MTH396 Spring 2011 Syllabus

Topic NumberMajor TopicText Section(s)Subtopics
1 Review of Sampling Distributions and the Central Limit Theorem 7.2Sampling Distributions Related to the Normal Distribution
7.3The Central Limit Theorem
7.4Proof of the Central Limit Theorem
2 Estimation 8.2Point Estimators: Bias and MSE
8.3Common Unbiased Estimators
8.4Evaluating Goodness of a Point Estimator
8.5Confidence Intervals
8.6Large-Sample Confidence Intervals
8.7Sample Size
8.8Small-Sample Confidence Intervals
8.9Confidence Intervals for the Variance
3 Properties of Point Estimators and Methods of Estimation 9.2Relative Efficiency
9.3Consistency
9.4Sufficiency
9.5The Rao-Blackwell Theorem and MVUEs
9.6The Method of Moments
9.7The Method of Maximum Likelihood
9.8Large-Sample Properties of MLEs
4 Hypothesis Testing 10.2Elements of a Statistical Test
10.3Common Large-Sample Tests
10.4Type II Error Probabilities and Sample Size
10.5Relationship to Confidence Intervals
10.6Reporting Resuults with P-Values
10.7Comments on the Theory
10.8Small-Sample Hypothesis Testing
10.9Testing Hypotheses Concerning Variances
10.10The Neyman-Pearson Lemma and Power of Tests
10.11Likelihood Ratio Tests
5 Linear Models 11.2Linear Statistical Models
11.3Least Squares Methods
11.4Simple Linear Regression
11.5Inferences Concerning the Parameters
11.6Inferences Concerning Linear Functions of the Model Parameters
11.7Predicting a Particular Y Value
11.8Correlation
11.9Practical Examples
11.10Matrix Formulation of the Linear Model
11.11Multiple Linear Regression
11.12Inferences Concerning Linear Functions
11.13Predicting a Particular Y Value
11.14Test for All Parameter Values Equal to Zero
6 Experimental Design 12.1The Information in a Sample
12.2Designing Experiments to Increase Accuracy
12.3The Matched Pairs Experiment
12.4Examples
7 Analysis of Variance 13.2The ANOVA Procedure
13.3Comparing More Than Two Means: The One-Way ANOVA
13.4The One-Way ANOVA Table
13.5Statistical Model for the One-Way ANOVA
13.7Estimation in the One-Way ANOVA
13.8Statistical Model for the Randomized Block Design
13.9ANOVA for the Randomized Block Design
13.10Estimation in the Randomized Block Design
13.11Sample Size
13.12Simultaneous Confidence Intervals
13.13ANOVA Using Linear Models
8 Analysis of Categorical Data 14.1The Experiment
14.2The Chi-Square Test
14.3A Goodness of Fit Test
14.4r by c Tables with Fixed Row or Column Totals
14.5Other Applications