## 18.443 Statistics for Applications

Course meets: Tuesday and Thursday, 9:30-11, Room 36-156.
Lecturer: Professor Sergey Fomin, Room 2-363B, 253-1713, fomin@math.mit.edu
Office hours: Wednesday, 10:30-12 (and by appointment).
Teaching assistant: Adrian Vetta, Room 2-342, avetta@math.mit.edu
Grade based on two 1.5-hour exams, 20% each; 20% homework; 40% final exam.
Text: R.V.Hogg and E.A.Tanis, Probability and Statistical Inference, 5th edition, Prentice Hall, 1997.
Course homepage: http://www-math.mit.edu/~fomin/18443.html

Course description from the MIT Catalog
A broad treatment of statistics, concentrating on specific statistical techniques used in science and industry. Topics: hypothesis testing and estimation. Confidence intervals, chi-square tests, nonparametric statistics, analysis of variance, regression, and correlation. Treatment more oriented toward application and less toward theory than 18.441. Prerequisites: 18.440 or 18.313 or 6.041.

Course Outline
1. Review of basic probability theory (Chapters 3-5, 11.1-11.4).
2. Statistical sampling. Summarizing data (Chapter 1).
3. Estimation of parameters. Method of moments (Section 6.1).
4. Confidence intervals for means, proportions, and variances (Sections 6.2-6.5).
5. Sample size (Section 6.6).
6. Maximum likelihood method. Efficiency (Sections 6.1, 12.3).
7. Hypothesis testing. z-tests and t-tests. Power and sample size (Sections 7.1-7.4).
8. Best critical regions. Likelihood ratio tests (Sections 12.5, 12.6).
9. Chi-square tests (Sections 7.5, 7.6).
10. Random number generators (Section 4.2)
11. Kolmogorov-Smirnov test (Section 10.7).
12. Confidence intervals for percentiles (Section 10.2).
13. Nonparametric tests (Section 10.3-10.6).
14. Analysis of variance (Sections 8.1, 8.2).
15. Linear regression (Sections 8.3, 8.4).
16. Correlation analysis (Section 11.5).

Reference texts
1. Z.A.Karian and E.A.Tanis, Probability and Statistics Explorations with Maple. Prentice Hall, 1995.
2. J.A.Rice, Mathematical Statistics and Data Analysis, Wadsworth, 1995.
3. W.Mendenhall, R.L.Scheaffer, and D.D.Wackerly, Mathematical Statistics with Applications, Duxbury Press, 1996.

Homework assignments (from Hogg and Tanis)
HW1, due 10/1: 6.1.18, 6.2.4, 6.2.16, 6.5.6, 6.5.8(a,b), 6.6.12, 6.6.14, 6.6.16
HW2, due 10/8: 6.3.2, 6.3.8, 6.4.4(a), 6.4.12, 6.5.12, 6.1.8, 6.1.20
HW3, due 10/22: 12.3.2, 12.3.4(c), 7.1.10, 7.3.8, 7.3.12, 7.3.18
HW4, due 11/3: 7.2.6, 7.4.10(a), 12.5.2, 7.5.4, 7.5.12, 7.6.6, 7.6.14
HW5, due 11/17: 10.7.10, 10.2.2, 10.2.6, 10.3.4, 10.3.6, 10.4.6, 10.4.8
HW6, due 11/24: 10.5.2(a,b), 10.6.2, 10.6.10, 8.1.8(a,b,c), 8.1.11
HW7, due 12/4: 8.2.3, 8.2.10, 8.3.12 (using 8.3.5, 8.3.6)

First midterm exam (Sections 6.1-6.6, 12.3): October 15
Practice problems for Exam 1 and answers to them

Second midterm exam (Sections 7.1-7.6, 10.1-10.7): November 19
Practice problems for Exam 2 and answers to them

Practice problems on topics not covered by homework assignments: 8.4.7, 8.4.9, 11.5.5

Final exam (Chapters 6, 7, 8, 10; Sections 11.5, 12.3):
Thursday, December 17, 1:30-4:30, Rm 13-1143