# Single sided lower confidence level

Hypothesis testing – Can one-sided confidence intervals have 95% coverage – Cross Validated, single sided lower confidence level.

Do not use this to test both $\mu>\mu_0$ or $\mu I was wondering given a one-sided (one-tailed) hypothesis with an alpha-level of .05 , can we be talking about 95% confidence intervals? For example, can we construct separately “one-sided” and “two-sided” confidence intervals for a one-sided Z or t test? what would be the “interpretation” of each of these confidence intervals given the one-sided test? I am a bit confused about this? Yes we can construct one sided confidence intervals with 95% coverage. The two sided confidence interval corresponds to the critical values in a two-tailed hypothesis test, the same applies to one sided confidence intervals and one-tailed hypothesis tests. For example, if you have data with sample statistics$\bar=7$,$s=4$from a sample size$n=40$If we were doing a hypothesis test for$\mu = \mu_0$then the null hypothesis would be rejected if we were using a value of$\mu_0$which is$\mu_0>8.24$or$\mu_0

The one-sided confidence interval is therefore $(-\infty,8.04)$

If we were doing a hypothesis test for $\mu \mu_0$ then check if $\mu_0\mu_0$ with a significance of 2.5%.

Do not use this to test both $\mu>\mu_0$ or $\mu ## Not the answer you’re looking for? Browse other questions tagged hypothesis-testing confidence-interval or ask your own question. 2 years, 3 months ago site design / logo © 2019 Stack Exchange Inc; user contributions licensed under cc by-sa 3.0 with attribution required. rev 2019.4.24.33401 Single sided lower confidence levelHypothesis testing – Can one-sided confidence intervals have 95% coverage – Cross Validated, single sided lower confidence level. Do not use this to test both$\mu>\mu_0$or$\mu

single sided lower confidence level