MAT 341
Mathematical Statistics
Davidson College

 

Instructor

Dr. Laurie Heyer
Chambers 3027
x-2267
                                              

Textbook

Mathematical Statistics with Applications, 7th Edition (2008), Duxbury, by Wackerly, Mendenhall and Sheaffer

Course Description

This course is a sequel to MAT 340, Probability.   We will focus primarily on the theory of statistics, though applications will also be discussed in class and analyzed in assignments.   A course in applied statistics (for example, those offered in the Biology, Economics, Political Science, Psychology and Sociology departments) would be an excellent complement to Mathematical Statistics.

Syllabus

Statistics: Lies, lies, lies

What can you do with statistics?

So you want to be an actuary...

NEW! Mathematician/Actuary/Statistician are the 2nd, 3rd, and 4th best jobs!

Applets discussed in the textbook

Date

Topic

Reading

Homework Assignment

Due

Jan 10

Sampling Distributions

7.2

Chapter 7
# 11, 12, 19, 20

Jan 12

Estimation, Bias and Mean Square Error of Point Estimators; Common Unbiased Point Estimators

8.1 - 8.3
Chapter 8
# 6, 10, 13, 18
Jan 14

Error of Estimation:
Zogby poll
Polling 101 (Margin of Error)
Margin of Error from ASA
Confidence Intervals

8.4
8.5
# 32, 33, 41, 44
HW #1
Jan 17 HOLIDAY  

 

Jan 19 Large-Sample Confidence Intervals and Sample Size
8.6
8.7

# 64, 66, 74, 75

Jan 21 Small-Sample Confidence Intervals for Means
8.8
# 88, 89
HW #2
Jan 24 Confidence Intervals for Variance
Efficiency
8.9
9.2
Chapter 8 # 96, 97, 98, 126
Chapter 9 # 2, 7, 8
Jan 26 Consistency
9.3
# 15, 16, 24
Jan 28 Sufficiency
9.4
# 39, 40, 43
HW #3
Jan 31 Catch-up
 
Feb 2 Method of Moments
9.6
# 74, 78
Feb 4 Method of Maximum Likelihood
9.7
# 82, 83, 84
Feb 7 Q&A Preparation for Review I   Review I
HW #4
Feb 9 Introduction to Hypothesis Testing
10.1-10.2
#4, 5, 6
Feb 11 Large-Sample Tests
10.3
#22, 28, 30, 34
Feb 14 Type II Errors and Sample Size
Relationship between CI and Hypothesis Testing
10.4 - 10.5
#38, 40, 41, 42
Review I
Feb 16 Attained Significance, or p-value
Small-Sample Tests for Means
10.6 - 10.8
#52, 54, 56, 66, 72, 75  
Feb 18 Testing Hypotheses about Variances
10.9
#78, 82
HW #5
Feb 21 Power and Neyman-Pearson Lemma
10.10
#89, 90, 91, 92, 95
Feb 23 Likelihood Ratio Tests
10.11
 
Feb 25 Likelihood Ratio Tests, cont.
10.11
#106, 112
HW #6
Mar 7 Linear Models and Least Squares
11.1-11.3
#10, 11, 12  
Mar 9 Properties of Least Squares Estimators
11.4
#15, 17  
Mar 11 Inferences with Parameters
Inferences with Linear Functions of Parameters
11.5-11.6
#23, 26, 35, 38
HW #7
Mar 14 Predicting using Simple Linear Regression
11.7
#44  
Mar 16 Correlation
11.8
#48, 55, 58  
Mar 18 Multiple Regression with Matrices
11.10-11.11
#68 + 2 problems assigned in class
HW #8
Mar 21 Inference and Prediction in Multiple Regression
11.12-11.13
#74, 75, 79
Mar 23 Testing for all coefficients = 0
11.14
#82, 83
Mar 25 Chi Square Test and Goodness of Fit
14.2-14.3
Review II distributed
Chapter 14 #4, 12
HW #9
Mar 28 Contingency and r x c Tables
14.4-14.5
#16, 25(a-b)
Mar 30 Analysis of Variance
13.2
Chapter 13 #2
Review II (due Mar 31 by 10 a.m.)
Apr 1 No Class (Project work day)
 
Apr 4 Comparison of More Than Two Means
13.3-13.4
#12
Apr 6 One-Way Layout
13.5-13.6
#17
Apr 8 Estimation in the One-Way Layout
13.7
#28
Apr 11 Randomized Block Design
13.8-13.10
#45, 54
Project Status Report
HW #10
Apr 13 Selecting the Sample Size
13.11
#61
Apr 15 Simultaneous Confidence Intervals
13.12
#67
Apr 18 ANOVA Using Linear Models
Anova files
13.13
#72
Apr 20 No Class (Project work day)
 
Apr 21 PROJECT POSTER SESSION
 
Poster
Apr 22 Sign Test
15.3
#5, 6
HW #11
Apr 25 HOLIDAY
 
Apr 27 Wilcoxon Signed-Rank
15.4
#14, 16
Apr 29 Randomness Test (over lunch)
15.9
#48, 49
May 2 Prepare for Final
 

Project Final Report

HW #12

May 4 Prepare for Final
Course evaluations