A critical value from the lemma
Independent readings are \operatorname{N}(\mu, 4), so \sigma=2, and n=25. For a test of H_0:\mu=10 against H_1:\mu>10 at level 0.05, find the critical value for \overline X. Then compute the power at \mu=11. Use z_{0.95}=1.645 and \Phi(0.855)=0.804.
Worked answer
The standard error is \sigma/\sqrt n=2/5=0.4. The level-0.05 test rejects when
\overline X>10+1.645\times 0.4=10.658.
At \mu=11 the power is
\Phi\Bigl(-1.645+\frac{11-10}{0.4}\Bigr)=\Phi(0.855)=0.804.