# Mathematical Foundations of Statistics II - MAT4383/MAT5383

Catalog entry

Prerequisite: MAT4373/MAT5373 Mathematical Foundations of Statistics I.

Content: Mathematical Statistics II is an advanced course that delves into the mathematical foundations of point estimation, sufficiency, confidence intervals, hypothesis testing, inferences based on two samples, analysis of variance (ANOVA), and regression analysis. The course builds on the foundations established in Mathematical Statistics I and equips students with a deeper understanding of statistical methods for data analysis, inference, and prediction, essential for numerous applications in various disciplines.

## List of Topics

Session Section Topic Prerequisites SLOs
7 Point Estimation
1 7.1 General Concepts and Criteria
2 7.2 Methods of Point Estimation
3 7.3 Sufficiency
4 7.4 Information and Efficiency
8 Statistical Intervals Based on a Single Sample
5 8.1 Basic Properties of Confidence Intervals
6 8.2 Large-Sample Confidence Intervals for a Population Mean and Proportion
7 8.3 Intervals Based on a Normal Population Distribution
8 8.4 Confidence Intervals for the Variance and Standard Deviation of a Normal Population
9 8.5 Bootstrap Confidence Intervals
10 REVIEW
11 TEST 1
9 Tests of Hypotheses Based on a Single Sample
12 9.1 Hypotheses and Test Procedures
13 9.2 Tests About a Population Mean
14 9.3 Tests Concerning a Population Proportion
15 9.4 P-Values
16 9.5 Some Comments on Selecting a Test Procedure
10 Inferences Based on Two Samples
17 10.1 z Tests and Confidence Intervals for a Difference Between Two Population Means
18 10.2 The Two-Sample t Test and Confidence Interval
19 10.3 Analysis of Paired Data
20 10.4 Inferences About Two Population Proportions
21 10.5 Inferences About Two Population Variances
22 10.6 Comparisons Using the Bootstrap and Permutation Methods
23 REVIEW
24 TEST 2
11 The Analysis of Variance
25 11.1 Single-Factor ANOVA
26 11.2 Multiple Comparisons in ANOVA
27 11.3 More on Single-Factor ANOVA
28 11.4 Two-Factor ANOVA with Kij = 1
29 11.5 Two-Factor ANOVA with Kij > 1
30 12 Regression and Correlation
31 12.1 The Simple Linear and Logistic Regression Models
32 12.2 Estimating Model Parameters
33 12.3 Inferences About the Regression Coefficient b1
34 12.4 Inferences Concerning mY ·x* and the Prediction of Future Y Values
35 12.5 Correlation