🐍 Python
From zero to full-stack Python — practical, exam-oriented courses for every level
🧠 AI & Neural Networks
ANN foundations through deep learning, competitive programming, and a full capstone project
∫ Complex Analysis
Complex functions, Cauchy-Riemann equations, conformal mappings, and contour integration
📊 Probability & Statistics
Distributions, curve fitting, regression, and hypothesis testing — all exam-oriented
Sampling Theory & Hypothesis Testing
t-test, chi-square test, Type I/II errors, and A/B testing
Pricing (per student)
Prerequisites
- Completion of Probability Distributions — Discrete, Continuous, and Joint (or equivalent)
Overview
Covers sampling distributions, standard error, hypothesis testing (z-test, t-test), and the chi-square goodness-of-fit test. Students learn to frame a hypothesis, choose the right test, and interpret p-values — with strong exam-oriented problem-solving throughout.
Topics
| Hour | Topic | Details |
|---|---|---|
| 1 | Introduction to Sampling Distributions | Definition, purpose, and examples. |
| 2 | Standard Error | Calculation and interpretation. |
| 3 | Type I and Type II Errors | Definition, differences, and real-world implications. |
| 4 | Hypothesis Testing Basics | Null hypothesis, alternative hypothesis, test statistics. |
| 5 | Testing for Single Mean | Z-test and t-test with worked examples. |
| 6 | Problem-Solving (Article 27.1, 27.2, 27.3) | Exam-style hypothesis testing problems. |
| 7 | Student's t-Distribution | Definition, properties, and when to use it. |
| 8 | Chi-Square Distribution | Goodness-of-fit test — definition and examples. |
| 9 | Problem-Solving (Article 27.7, 27.13, 27.14, 27.15) | Exam-style chi-square problems. |
| 10 | Applications in Engineering & Business | Quality control, A/B testing, and process validation. |
| 11 | Additional Problem-Solving | Mixed hypothesis testing problems. |
| 12 | Recap & Doubt Clearing | Revision and timed Q&A session. |
Expected Outcomes
- Understand sampling distributions and standard error.
- Perform hypothesis testing using t-distribution confidently.
- Apply chi-square test for goodness-of-fit problems.