Confidence Interval difference in means Interpretation I have a negative confidence interval ((-35.346,-8.570) for an independent samples t-test.
I understand confidence intervals for the mean. However, I am uncertain about the interpretation of the confidence interval for a difference in means. 
Is this an accurate interpretation? 
The confidence interval for mean difference in life satisfaction for the two groups is (-35.346,-8.570); as this interval does not contain zero, I can be confident that I have used a method that that will produce significantly different or unequal population means 95% of the time. 
Or should I interpret the CI as follows:
The confidence interval for mean difference in life satisfaction for the two groups is (-35.346,-8.570); as this interval does not contain zero, I can be 95% confident that the population means are significantly different or unequal.
Is this splitting hairs?
 A: The first interpretation is incorrect, but the second one is correct.
What will happen in multiple studies is dependent on the power and the true difference, not the confidence interval, so saying that something will happen 95% of the time based on this interval is incorrect.
The second paragraph is a correct interpretation, further you can conclude that the 2nd group has a higher mean than the first group (the entire interval is negative).
A: By this confidence interval you are confident that if you draw random samples 100 times that in 95 cases (95%) the mean of the second sample is statistically signifanct larger than the mean of the first sample. Hence, you are 95% confident that the mean of the second sample's population is larger than the mean of the first sample's population. This is, since the test adresses to draw inference from the samples to the population.
Therefore you can also interpret that the two samples do not come from the same population since they have different means. 
