Confidence Intervals

[mathhh10670]

If you create a 95% confidence interval for the mean of one thing (call this x), and want to compare if there is a difference between the mean of x and another thing (call this y), if the mean value of y is not in the confidence interval of x, is it then suffice to say that there is a difference in the means? The mean of y lies over 1000 values outside the lower end of the confidence interval of x.
My guess is that it is suffice to say there is a difference. Because the mean of x is likely to lie in that confidence interval, if the mean of y isn't in it, then there is likely a difference. But since it is not 100% confidence, I am not sure if this is correct to say, as the mean of x could in fact be outside the confidence interval.

 

[tkhunny]

No, it is not safe to assume that mean-x <> mean y unless you have a Census. If you have only sample means, there are rules for that. Of course, if you are building Confidence Intervals, it seems like you have Sample Means, not a Census.

Mean-y may be outside Confidence Interval-X (CI-X), but is ALL of CI-Y outside ALL of CI-X? Seems unlikely.

It is never 100% confidence, even with a Census. All sorts of things can go wrong.