I'm currently doing a project for my AP Stats class. I performed a 2 sample t test for difference of means with an alpha value of .05. I rejected my null hypothesis that the means of two populations were equal, in favor of the population mean of A being greater than that of B.
I am supposed to provide a confidence interval to support my answer, but I am having trouble with this. My current understanding is that we always use two sided confidence intervals. However, the two sided confidence interval results in (-.02 , 1.02). Because 0 is included in the interval, it refutes my conclusion from the test. But an upper bound one sided interval does not contain 0.
My real question is: is it possible for my interval to suggest a different conclusion than my test at the same confidence level? And when do we use a one sided confidence interval?