Canvas. The syllabus can be found in the Syllabus tab in the Navigation bar.

Use the navigation bar above to explore the content.

Lectures

Lectures will be uploaded here. These slides were built using Quarto and includes a built in version of the reveal.js-menu plugin. You can access the navigation menu using the button located in the bottom left corner of the presentation1. Clicking the button opens a slide navigation menu that enables you to easily jump to any slide.

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Tentative Schedule

Table 1: Tentative lecture schedule: Supplementary materials are optional and provide additional, in-depth coverage related to the slides. Practice problems are recommended but not mandatory.
Lecture: Topic Supplementary Material Practice Problems
1: Introduction to the instructor/course + Course Syllabus + Introduction to Data Diez, Barr, and Çetinkaya-Rundel (2016) Section 1.2, 1.3 Diez, Barr, and Çetinkaya-Rundel (2016): Exercises: 1.1, 1.9, 1.13, 1.15, 1.17, 1.27, 1.39, 1.43
2: Summarizing Data

Diez, Barr, and Çetinkaya-Rundel (2016) Sections 2.1 and 2.2 (can skip special topics)

R basics

Diez, Barr, and Çetinkaya-Rundel (2016) Exercises: 2.1, 2.5, 2.11, 2.13, 2.15, 2.17, 2.27, 2.33

JB exercises3 Ch 3 Exercises: 10, 20, 21, 22, 23, 31, 32, 34, 39, 36, 37, 39, 40, 41, 45, 46, 48, 49, 50
34: Getting Started with Quarto: stat205demo (source qmd), cheer.csv Wickham, Çetinkaya-Rundel, and Grolemund (2023) Chapter 28
Quarto tutorial Hello, Quarto

Assignment 1 for practice with quarto.

Wickham, Çetinkaya-Rundel, and Grolemund (2023) 28.3.1: 1, 2, 3; 28.5.5: 1, 2; 28.6.3: 1, 2, 3
4: Sampling Distributions ⚬ Ross - Ch 6;
Balka 4.1, 4.2, 4.3, 4.4, 4.5
⚬ What is the CLT Video
⚬ StatKey: Sampling Distribution for a Mean
⚬ Khan: Sampling Distribution for proportions		 JB exercises5 Ch 7: 1, 6, 7, 8, 9, 10, 11, 12, 13, 19, 20, 21, 24, 25
5: Likelihood and Parameter Estimation (Ramachandran and Tsokos 2020) - Ch 5.1-5.3; Ross - Ch 6

JB exercises (solutions found here) Ch 7: 14, 15

Rice (2007) Section 8.10: 4, 5, 6, 7 (excluding part d), 16, 21, 27, 47, 50, 52, 60
4b: Examples with Sampling Distributions Sampling Distributions in Action See exercises for lecture 4
6: Confidence Intervals for Means and Proportions (Illowsky and Dean 2022) - Ch 8
(Balka n.d.) Ch 5
(Ramachandran and Tsokos 2020) Ch 5.4-5.5

JB exercises Ch 8:

  • interpretation 4, 5, 6, 18, 19, 24, 35
  • CI for \(\mu\) with \(\sigma\) unknown: 8, 9, 10, 11, 13, 14, 26, 27, 29, 31, 32, 34, 42
  • basic calculations: 1, 2, 3, 7, 15, 16, 21

CI for \(p\): Diez, Barr, and Çetinkaya-Rundel (2016) Ch 6: 6.1, 6.5, 6.7, 6.9, 6.10, 6.11, 6.13, 6.15
7: Hypothesis Testing for one-sample mean (critical value approach) Devore, Berk, and Carlton (2021) 9.1,
8: Hypothesis Testing for one-sample proportions (\(p\) -value approach) Devore, Berk, and Carlton (2021) 9.4, Diez, Barr, and Çetinkaya-Rundel (2016) 5.3
Midterm 1 Practice Problems and Suggested Problems
9: \(t\) tests and CI for one-sample mean (\(\sigma\) unknown) Diez, Barr, and Çetinkaya-Rundel (2016) Chapter 6 and 7, Balka (n.d.) Section 9.10
Inference for difference of Two Means Balka (n.d.) chapter 10, Diez, Barr, and Çetinkaya-Rundel (2016) 7.2, 7.3
Examples involving two-sample \(t\)-tests
Analysis of Variance (ANOVA) Lesson 10 Penn Stat 500, Chapter 14 Balka (n.d.)
Chi-squared test for one-sample variance Balka (n.d.) 12.1 – 12.3 (Ramachandran and Tsokos 2020) 4.2
Contingency Table Analysis Balka (n.d.) Chapter 13, Penn Stat STAT 500 Lesson 8, Diez, Barr, and Çetinkaya-Rundel (2016) 6.3, 6.4
Sampling from a Finite Population Casella and Berger (2002) 5.1, Rice (2007) 7.3
Properties of Parameter Estimators Devore, Berk, and Carlton (2021) 7.3, 7.4
18: Linear Regression and Correlation
Post Midterm Review See the list of learning outcomes coded by importance here and suggested practice problems here

References

Balka, Jeremy. n.d. “Making Statistics Make Sense.” Accessed January 6, 2024. https://www.jbstatistics.com/.
Casella, G., and R. L. Berger. 2002. Statistical Inference. Duxbury Advanced Series in Statistics and Decision Sciences. Thomson Learning. https://books.google.ca/books?id=0x_vAAAAMAAJ.
Devore, J. L., K. N. Berk, and M. A. Carlton. 2021. Modern Mathematical Statistics with Applications. Springer Texts in Statistics. Springer International Publishing. https://books.google.ca/books?id=ghcsEAAAQBAJ.
Diez, D. M., C. D. Barr, and M. Çetinkaya-Rundel. 2016. OpenIntro Statistics. OpenIntro, Incorporated. https://books.google.ca/books?id=wfcPswEACAAJ.
Illowsky, B., and S. Dean. 2022. Introductory Statistics. Open Stax Textbooks. https://books.google.ca/books?id=-GQIzwEACAAJ.
Ramachandran, K. M., and C. P. Tsokos. 2020. Mathematical Statistics with Applications in r. Elsevier Science. https://books.google.ca/books?id=t3bLDwAAQBAJ.
Rice, J. A. 2007. Mathematical Statistics and Data Analysis. Advanced Series. Cengage Learning. https://books.google.ca/books?id=KfkYAQAAIAAJ.
Wickham, H., M. Çetinkaya-Rundel, and G. Grolemund. 2023. R for Data Science: Import, Tidy, Transform, Visualize, and Model Data. O’Reilly. https://books.google.ca/books?id=xU-gzwEACAAJ.

Footnotes

  1. You can also open the navigation menu by pressing the M key.↩︎

  2. Note: This feature has only been confirmed to work in Google Chrome and Chromium.↩︎

  3. solutions found here↩︎

  4. This lecture document is a continuous HTML page for easier readability, rather than a slideshow format↩︎

  5. note that the exercise chapters don’t match up with the website.↩︎