HYPOTHESIS TESTING QUICK REFERENCE
Module 8 | One-Page Cheat Sheet
1. HYPOTHESES
| Type | H₀ | Hₐ |
|---|---|---|
| Two-tailed | μ = μ₀ | μ ≠ μ₀ |
| Right-tailed | μ = μ₀ | μ > μ₀ |
| Left-tailed | μ = μ₀ | μ < μ₀ |
2. TEST FORMULAS
Z-Test for Mean (σ known)
z = (x̄ - μ₀) / (σ/√n)
T-Test for Mean (σ unknown)
t = (x̄ - μ₀) / (s/√n) | df = n - 1
Z-Test for Proportion
z = (p̂ - p₀) / √(p₀(1-p₀)/n)
where p̂ = x/n
Conditions: np₀ ≥ 10 AND n(1-p₀) ≥ 10
3. CRITICAL VALUES (z)
| Test | α=0.10 | α=0.05 | α=0.01 |
|---|---|---|---|
| Two-tailed | ±1.645 | ±1.96 | ±2.576 |
| Right-tailed | 1.282 | 1.645 | 2.326 |
| Left-tailed | -1.282 | -1.645 | -2.326 |
4. DECISION RULES
Critical Value Approach:
- Two-tailed: Reject if |test stat| > critical value
- Right-tailed: Reject if test stat > critical value
- Left-tailed: Reject if test stat < critical value
P-Value Approach:
- Reject H₀ if p-value ≤ α
- Fail to reject H₀ if p-value > α
5. ERRORS & POWER
| Error | Description | Prob. |
|---|---|---|
| Type I | Reject true H₀ (false +) | α |
| Type II | Fail to reject false H₀ (false -) | β |
Power = 1 - β (aim for ≥ 0.80)
Increase Power By:
- ↑ Sample size (most practical)
- ↑ α (more Type I errors)
- ↓ Variability
6. HYPOTHESIS TEST STEPS
- State H₀ and Hₐ, choose α
- Calculate test statistic
- Find critical value or p-value
- Make decision (reject or fail to reject)
- Conclude in context
7. Z-TEST vs T-TEST
Use Z-Test when:
- σ (population SD) is KNOWN
Use T-Test when:
- σ is UNKNOWN (use sample s)
- df = n - 1
Real-world: Almost always T-TEST!
8. P-VALUE INTERPRETATION
| P-value | Evidence vs H₀ |
|---|---|
| < 0.01 | Very strong |
| 0.01 - 0.05 | Strong |
| 0.05 - 0.10 | Weak |
| ≥ 0.10 | Little/none |
9. KEY REMINDERS
- H₀ always has = sign
- Never "accept" H₀, only "fail to reject"
- For proportions, use p₀ in SE formula
- Check conditions before testing!
- Always interpret in context
Module 8: Hypothesis Testing | Safaa Dabagh | Free Statistics Learning Platform