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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?

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  • $\begingroup$ A 95% confidence interval will yield the same inference as a p-value with alpha of .05. $\endgroup$ – Jay Schyler Raadt May 3 at 1:46
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The type of test depends upon the alternate hypothesis if h_a uses not equal then you use 2 tailed confidence interval and if it is either one of greater than or less than, then you use 1 tailed confidence interval.

For the above problem, you will use 1 tailed. Also, note you have to reduce the alpha value to half that is 0.025 when using 2 tailed.

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