1. What is the Z-Score for Single Proportion?

The Z-score for a single proportion measures how many standard deviations an observed proportion is from the hypothesized population proportion. It's used in hypothesis testing for proportions.

2. How Does the Calculator Work?

The calculator uses the Z-score formula for proportions:

Where:

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

Explanation: The numerator measures the difference between observed and expected proportion, while the denominator calculates the standard error of the proportion.

3. Importance of Z-Score Calculation

Details: The Z-score helps determine whether an observed proportion is significantly different from a hypothesized value, which is fundamental in statistical hypothesis testing.

4. Using the Calculator

Tips: Enter sample proportion and hypothesized proportion as decimals between 0 and 1. Sample size must be a positive integer. All fields are required.

5. Frequently Asked Questions (FAQ)

Q1: When should I use this Z-score calculation?
A: Use when testing if a sample proportion differs significantly from a population proportion (one-sample proportion test).

Q2: What's a significant Z-score value?
A: Typically, |Z| > 1.96 indicates significance at α=0.05 level (two-tailed test).

Q3: What are the assumptions for this test?
A: The sample should be random, and np₀ and n(1-p₀) should both be ≥5 for normal approximation.

Q4: Can I use this for small sample sizes?
A: For small samples (n < 30), exact binomial test may be more appropriate.

Q5: How do I interpret a negative Z-score?
A: A negative Z-score means the sample proportion is less than the hypothesized proportion.