The standard for physics reporting on things like this is &quot;five sigma&quot; or that the test statistic in their hypothesis test must be greater than 5.  Since this is a one-tailed test, this corresponds to a p-value smaller than 0.00000029, so the chances of being wrong are about 1 in 3.5 million.  This isn&#x27;t a &quot;confidence interval&quot; like you were asking about, but I think that it answers what you meant to ask.  Let me know if you wanted something else.