1. What is the One Sample Z-Test?

The one sample z-test is a statistical procedure used to determine whether the sample mean is significantly different from a known or hypothesized population mean when the population standard deviation is known.

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 the sample mean is from the population mean. A higher absolute z-score indicates greater deviation.

3. Importance of Z-Test Calculation

Details: The z-test is crucial for hypothesis testing in research and quality control, helping determine if observed differences are statistically significant or due to 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 t-test?
A: Use z-test when population standard deviation is known and sample size is large (>30). Use t-test when population standard deviation is unknown.

Q2: What does the z-score tell me?
A: The z-score indicates how far (in standard deviations) your sample mean is from the population mean. Higher absolute values suggest stronger evidence against the null hypothesis.

Q3: What's a significant z-score?
A: Typically, z-scores beyond ±1.96 (for α=0.05) or ±2.58 (for α=0.01) are considered statistically significant.

Q4: What are the assumptions of the z-test?
A: Assumes normal distribution, known population standard deviation, random sampling, and independent observations.

Q5: Can I use this for proportions?
A: For proportion z-tests, a different formula is used that accounts for binomial distribution characteristics.