To construct the confidence interval for the difference between two population means ($\mu_1 - \mu_2$), we need the following information:

1. Sample means ($\bar{x}_1$ and $\bar{x}_2$) for each group.
2. Sample standard deviations ($s_1$ and $s_2$) for each group.
3. Sample sizes ($n_1$ and $n_2$) for each group.
4. Confidence level (e.g., 95%).

The confidence interval for $\mu_1 - \mu_2$ can be calculated using the formula: $(\bar{x}_1 - \bar{x}_2) \pm t^* \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$ where $t^*$ is the critical t-value for the chosen confidence level, based on the degrees of freedom.

If you can provide the sample means, standard deviations, and sizes, I can calculate the confidence interval for you.

Would you like to proceed with these details, or do you have any questions?

Here are five questions to consider:

1. What confidence level are we using (e.g., 90%, 95%)?
2. Are the two samples independent of each other?
3. Do we assume equal variances between the two populations?
4. Is this a one-sided or two-sided confidence interval?
5. Do you have the raw data, or only summary statistics?

Tip: For a quick estimation, the 95% confidence interval requires approximately 2 standard errors around the mean difference, but exact values depend on the t-distribution.