The Z critical value for a 95% confidence interval is:

• 1.96 for a two-tailed test;
• 1.64 for a right-tailed test; and
• -1.64 for a left-tailed test.

A Z critical value is the value that defines the critical region in hypothesis testing when the test statistic follows the standard normal distribution. If the value of the test statistic falls into the critical region, you should reject the null hypothesis and accept the alternative hypothesis.

To find a Z critical value for a given confidence level α:

1. Check if you perform a one- or two-tailed test.
2. For a one-tailed test:
   • Left-tailed: critical value is the α-th quantile of the standard normal distribution N(0,1).
   • Right-tailed: critical value is the (1-α)-th quantile.
3. Two-tailed test: critical value equals ±(1-α/2)-th quantile of N(0,1).
4. No quantile tables? Use CDF tables! (The quantile function is the inverse of the CDF.)
5. Verify your answer with an online critical value calculator.