# MAT5383

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# 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 | ||

36 | 12.6 | Assessing Model Adequacy | ||

37 | 12.7 | Multiple Regression Analysis | ||

38 | 12.8 | Regression with Matrices | ||

39 | REVIEW |