1. What is Hypothesis Testing for Proportion?

The z-test for proportions is used to determine whether the observed sample proportion differs significantly from a hypothesized population proportion. It's commonly used in quality control, survey analysis, and A/B testing.

2. How Does the Calculator Work?

The calculator uses the z-score formula for proportions:

Where:

• \( p \) — Sample proportion
• \( p_0 \) — Hypothesized population proportion
• \( n \) — Sample size

Explanation: The formula measures how many standard deviations the observed proportion is from the hypothesized proportion.

3. Interpretation of Results

Details:

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

4. Using the Calculator

Tips:

• Proportions must be between 0 and 1
• Sample size must be large enough (n*p₀ > 5 and n*(1-p₀) > 5)
• For small samples, consider exact binomial tests

5. Frequently Asked Questions (FAQ)

Q1: When should I use this test?
A: Use when testing if a sample proportion differs from a known population proportion with large sample sizes.

Q2: What are the assumptions?
A: Independent observations, random sampling, and sufficiently large sample size.

Q3: How does sample size affect the test?
A: Larger samples increase test power but require smaller differences to be significant.

Q4: What's the difference between one-tailed and two-tailed tests?
A: One-tailed tests directionality (greater/less than), two-tailed tests any difference.

Q5: When should I use exact tests instead?
A: When sample size is small or proportions are extreme (close to 0 or 1).