STAT 205
Introduction to Mathematical Statistics
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Lectures
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Tentative Schedule
| 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) 📈 |
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 📈 📈
|
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 |
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 Online 5.8 (Finding \(p\)-value5 ) |
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 |
| Hypothesis Testing for one-sample mean (critical value approach) [slides] | Devore, Berk, and Carlton (2021) 9.1, 🎬 JB Online 6.1 (Intro to Hypothesis Testing) 🎬 JB online 6.2 (Tests for One Mean) 🎬 JB online 6.8 (One-Sided Test or Two-Sided Test?) 🎬 JB online 6.9 (The Relationship Between Confidence Intervals and Hypothesis Tests) |
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, |
Hypothesis Testing for one-sample mean (\(p\)-value approach + t.test()) [slides] |
Diez, Barr, and Çetinkaya-Rundel (2016) Chapter 6 and 7, Balka (n.d.) Section 9.10 🎬 JB online 6.4 (Z Tests for One Mean: The p-value) 🎬 JB online 6.5 (Z Tests for One Mean: An Example) 🎬 JB online 6.6 (What is a p-value?) 🎬 JB online 6.16 (t Tests for One Mean: An Example) 🎬 JB Online 6.17 (t-tests for One Mean: Investigating the Normality Assumption) 🎬 JB Online 6.18 (Hypothesis tests on one mean: t or z?) |
JB exercises Ch 8 Extra Ex: 📈 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, 📈 |
| Type I/II errors and power [slides] | 🌐 StatSig |
Ch 9: 16-19, 20, 21, 22, 47, 51, 54, 55, 57, 58, Ch 10: 15 |
| ✂✂✂✂ | Midterm 1 material cut off | ✂✂✂✂ |
| Inference for Proportions [slides] | ||
| ✅ above is all adapted current material 👆 | ||
| ⛔️ below is old material that will likely change 👇 | ||
| 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 |
| 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 JB exercises Ch 10: 📈 |
| 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:
Diez, Barr, and Çetinkaya-Rundel (2016) Ch 6:
|
| Midterm 1 | Practice Problems and Suggested Problems | |
| 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:
|
| 11: Examples involving two-populations | see above | |
| 12: Examples using the R formulas in t.test |
|
|
| 13: Inference on two proportions | Balka (n.d.) chapter 11.3, Diez, Barr, and Çetinkaya-Rundel (2016) 6.2 | JB exercises Ch 11:
|
| Midterm 2 Review | ||
| Midterm 2 | Practice Problems (Set 2), Suggested problems8, plus Review questions from JB exercises (solutions found here): Ch 9
Extra Practice:
|
|
| Chi-squared tests for one 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 |
| 17: Linear Regression and Correlation |
14: Type I/II errors and power
References
Footnotes
You can also open the navigation menu by pressing the
Mkey.↩︎Note: This feature has only been confirmed to work in Google Chrome and Chromium.↩︎
note that the exercise chapters don’t match up with the website.↩︎
we will cover \(p\)-values later, for now you can just think of \(p\)-values as generic probabilities↩︎
I would priorities the questions in bold↩︎
these contain repeats from this column↩︎
the listed practice problems from this column of the table for the appropriate Lectures↩︎