1. What is the Z Critical Value?

The Z critical value (Zc) is the number of standard deviations from the mean that corresponds to a given confidence level in a standard normal distribution. It's used in constructing confidence intervals and hypothesis testing.

2. How Does the Calculator Work?

The calculator uses the inverse normal distribution function:

Where:

• \( Z_c \) — Z critical value (dimensionless)
• \( CI \) — Confidence interval (as a fraction between 0 and 1)
• \( \text{invNorm} \) — Inverse standard normal distribution function

Explanation: The formula calculates the Z-score that corresponds to the desired confidence level in a standard normal distribution.

3. Importance of Z Critical Value

Details: Z critical values are essential in statistics for constructing confidence intervals and performing hypothesis tests. They help determine the margin of error and the range within which population parameters are likely to fall.

4. Using the Calculator

Tips: Enter the desired confidence level as a fraction between 0 and 1 (e.g., 0.95 for 95% confidence). The calculator will compute the corresponding Z critical value.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between Zc and t-critical value?
A: Zc is used when population standard deviation is known or sample size is large (>30), while t-critical is used with small samples and unknown population standard deviation.

Q2: What are common Zc values?
A: Common values are 1.96 for 95% CI, 1.645 for 90% CI, and 2.576 for 99% CI.

Q3: Why is the formula using (1 - CI)/2?
A: This accounts for the two-tailed nature of confidence intervals, splitting the alpha (1-CI) equally between both tails.

Q4: How accurate is this calculator?
A: It provides a good approximation, though exact values may differ slightly from statistical tables due to the approximation method used.

Q5: Can I use this for one-tailed tests?
A: For one-tailed tests, you would use invNorm(CI) directly rather than invNorm(1 - (1-CI)/2).