1. What is the Critical Value Zc?

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

2. How Does the Calculator Work?

The calculator uses the inverse normal distribution function:

Where:

• \( Z_c \) — Critical value from standard normal distribution
• \( \alpha \) — Significance level (typically 0.05, 0.01, etc.)
• \( \text{invNorm} \) — Inverse standard normal cumulative distribution function

Explanation: For a two-tailed test with significance level α, we find the Z-score that leaves α/2 in each tail of the distribution.

3. Importance of Critical Values

Details: Critical values define the rejection region for hypothesis tests. They help determine whether observed test statistics are statistically significant.

4. Using the Calculator

Tips: Enter your desired significance level (α) between 0 and 1 (typically 0.05 for 5% significance). The calculator will return the corresponding Z critical 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: For one-tailed tests, use invNorm(1-α) instead of invNorm(1-α/2). Two-tailed tests split α between both tails.

Q2: What are common critical values?
A: For α=0.05 (95% confidence), Zc≈1.96. For α=0.01 (99% confidence), Zc≈2.576.

Q3: When should I use Z critical values vs t critical values?
A: Use Z when population standard deviation is known or sample size is large (>30). Use t for small samples with unknown σ.

Q4: How accurate is this calculator?
A: It provides a good approximation (within ±0.0001) of the true inverse normal values.

Q5: Can I get critical values for other distributions?
A: This calculator is for standard normal only. Other distributions (t, χ², F) require different calculators.