- Summary
- Must a one sided hypothesis test agree with the confidence interval of the same level of significance?

I learned that the confidence interval and a two sided hypothesis test (test for difference) agree if both have the same significance level.

Is that also true for one sided hypothesis tests? For instance, must a right-tailed Hypothesis test with alpha = 0.05 agree with the 95% confidence level centered at the estimator? I'm thinking if alpha is 0.05 then the tail areas in a confidence interval would be 0.025. But in the right sided hypothesis test the right tail area of alpha is 0.05 and not 0.025.

Is that also true for one sided hypothesis tests? For instance, must a right-tailed Hypothesis test with alpha = 0.05 agree with the 95% confidence level centered at the estimator? I'm thinking if alpha is 0.05 then the tail areas in a confidence interval would be 0.025. But in the right sided hypothesis test the right tail area of alpha is 0.05 and not 0.025.