Let $(X_1,X_2,\ldots,X_n)$ be a random sample from $N(\mu,\sigma^2)$, where $\sigma$ is known. Find the power function of the test of significance of $H_0:\mu=\mu_0$ against $H_1:\mu\neq\mu_0$ . Also, show that power${}>{}$size. My first step is to define the critical region as $W=\{(x_1,x_2,\ldots,x_n):|\sqrt{n}(\bar x-\mu_0)/\sigma|>\tau _{\alpha/2}\}$ where $P[Z>\tau_\alpha]=\alpha$, $Z\sim N(0,1)$, and $\alpha$ is the level of significance.
The power function of the test of significance is then,
$\beta(\mu)=P[(X_1,\ldots,X_n)\in W|\mu\in\Omega_1]=P[|\sqrt{n}(\bar x-\mu_0)/\sigma|>\tau _{\alpha/2}|\mu\neq\mu_0]$
and the size of the test of significance is,
$\sup\limits_{\mu \in\Omega_0}P[ (X_1,\ldots,X_n)\in W|\mu\in\Omega_0]=P[|\sqrt{n}(\bar x-\mu_0)/\sigma|>\tau _{\alpha/2}|\mu=\mu_0]$.
How do I proceed from here?