To calculate the p-value corresponding to a $z$-statistic of $z = -1.96$, we need to determine the area to the left of $z = -1.96$ under the standard normal distribution.

Step-by-Step Process:

1. Find the cumulative probability for $z = -1.96$: Using standard normal distribution tables or software, the cumulative probability for $z = -1.96$ is approximately: $P(Z \leq -1.96) \approx 0.025$

2. Determine the p-value: Since the alternative hypothesis is $H_A: \mu_1 - \mu_2 < 0$ (a one-tailed test), the p-value is the cumulative probability corresponding to $z = -1.96$.

   Therefore, the p-value is: $\text{p-value} = 0.025$

Final Answer:

D. 0.025

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