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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

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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