1. What is Z Critical Value?

The Z critical value is the threshold on the standard normal distribution that corresponds to a specified significance level (α). It's used in hypothesis testing to determine the cutoff point for rejecting the null hypothesis.

2. How Does the Calculator Work?

The calculator uses the inverse standard normal distribution:

Where:

• \( Z_{crit} \) — Critical value for one-tailed Z-test
• \( \Phi^{-1} \) — Inverse standard normal cumulative distribution function
• \( \alpha \) — Significance level (probability of Type I error)

Explanation: The function finds the Z-score where the cumulative probability equals 1-α.

3. Importance of Z Critical Value

Details: Critical values are essential for determining statistical significance in hypothesis testing. They define the rejection region for the null hypothesis.

4. Using the Calculator

Tips: Enter the desired significance level (α) between 0 and 1 (e.g., 0.05 for 5% significance). The calculator will return the corresponding Z critical value.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between one-tailed and two-tailed critical values?
A: For two-tailed tests, use α/2 (e.g., 0.025 for α=0.05) to get each tail's critical value.

Q2: What are common Z critical values?
A: Common values are ±1.96 (α=0.05 two-tailed), ±2.576 (α=0.01 two-tailed), and 1.645 (α=0.05 one-tailed).

Q3: When should I use Z critical values?
A: Use them when population standard deviation is known and sample size is large (>30), or when data is normally distributed.

Q4: How is this related to p-values?
A: The p-value is compared to α, while the test statistic is compared to the critical value - both approaches are equivalent.

Q5: What if I need t critical values instead?
A: Use a t-distribution calculator when population standard deviation is unknown and sample size is small.