Does anybody know the protocol for when you use two different methods to create confidence intervals and get differing results in the test.

I ran a test for a parameter estimation MLE and got different results for my confidence interval. And would like some advice.

For example,

you have a null hypothesis

H0 : m = 20

HA: m is not equal to 20.

Then you use one method for hypothesis testing and you get a confidence interval

(10,15) (reject the null)

Then you use a different method to test a hypothesis and you get;

(15,25) (fail to reject)

What would you do under these circumstances?

e.g Not use multiple tests, or fail to reject because one was failed, yeah I am not sure, hopefully you understand the problem and can help me thanks.