1. What is Critical Z Value?

The critical z-value is the point on the standard normal distribution that corresponds to a specific confidence level. It is used in hypothesis testing and confidence interval construction to determine the boundary between rejecting and failing to reject the null hypothesis.

2. How Does the Calculator Work?

The calculator uses the inverse normal distribution function:

Where:

• \( Z \) — Critical z-value
• \( \text{invNorm} \) — Inverse normal distribution function
• \( Confidence\ Level \) — Desired confidence level as a decimal (e.g., 0.95 for 95%)

Explanation: The function finds the z-score that corresponds to the given cumulative probability in a standard normal distribution.

3. Importance of Critical Z Value

Details: Critical z-values are essential for constructing confidence intervals and conducting hypothesis tests in statistics. They help determine the margin of error and establish decision boundaries for statistical significance.

4. Using the Calculator

Tips: Enter the desired confidence level as a decimal between 0 and 1 (e.g., 0.95 for 95% confidence). The calculator will return the corresponding critical z-value for a two-tailed test.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between one-tailed and two-tailed critical values?
A: One-tailed tests use the full alpha in one tail, while two-tailed tests split alpha between both tails. This calculator provides values for two-tailed tests.

Q2: What are common critical z-values?
A: Common values include: 1.96 for 95% confidence, 2.576 for 99% confidence, and 1.645 for 90% confidence (two-tailed tests).

Q3: When should I use z-values vs t-values?
A: Use z-values when population standard deviation is known or sample size is large (n > 30). Use t-values when population standard deviation is unknown and sample size is small.

Q4: How is the critical z-value related to p-values?
A: The critical z-value establishes the threshold for statistical significance. If the calculated test statistic exceeds the critical value, the result is statistically significant.

Q5: Can I use this for non-normal distributions?
A: Critical z-values are specifically for normal distributions. For non-normal distributions, other methods or transformations may be needed.