1. What is a Z-Test?

The Z-test is a statistical test used to determine whether two population means are different when the variances are known and the sample size is large (typically n > 30). It's commonly used for hypothesis testing in statistics.

2. How Does the Calculator Work?

The calculator uses the Z-test formula:

Where:

• \( x \) — Sample mean
• \( \mu \) — Population mean
• \( \sigma \) — Population standard deviation
• \( n \) — Sample size

Explanation: The Z-score measures how many standard deviations an element is from the population mean. A higher absolute value of Z indicates a more significant difference.

3. Importance of Z-Test

Details: Z-tests are crucial for hypothesis testing in statistics, quality control, and research studies. They help determine if observed differences are statistically significant or due to random chance.

4. Using the Calculator

Tips: Enter the sample mean, population mean, population standard deviation, and sample size. All values must be valid (n > 0, σ > 0).

5. Frequently Asked Questions (FAQ)

Q1: When should I use a Z-test vs a T-test?
A: Use Z-test when population standard deviation is known and sample size is large (n > 30). Use T-test when σ is unknown or sample size is small.

Q2: What does the Z-score tell me?
A: The Z-score tells you how many standard deviations your sample mean is from the population mean. Higher absolute values indicate more significant differences.

Q3: What is a good sample size for Z-test?
A: Typically n > 30 is recommended, though the exact requirement depends on population distribution and desired confidence level.

Q4: How do I interpret the Z-score?
A: Compare your Z-score to critical values from the standard normal distribution. Typically, |Z| > 1.96 indicates significance at α = 0.05 level.

Q5: Can I use this for proportions?
A: This calculator is for means. For proportion Z-tests, a different formula is needed (using p instead of x).