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#### AMS 412, Mathematical Statistics

Catalog Description: Estimation, confidence intervals, Neyman Pearson lemma, likelihood ratio test, hypothesis testing, chi square test, regression, analysis of variance, nonparametric methods.

PrerequisiteAMS 311

3 credits

SBC: CER, ESI, EXP+

Required Textbook:
"Mathematical Statistics with Applications" by Kandethody Ramachandran & Chris P. Tsokos; 2nd Edition; Publisher: Elsevier/Academic Press, 2015;
ISBN:  978-0-12417113-8

AMS 412 Instructor page

THIS COURSE IS TAUGHT IN THE SPRING SEMESTER AND SUMMER SESSION STARTING 2020

Topics
1.  Point Estimation (first half of Chap. 8) –  4 class hours.
2.  Sampling Distributions (Chap. 7) –  2 class hours.
3.  Properties of Point Estimators and Methods of Estimation (Chap. 9) –  8 class hours.
4.  Interval Estimation (second half of Chap. 8) –  6 class hours.
5.  Hypothesis Testing (Chap. 10) – 7 class hours
6. Linear Models and Least Squares (Chap. 11) – 6 class hours.
7. Analysis of Variance (Cap. 13) –5 class hours.
8.  Examinations and Review – 4 class hours.

Learning Outcomes for AMS 412, Mathematical Statistics

1.) Demonstrate an understanding of point estimation and its applications – beginning of the learning of statistical inference:
* the method of moment estimator (MOME);
* the maximum likelihood estimator (MLE);
* order statistics and their application in deriving the MLE;
* the difference between the MOME and the MLE;
* unbiasedness, the minimum variance unbiased estimator (MVUE) and the Cramer-Rao Lower Bound (to identify efficient estimator, best estimator).

2.) Demonstrate an understanding of confidence intervals and their applications –continuing the learning of statistical inference:
* pivotal quantity;
* variable transformation techniques especially the moment generating function technique;
* confidence interval for one population mean (including paired samples) and for one populatin variance when the population distribution is normal;
* large sample confidence interval using the Central Limit Theorem with focus on CI for one population mean (including paired samples), and one population proportion;
* confidence interval for a modified problem for one population mean or proportion or variance;
* the right confidence intervals for real world problems.

3.) Demonstrate an understanding of hypothesis testing and its applications –continuing the learning of statistical inference:
* hypothesis testing including the type I and II errors, significance level, rejection region, effect size, power of the test, and p-value;
* hypothesis test using the pivotal quantity method for one population mean (including paired samples) and one population variance when the population distribution is normal;
* large sample hypothesis test using the pivotal quantity method and the Central Limit Theorem for one population mean (including paired samples) or proportion;
* hypothesis test using the likelihood ratio test method for one population mean and for one population variance when the population distribution is normal;
* hypothesis test using the likelihood ratio test method for one population proportion;
* asymptotic distribution of the likelihood ratio test;
* relationship between tests derived using the likelihood ratio test method and the pivotal quantity method;
* hypothesis test for a modified problem for one population mean or proportion or variance;
* right hypothesis tests for real world problems.

4.) Undertake group statistical projects involving one of the following topics, including written and spoken presentation of results:
* confidence interval and hypothesis tests for two population means, variances or proportions based on independent samples;
* non-parametric tests for one mean, two means and several means, and the Spearman rank correlation;
* one-way ANOVA;
* simple linear regression and the Pearson product moment correlation;
* multiple linear regression.