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.

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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
Introduction [slides] 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
Summarizing Data [slides]

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

Irene’s tutorial: 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
📝 Assignment 1 (see Canvas)

Wickham, Çetinkaya-Rundel, and Grolemund (2023) Chapter 28

Quarto tutorial: Hello, Quarto
Irene’s tutorial: Quarto documents

 Wickham, Çetinkaya-Rundel, and Grolemund (2023)
28.3.1: 1, 2, 3; 28.5.5: 1, 2; 28.6.3: 1, 2, 3
Sampling Distribution for the mean [slides] ⚬ 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
JB exercises4 Ch 7: 1, 6, 7, 8, 9, 10, 11, 12, 13, 19, 20, 21, 24, 25
Confidence Intervals for the mean (known \(\sigma\)) [slides] (Balka n.d.) Ch 5: 5.1 – 5.6
(Illowsky and Dean 2022) Ch 8: 8.1, 8.4
(Diez, Barr, and Çetinkaya-Rundel 2016) Ch 4.1, 4.2

JB exercises Ch 8.2

🧮 calculations: 1, 2

🧠interpretation 3, 4, 5, 6, 7

JB exercises Ch 8.5

📏 CI \(\sigma\) unknown: 20
Finite Population Correction and Choosing a Sample Size [slides] Illowsky and Dean (2022) 7.4

Illowsky and Dean (2022) Ch 7: Practice 41-48

JB exercises Ch 8.4

🧮 calculations: 14
Confidence Intervals for the mean (unknown \(\sigma\)) [slides] 🎬 JB Online 5.7 (unknown \(\sigma\) method)
🎬 JB Online 5.8 (t-distribution)

JB exercises Ch 8.3-8.5

🧮 calculations: 8, 14, 15, 16, 21

🧠 9, 10, 11, 12, 13, 18, 19, 21, 24, 25, 35

📏 CI \(\sigma\) unknown: 17, 26, 27, 29, 31, 32, 34, 42

JB exercises Ch Extra Ex:

📈 R: 36, 39
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 5.7-
(Ramachandran and Tsokos 2020) Ch 5.4-5.5
Khan: Sampling Distribution for proportions		 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,

JB exercises Ch 9:5

  • concepts and setup: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 23, 26, 27, 53, 59, 60

  • applied: 12, 13,
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

JB exercises Ch 11:

  • concepts and setup: 1, 2, 4, 5, 6

  • applied: 7, 19, 20, 21

Diez, Barr, and Çetinkaya-Rundel (2016) Ch 6:

  • 6.1, 6.5, 6.9, 6.13
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

JB exercises Ch 9:

  • concepts and setup: 28, 29, 33, 34, 36, 37, 38, 39, 40, 52,

  • applied: 30, 31, 32, 43, 46, 47, 56,
10: Inference for difference of Two Means Balka (n.d.) chapter 10, Diez, Barr, and Çetinkaya-Rundel (2016) 7.2, 7.3

JB exercises Ch 10:

  • Concepts: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 19, 20, 22, 23, 24, 25

  • Applied: 26, 27, 28, 29, 30, 31
11: Examples involving two-populations see above
12: Examples using the R formulas in t.test

JB exercises6

  • Ch 8: 36, 39

  • Ch 9: 35, 44, 62f, 63f, 64f, 67f, 71

  • Ch 10: 14, 18, 19, 30
13: Inference on two proportions Balka (n.d.) chapter 11.3, Diez, Barr, and Çetinkaya-Rundel (2016) 6.2

JB exercises Ch 11:

  • Concepts: 8, 9, 10, 11, 12, 13, 14, 15, 17, 18

  • Applied: 22, 23, 24-26
14: Type I/II errors and power

JB exercises Ch 9:

  • 16-19, 20, 21, 22, 47, 51, 54, 55, 57, 58,

Ch 10:

  • 15
Midterm 2 Review
Midterm 2

Practice Problems (Set 2), Suggested problems7, plus

Review questions from JB exercises (solutions found here):

Ch 9

  • 62, 63, 64, 65, 66, 67

Extra Practice:

  • Ch 9:68 - 75

  • Ch 10: 32-41

  • Ch 11: 27-33
Chi-squared test for one-sample variance [slides] Balka (n.d.) 12.1 – 12.3 (Ramachandran and Tsokos 2020) 4.2
15: Analysis of Variance (ANOVA) Lesson 10 Penn Stat 500, Chapter 14 Balka (n.d.) JB exercises Ch 14: 1, 2, 3, 5, 12, 14–23, 25–30
16: Contingency Table Analysis Balka (n.d.) Chapter 13, Penn Stat STAT 500 Lesson 8, Diez, Barr, and Çetinkaya-Rundel (2016) 6.3, 6.4 JB exercises Ch 13: 1, 2, 3, 8, 11, 12, 13, 14, 17, 18, 19, 22, 23, 28
[slides]: Linear Regression and Correlation

Extra Material

  • Chi-squared tests for one variance [slides]

References

Balka, Jeremy. n.d. “Making Statistics Make Sense.” Accessed January 6, 2024. https://www.jbstatistics.com/.
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. note that the exercise chapters don’t match up with the website.↩︎

  5. I would priorities thequestions in bold↩︎

  6. these contain repeats from this column↩︎

  7. the listed practice problems from this column of the table for the appropriate Lectures↩︎