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.

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.

The significance level is a pre-determined threshold used to decide whether to reject the null hypothesis in a statistical test. The most commonly used significance level is 0.05, which means there is a 5% probability of rejecting the null hypothesis when it is actually true.