STAT 205

Introduction to Mathematical Statistics

Welcome

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Lectures

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Schedule

Lecture Topics Covered Supplementary Readings
1 Introduction to the instructor/course + Course Syllabus + Introduction to Data
2 Summarizing Data

Openintro - 2.1 and 2.2 (can skip special topics)

R basics
3 Sampling Distributions

Ross - Ch 6; Balka Ch 4

Video on the CLT
4 Getting Started with Quarto (Wickham, Çetinkaya-Rundel, and Grolemund 2023) 28 - Quarto
5 Likelihood and Parameter Estimation (Ramachandran and Tsokos 2020) - Ch 5.1-5.3; Ross - Ch 6
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
7

Confidence Intervals for Variance (Chi-squared table)

Non-parameter CI for median and variance

 (Ramachandran and Tsokos 2020) Section 5.6 and 12.2
8 Sampling Distribution Theory Rice (2007) 6.2, Ross (2020) 6.6
9 Sampling from a Finite Population Casella and Berger (2002) 5.1, Rice (2007) 7.3
10 Properties of Parameter Estimators Devore, Berk, and Carlton (2021) 7.3, 7.4
11 Hypothesis Testing for one-sample mean (critical value approach) Devore, Berk, and Carlton (2021) 9.1,
12 Hypothesis Testing for one-sample proportions (\(p\) -value approach) Devore, Berk, and Carlton (2021) 9.4, Diez, Barr, and Çetinkaya-Rundel (2016) 5.3
Reading week
Midterm Review
13 \(t\) 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
14 Chi-squared test for one-sample variance Balka (n.d.) 12.1 – 12.3 (Ramachandran and Tsokos 2020) 4.2
15 Inference for difference of Two Means Balka (n.d.) chapter 10, Diez, Barr, and Çetinkaya-Rundel (2016) 7.2, 7.3
16 Examples involving two-sample \(t\)-tests
17 Analysis of Variance (ANOVA) Lesson 10 Penn Stat 500, Chapter 14 Balka (n.d.)
18 Linear Regression and Correlation
19 Contingency Table Analysis Balka (n.d.) Chapter 13, Penn Stat STAT 500 Lesson 8, Diez, Barr, and Çetinkaya-Rundel (2016) 6.3, 6.4
Post Midterm Review See the list of learning outcomes coded by importance here and suggested practice problems here

Resources

Tables for distributions:

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.
Ross, S. M. 2020. Introduction to Probability and Statistics for Engineers and Scientists. Elsevier Science. https://books.google.ca/books?id=eW_hDwAAQBAJ.
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

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