Hypothesis Tests · Superchallenge problem

Two groups' means are estimated independently with the same standard error $s$, and each group gets its own 95% interval, estimate $\pm 1.96s$. Separately, the difference is tested with the two-sided $z$ test at 5%, using standard error $\sqrt2\,s$. If the two true means are EQUAL, what is the probability that the two intervals overlap and yet the test rejects? Round to three decimal places.