1. What is the 1 Proportion Z-Test?

The 1 Proportion Z-Test is a statistical test used to determine whether a sample proportion differs significantly from a hypothesized population proportion. It's commonly used in hypothesis testing for proportions.

2. How Does the Calculator Work?

The calculator uses the 1 Proportion Z-Test formula:

Where:

• \( p \) — Sample proportion (dimensionless)
• \( p_0 \) — Hypothesized population proportion (dimensionless)
• \( n \) — Sample size (dimensionless)
• \( z \) — Z-score (dimensionless)

Explanation: The formula calculates how many standard deviations the observed sample proportion is from the hypothesized population proportion.

3. Importance of Z-Test Calculation

Details: The z-score helps determine whether the difference between the sample and population proportions is statistically significant, which is crucial for hypothesis testing in research and data analysis.

4. Using the Calculator

Tips: Enter the sample proportion (between 0 and 1), hypothesized proportion (between 0 and 1), and sample size (positive integer). All values must be valid.

5. Frequently Asked Questions (FAQ)

Q1: When should I use a 1 Proportion Z-Test?
A: Use it when you want to test whether a single sample proportion differs from a known or hypothesized population proportion.

Q2: What are typical z-score thresholds?
A: Common critical values are ±1.96 for 95% confidence (α=0.05) and ±2.576 for 99% confidence (α=0.01).

Q3: What sample size is needed?
A: The test works best when np₀ and n(1-p₀) are both ≥10. Larger samples give more reliable results.

Q4: How does this differ from t-test?
A: Z-tests are for proportions with known variance, while t-tests are typically for means with unknown variance.

Q5: Can I use this for small samples?
A: For small samples (n < 30), consider using exact binomial tests instead as z-tests may not be accurate.