Statistics II
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Course Title: Statistics II
Course No: STA215
Nature of the Course: Theory + Lab
Semester: 3
Full Marks: 60 + 20 + 20
Pass Marks: 24 + 8 + 8
Credit Hours: 3
Course Description
Course Objectives
Course Contents
1.1. Sampling and Estimation Theory
- Sampling distribution
- Sampling distribution of mean and proportion
- Central Limit Theorem
- Concept of inferential Statistics
- Estimation
- Methods of estimation
- Properties of good estimator
- Determination of sample size
- Relationship of sample size with desired level of error
- Problems and illustrative examples related to computer Science and IT
2.1. Hypothesis Testing Fundamentals
- Types of statistical hypotheses
- Power of the test
- Concept of p-value and use of p-value in decision making
- Steps used in testing of hypothesis
2.2. Parametric Tests
- One sample tests for mean of normal population (for known and unknown variance)
- Test for single proportion
- Test for difference between two means and two proportions
- Paired sample t-test
- Linkage between confidence interval and testing of hypothesis
- Problems and illustrative examples related to computer Science and IT
3.1. Introduction to Non-parametric Tests
- Parametric vs. non-parametric tests
- Needs of applying non-parametric tests
3.2. One-sample Tests
- Run test
- Binomial test
- Kolmogorov–Smirnov test
3.3. Two Independent Sample Tests
- Median test
- Kolmogorov-Smirnov test
- Wilcoxon Mann Whitney test
- Chi-square test
3.4. Paired-sample and Multiple Sample Tests
- Wilcoxon signed rank test
- Cochran's Q test
- Friedman two way analysis of variance test
- Kruskal Wallis test
- Problems and illustrative examples related to computer Science and IT
4.1. Multiple Regression Analysis
- Multiple and partial correlation
- Introduction of multiple linear regression
- Hypothesis testing of multiple regression
- Test of significance of regression
- Test of individual regression coefficient
- Model adequacy tests
- Problems and illustrative examples related to computer Science and IT
5. Design of Experiments
10 hrs
5.1. Experimental Design Principles
- Experimental design
- Basic principles of experimental designs
5.3. Randomized Block Design (RBD)
- ANOVA table
- Efficiency of RBD relative to CRD
- Estimations of missing value (one observation only)
- Advantages and disadvantages
5.4. Latin Square Design (LSD)
- Statistical analysis of m × m LSD for one observation per experimental unit
- ANOVA table
- Estimation of missing value in LSD (one observation only)
- Efficiency of LSD relative to RBD
- Advantage and disadvantages
- Problems and illustrative examples related to computer Science and IT
6.1. Introduction to Stochastic Processes
- Definition and classification
6.2. Markov Process
- Markov chain
- Matrix approach
- Steady-State distribution
6.3. Counting Process
- Binomial process
- Poisson process
- Simulation of stochastic process
6.4. Queuing System
- Main components of queuing system
- Little's law
- Bernoulli single server queuing process: system with limited capacity
- M/M/1 system: Evaluating the system performance
Laboratory Works
- 1.Sampling distribution, random number generation, and computation of sample size
- 2.Methods of estimation (including interval estimation)
- 3.Parametric tests
- 4.Non-parametric test
- 5.Partial correlation
- 6.Multiple regression
- 7.Design of Experiments
- 8.Stochastic process
Text Books
- 1.Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, & Keying Ye (2012). Probability & Statistics for Engineers & Scientists. 9th Ed., Prentice Hall
- 2.Michael Baron (2013). Probability and Statistics for Computer Scientists. 2nd Ed., CRC Press, Taylor & Francis Group, A Chapman & Hall Book
Reference Books
- 1.Douglas C. Montgomery & George C. Runger (2003). Applied Statistics and Probability for Engineers. 3rd Ed., John Wiley and Sons, Inc.
- 2.Sidney Siegel, & N. John Castellan, Jr. Nonparametric Statistics for the Behavioral Sciences, 2nd Ed., McGraw Hill International Editions