14. Hypothesis Testing: Null Hypothesis, p-Values, Z-Test, Student's t-Test & Chi-Square Test • Mathematics, Statistics & Machine Learning (Big Tech Prep) • Rishabh Ki Kaksha

Mathematics, Statistics & Machine Learning (Big Tech Prep) › 14. Hypothesis Testing: Null Hypothesis, p-Values, Z-Test, Student's t-Test & Chi-Square Test

45 mins

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Course Syllabus

Module 1: Linear Algebra for Machine Learning & Deep Learning

01. Vectors, Vector Spaces, Dot Products & Norms (L1, L2, L-Infinity) in High Dimensions 02. Matrices, Matrix Multiplication & Linear Transformations (Rotation, Scaling, Shear) 03. Eigenvalues & Eigenvectors: Geometric Intuition, Diagonalization & Spectral Theorem 04. Principal Component Analysis (PCA) & Singular Value Decomposition (SVD) Math

Module 2: Multivariable Calculus, Gradients & Optimization Algorithms

05. Partial Derivatives, Directional Derivatives & The Gradient Vector (Del Operator) 06. The Jacobian Matrix & Hessian Matrix (Second Derivative Curvature Analysis) 07. Multivariate Chain Rule & The Mathematical Backbone of Neural Backpropagation 08. Optimization Algorithms: Gradient Descent, SGD with Momentum, RMSprop & Adam Optimizer Math

Module 3: Probability Theory & Random Variables

09. Probability Foundations: Axioms of Probability, Conditional Probability & Independence 10. Bayes' Theorem & Bayesian Inference: Prior, Likelihood, Posterior & Evidence 11. Probability Distributions: Gaussian (Normal), Bernoulli, Binomial, Poisson & Exponential Distributions

Module 4: Inferential Statistics & Hypothesis Testing

12. Expectation, Variance, Covariance & Pearson Correlation Coefficient 13. Law of Large Numbers & Central Limit Theorem (CLT) with Monte Carlo Simulations 14. Hypothesis Testing: Null Hypothesis, p-Values, Z-Test, Student's t-Test & Chi-Square Test 15. Maximum Likelihood Estimation (MLE) vs Maximum A Posteriori (MAP) Estimation

Module 5: Classical Machine Learning Algorithms from Scratch (NumPy)

16. Linear Regression from Scratch: Ordinary Least Squares (OLS) Closed Form vs Gradient Descent 17. Logistic Regression & Binary Cross-Entropy Loss from Scratch with NumPy 18. Regularization Mathematics: L1 Lasso (Sparsity) vs L2 Ridge (Weight Decay) Penalties

Interactive Lesson Studio

# 14. Hypothesis Testing: Null Hypothesis, p-Values, Z-Test, Student's t-Test & Chi-Square Test

> Mathematics & ML Foundations Notes by Rishabh - Topic 14

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### 1. The Core Scientific Framework 🔬

*   **Null Hypothesis ($H_0$):** Default assumption ki koi real effect nahi hai (e.g. New UI button converts same as old button).
*   **Alternative Hypothesis ($H_1$):** Naya feature actually significant change create kar raha hai.
*   **p-Value:** Probability ki observed result purely random coincidence/chance se aya hai agar $H_0$ sach tha.
    *   If **$p < 0.05$**: **Reject $H_0$ (Statistically Significant Victory!)**

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### 2. Type I vs Type II Errors Matrix 🎯

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### 3. Master Comparison Matrix

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### 4. Interview Ke 3 Sawal Is Topic Se

1. **A/B Testing me Peeking Problem (Continuous p-value checking) Type I error rate ko kaise inflate karta hai?** -> Har ghante test check karne se multiple testing problem hoti hai jisse false positive rate 5% se badhakar 30%+ ho jata hai (Sequential Testing / Bonferroni correction fixes this).
2. **Paired t-Test vs Two-Sample Independent t-Test me kya difference hai?** -> Paired test same subjects par Before-After metrics compare karta hai; Independent test do alag user cohorts (Control vs Variant) ko compare karta hai.
3. **Statistical Power ($1 - \beta$) kya hota hai?** -> Ye probability ki hamara A/B test sach me exist karne wale real metric uplift ko successfully detect kar payega (Standard target: 80%).

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**Next Topic:** 15. Maximum Likelihood Estimation (MLE) vs Maximum A Posteriori (MAP) Estimation

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