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:

• The course syllabus.
• Weekly lecture slides (see links in Table 1)
• About the instructor.

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

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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,	JB exercises Ch 9:6 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 exercises7 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 problems8, 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.)
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
[slides]: Linear Regression and Correlation
	Post Midterm Review	See the list of learning outcomes coded by importance here and suggested practice problems here

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. 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.

6. I would priorities thequestions in bold

7. these contain repeats from this column

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