1. What is Proportion Hypothesis Testing?

The proportion hypothesis test (z-test for proportions) determines whether observed sample proportions differ significantly from hypothesized population proportions. It's commonly used in quality control, survey analysis, and medical studies.

2. How Does the Calculator Work?

The calculator uses the z-score formula for proportion hypothesis testing:

Where:

• \( \hat{p} \) — Sample proportion (observed)
• \( p_0 \) — Hypothesized population proportion
• \( n \) — Sample size

Explanation: The z-score measures how many standard deviations the observed proportion is from the hypothesized proportion.

3. Interpretation of Results

Details:

• |z| > 1.96 suggests statistical significance at α=0.05 (two-tailed)
• |z| > 2.58 suggests statistical significance at α=0.01 (two-tailed)
• Positive z indicates observed proportion > hypothesized
• Negative z indicates observed proportion < hypothesized

4. Using the Calculator

Tips:

• Proportions must be between 0 and 1
• Sample size must be positive integer
• Ensure sample size is large enough (n*p0 ≥ 10 and n*(1-p0) ≥ 10)

5. Frequently Asked Questions (FAQ)

Q1: When should I use this test?
A: When testing if a sample proportion differs from a known population proportion with large sample sizes (n > 30).

Q2: What are the assumptions?
A: Random sampling, normal approximation valid (np₀ ≥ 10 and n(1-p₀) ≥ 10), independent observations.

Q3: How does this differ from t-test?
A: This tests proportions rather than means. Use t-test for continuous data.

Q4: What if my sample size is small?
A: Consider exact binomial tests instead of normal approximation.

Q5: How do I determine statistical significance?
A: Compare z-score to critical values (e.g., ±1.96 for α=0.05) or calculate p-value.