Hypothesis Testing

# Hypothesis Testing

Hypothesis testing is a fundamental statistical method for making decisions based on data. This lecture covers the complete process from formulating hypotheses to interpreting results.

## Learning Objectives

In this lecture, you will learn:
- The logic and process of hypothesis testing
- Type I and Type II errors
- p-values and significance levels
- One-sample and two-sample tests
- Practical applications and interpretation

## The Hypothesis Testing Process

1. **State the hypotheses**: Null (H₀) and Alternative (H₁)
2. **Choose significance level**: Typically α = 0.05
3. **Calculate test statistic**: Based on sample data
4. **Find p-value**: Probability of observing the data
5. **Make decision**: Reject or fail to reject H₀
6. **Interpret results**: In context of the problem

## Common Test Types

- **t-tests**: For means and differences
- **Chi-square tests**: For categorical data
- **ANOVA**: For multiple group comparisons
- **Non-parametric tests**: When assumptions aren't met

## Practical Example

Testing whether a new teaching method improves student performance:
- H₀: μ₁ = μ₂ (no difference)
- H₁: μ₁ > μ₂ (new method better)
- α = 0.05
- Calculate t-statistic and p-value
- Make decision based on results