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How do I interpret a negative confidence interval when comparing two population means?

For example, a confidence interval is $(-23.11, -1.02)$, what is the significance of these values being negative? Is it strictly signifying that $\bar{x}_1 < \bar{x}_2$ ?

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    $\begingroup$ Basically, statistically yes, but there are a couple more technical details (e.g. the type I error rate and the percentage of the confidence interval, etc.) Maybe this page can give you some insight. $\endgroup$
    – Penguin_Knight
    Commented Oct 23, 2013 at 3:00

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You should write your hypothesis first :)

But I guess your hyp was x_1 >= x_2 ? Then we can say that we are (1-alfa)% confident that the difference between the true mean of x_1 and x_2 is between (−23.11,−1.02)

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