beta 0.7: mean estimate 0.701, CI coverage 95%, rejects beta=1 in 100%
beta 1.0: mean estimate 0.990, CI coverage 98%, rejects beta=1 in 2%
beta 1.6: mean estimate 1.600, CI coverage 95%, rejects beta=1 in 100%
beta 3.0: mean estimate 3.001, CI coverage 96%, rejects beta=1 in 100%