1. What is the Z Test Statistic?

The Z test statistic measures how many standard deviations an observed sample mean is from the population mean. It's used in hypothesis testing to determine whether to reject the null hypothesis.

2. How Does the Calculator Work?

The calculator uses the Z test statistic formula:

Where:

• \( \bar{X} \) — Sample mean
• \( \mu \) — Population mean
• \( \sigma \) — Population standard deviation
• \( n \) — Sample size

Explanation: The numerator measures the difference between the sample and population means, while the denominator standardizes this difference by the standard error of the mean.

3. Importance of Z Test Statistic

Details: The Z test statistic is crucial for determining statistical significance in hypothesis testing, especially when sample sizes are large (typically n > 30) and population parameters are known.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

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

Q2: What does the Z score tell me?
A: The Z score indicates how many standard deviations your sample mean is from the population mean. Higher absolute values indicate greater statistical significance.

Q3: What is a significant Z value?
A: Typically, |Z| > 1.96 indicates significance at α = 0.05 level (two-tailed test), but this depends on your chosen significance level.

Q4: Can I use this for proportions?
A: Yes, with modifications. For proportions, the standard deviation is calculated as √(p(1-p)/n).

Q5: What if my sample size is small?
A: For small samples (typically n < 30), consider using a t-test instead, which accounts for additional uncertainty in small samples.