What is asymmetrical confidence interval?

A confidence interval, for a given probability, is the interval within which the true value may be found with that probability if the null hypothesis is true.

There are two possible reasons why a confidence interval may be asymmetrical. One is that the alternative hypothesis is asymmetrical: for example, H0 is X = 5 and H1 is X > 5 (rather than X ≠5).

The other possible reason is that the test statistic has an asymmetrical distribution.

Either of these can give rise to asymmetrical CIs.