Stat 105 - Introduction to Statistical Analysis
Course Description
Organization and presentation of data; probability functions; random variables; elements of statistical inference; analysis of variance.
Course Learning Outcomes
After completion of the course, the student should be able to:
- Demonstrate mastery of advanced statistical terms and concepts;
- Formulate steps in explaining phenomena and making decisions based on available data;
- Generate and present appropriate statistical analysis given statistical data; and
- Apply statistical procedures using software that are appropriate for different types of data.
Course Outline
UNIT 1. 1. Review of Set Theory
- Definition
- Notations and Symbols
- Methods of Describing a Set
- Operations
- Set Relations
- Properties
UNIT 2. Building Blocks of Probability Structure
- Counting Principles
- Random Experiment and Sample Space
- The Event Space
- Verbal and Set theoretic Equivalence
- Probability of an Event
- Conditional Probability
- Independence of Events
UNIT 3. Random Variables and Distribution Functions
- Concepts of a Random Variable
- Classification of Random Variables
- Cumulative Distribution Function
- Mean and Variance of a Random Variable
UNIT 4. Special Parametric Families of Univariate Distributions
- Discrete Distributions
- Continuous Distributions
UNIT 5. Sampling Distributions
- Sampling Distribution of the Mean
- The Central Limit Theorem
- t-distribution
UNIT 6. Estimation
- Basic Concepts of Estimation
- Estimating the Mean
- Estimating the Difference of Two Population Means
- Estimating Proportions
- Estimating the Difference of Two Proportions
- Sample Size Determination
UNIT 7. Hypothesis Testing
- Basic Concepts of Statistical Hypothesis Testing
- Testing the Hypothesis on the Population Mean
- Testing the Difference between Two Population Means
- Testing Hypothesis on Proportions
- Testing the Difference between Two Proportions
- Test of Independence