1. **State the problem:** Find the critical z-value for a left-tailed test with significance level $\alpha = 0.04$. 2. **Formula and concept:** For a left-tailed test, the critical z-value corresponds to the z-score where the cumulative probability to the left is $\alpha$. This means we want $P(Z \leq z_\alpha) = 0.04$. 3. **Find the critical z-value:** Using the standard normal distribution table or a calculator, find the z-score such that the area to the left is 0.04. 4. **Look up or calculate:** The z-score for $P(Z \leq z) = 0.04$ is approximately $-1.75$. 5. **Interpretation:** Since it is a left-tailed test, the critical value is negative, so $z = -1.75$. **Final answer:** The critical z-value is **$-1.75$**.