Math 5090-1: Statistical Inference II. Fall 2014
Schedule: Meets 6:00--7:30 pm Mondays and Wednesdays in SW 133. PhD students may want to register under the number 6828.
Instructor: S. Ethier (Prof.), 581-6148, ethier@math.utah.edu.
Instructor office hours: 3:45--5:00 MW, JWB 119. Other times may be available by appointment.
Prerequisite: Math 5080, Statistical Inference I, with a grade of C or better.
Text: Introduction to Probability and Mathematical Statistics, 2nd Ed., by Bain and Engelhardt. You should already have this book from Math 5080.
Topics covered: Tests of hypotheses, including likelihood ratio tests and sequential tests. Contingency tables and goodness-of-fit tests. Nonparametric tests. Introduction to regression and linear models. Finally, as time permits, reliability and survival distributions.
Grades: Based on weekly 15-minute quizzes (20%), two one-hour midterm exams (25% each), tentatively Oct. 8 and Nov. 19, and a final exam (30%). The dates of the midterms will be confirmed at least a week in advance and posted on this page. The final exam is scheduled for Monday, Dec. 15, 6--8 pm but in a different room, JWB 333. Early exams are never given.
Homework/Quizzes: Assigned problems will be posted on this webpage on Thursdays with solutions posted on Canvas by the following Tuesday. Because these solutions can probably be found on the Internet, you will not have to turn in your work. But you should attempt these problems before looking at the solutions, because a quiz will be given on Wednesday to test your understanding of the material. Your two lowest quiz scores will be dropped before averaging, to allow for up to two absences. There are no make-up quizzes.
Exams: Exams can be made up if there is a very good justification and if arrangements are made in advance, but this is rare.
(Phone the department office before the exam begins to give notification if the instructor is not available; 581-6851.) Students with disabilities can take exams at the CDS the next day.
Expected learning outcomes: The student who successfully completes the course will be conversant with the basics of hypothesis testing, goodness-of-fit tests, nonparametric tests, and the basics of linear models.
- Week 1 (Aug. 25, 27). Starting with Chapter 12, we got through about page 398. Assignment 1: Chapter 12, Exercises 1, 2, 3(a,b,c).
- Week 2 (Sep. 3). We continued, getting to about page 402. Assignment 2: Chapter 12, Exercises 3(d,e,f), 5, 6.
- Week 3 (Sep. 8, 10). We covered MP and UMP tests, getting to about page 414. Assignment 3: Chapter 12, Exercises 9, 11, 16, 18, 22.
- Week 4 (Sep. 15, 17). We nearly finished generalized likelihood ratio tests. Assignment 4: Chapter 12, Exercises 27, 28, 30.
- Week 5 (Sep. 22, 24). We finished Chapter 12 (omitting Sections 12.4, 12.5, and 12.9). Assignment 5: Chapter 12, Exercises 37, 39.
- Week 6 (Sep. 29, Oct. 1). We started Chapter 13, getting to the CvM statistic (Section 13.8). Assignment 6: Chapter 13, Exercises 3, 9, 12, and the following problem from Mood, Graybill, and Boes: According to a genetic model, the proportions of blood types should have the form O: q^2; A: p^2+2pq; B: r^2+2qr; AB: 2pr, where p+q+r=1. Given the sample O: 374; A: 436; B: 132; AB: 58, test whether the data fit the model. See Canvas for solutions.
- Week 7 (Oct. 6, 8). We essentially finished Chap. 13 and had Exam 1. Assignment 7: Chapter 13, Exercises 20, 21.
- Week 8 (Oct. 20, 22). We started nonparametric statistics, getting through the Wilcoxon signed rank test. Assignment 8: Chapter 14, Exercises 1, 5, 11, 13.
- Week 9 (Oct. 27, 29). We covered through Spearman's rank correlation coefficient. Assignment 9: Chapter 14, Exercises 15, 16, 17, 19.
- Week 10 (Nov. 3, 5). We finished Chapter 14 and started Chapter 15 (linear regression).
Assignment 10: 1. (a) Toss a fair coin 100 times (or do a computer simulation) and record the sequence of heads and tails. (b) Make up a sequence 100 coin tosses that "looks" random. Use the runs test to test both sequences for randomness at the 0.10 level. Also, Chapter 15, Exercises 1 and 2.
- Week 11 (Nov. 10, 12). We nearly finished the simple linear regression model. (Simple linear regression example.) Assignment 11: Chapter 15, Exercises 8, 15. Also, prepare for Exam 2.
- Week 12 (Nov. 17, 19). We nearly finished Section 15.4 and had Exam 2. Assignment 12a: Chapter 15, Exercises 17, 18. There will not be a quiz next week because attendance is usually poor the night before Thanksgiving Day.
- Week 13 (Nov. 24, 26). We finished Chapter 15. (Polynomial regression example.) Assignment 12b: Chapter 15, Exercises 28, 33.
- Week 14 (Dec. 1, 3). We began Chapter 16 and will get through Section 16.3 on the exponential distribution. Next week we will work some of the Chapter 16 problems in class.
- Week 15 (Dec. 8, 10). We got to the first part of Section 16.4 and we reviewed GLR tests.
Final exam is scheduled for Monday, Dec. 15, 6--8 pm, but in a different room, JWB 333. You may bring one sheet of notes and a calculator. Last year's exam is posted on Canvas, as are handwritten solutions.