What is Hypothesis Testing?
Hypothesis Testing is a statistical method used to make decisions based on data. It helps determine whether there is enough evidence to reject a statement (hypothesis) about a population parameter.
Formulating Hypotheses
- Null Hypothesis (H₀): A statement of no effect or no difference (e.g., μ = 50)
- Alternative Hypothesis (H₁ or Hₐ): What we want to test (e.g., μ ≠ 50)
Type I and Type II Errors
- Type I Error (α): Rejecting H₀ when it is actually true (false positive)
- Type II Error (β): Failing to reject H₀ when it is false (false negative)
z-tests and t-tests
z-test: Used when population standard deviation (σ) is known and sample size is large.
t-test: Used when σ is unknown and sample size is small.
Both tests compare sample data to population parameters to decide if the difference is significant.
Chi-Squared Tests
- Goodness of Fit: Tests if observed data matches expected distribution
- Test of Independence: Tests if two categorical variables are related
Understanding p-values
The p-value is the probability of observing a test statistic as extreme as the one observed, under the assumption that the null hypothesis is true.
If p-value < α (e.g., 0.05), we reject the null hypothesis.
Significance Levels (α)
The significance level is the threshold for rejecting the null hypothesis. Common values are 0.05 (5%) or 0.01 (1%).