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Understanding Hypothesis Testing
What is Hypothesis Testing?
Hypothesis testing is a statistical method used to make decisions about populations based on sample data. Key concepts include:
- Null hypothesis (H₀) - Initial assumption
- Alternative hypothesis (H₁) - Competing claim
- Test statistic - Standardized sample measure
- P-value - Probability of more extreme results
- Significance level - Decision threshold
- Critical values - Decision boundaries
- Type I error - False rejection of H₀
- Type II error - False acceptance of H₀
Key Formulas
Z-Test Statistic:
z = (x̄ - μ₀)/(σ/√n)
T-Test Statistic:
t = (x̄ - μ₀)/(s/√n)
Proportion Test Statistic:
z = (p̂ - p₀)/√(p₀(1-p₀)/n)
Critical Values:
Two-tailed: ±z_(α/2) or ±t_(α/2,n-1)
One-tailed: z_α or t_(α,n-1)
Test Types
Z-Test
- Known population standard deviation
- Large sample size (n ≥ 30)
- Normal distribution assumption
- Uses standard normal distribution
T-Test
- Unknown population standard deviation
- Small sample size (n < 30)
- Normal distribution assumption
- Uses t-distribution
Proportion Test
- Binary outcomes
- Large sample size (np₀ ≥ 10)
- Normal approximation
- Uses standard normal distribution
Applications
Scientific Research
- Clinical trials
- Drug testing
- Treatment effects
- Experimental validation
Business
- Quality control
- Market research
- A/B testing
- Process improvement
Social Sciences
- Survey analysis
- Behavioral studies
- Educational research
- Policy evaluation