Let's assume that the mean difference between a before and after score measured in 10 subjects is 4.5, the estimated standard deviation is 5.06, and the calculated t-statistic derived from the sample mean is 2.812. What is the lower bound of the 95% confidence interval around the mean difference?

Assume we're testing differences in the bedside manner of east-coast based vs west-coast based doctors, rated on a scale from 1-10. Let's assume we know the following information about the two groups:

Group 1 (X): n = 6 Group 2 (Y): n = 4 S_x² = 0.945 S_y² = 0.455

What is the standard error of the distribution of differences between means?