Example 9.2 (continued) Applying the above reasoning, we obtain
the signi¯cance probabilities sketched in Figure 9.2. Notice that pb = pa=2
and that pb + pc = 1. The probability pb is fairly small, about 7%. This
makes sense: we observed ¹xn
:=
21:8 > 20 = ¹0, so the sample does contain
some evidence that ¹ > 20. However, the statistical test reveals that the
strength of this evidence is not su±ciently compelling to reject H0 : ¹ · 20.
In contrast, the probability of pc is quite large, about 93%. This also
makes sense, because the sample contains no evidence that ¹ < 20. In such
instances, performing a statistical test only con¯rms that which is transparent
from comparing the sample and hypothesized means.
9.4.2