To find the critical z value for a two-tailed test with a significance level \( \alpha = 0.1 \), we first need to determine the critical values that correspond to this significance level.
For a two-tailed test with \( \alpha = 0.1 \), the significance level in each tail will be \( \frac{\alpha}{2} = 0.05 \).
Next, we look for the z values that correspond to the cumulative probabilities of 0.05 and 0.95 on the standard normal distribution.
Using standard z-tables or a calculator:
- The critical z value associated with a cumulative probability of 0.05 is approximately \(-1.645\).
- The critical z value associated with a cumulative probability of 0.95 is approximately \(1.645\).
Thus, the critical z values for this two-tailed test are:
\[ \pm 1.645 \]
Therefore, the correct answer is:
A) ±1.645