Error types

Type 1 error rate = $α$ = $P (Type 1 error) = P (reject H_{0} | H_{0} is true)$
Type 2 error rate = $β$ = $P (Type 2 error) = P (do not reject H_{0} | H_{0} is false)$
$Power = 1 - P (Type 2 error) = 1 - β = P (reject H_{0} | H_{0} is false)$

Trying to decrease one of the error rates by changing the Critical Region increases the other one

\begin{aligned} 0.05 & = P (reject H_{0} | μ = 2) \\ 0.05 & = P (\bar{X} > C^{*} | μ = 2) \\ 0.05 & = P (\frac{\bar{X} - 2}{\sqrt{1.2 / n}} > \frac{C^{*} - 2}{\sqrt{1.2 / n}} | μ = 2) \\ \to p a g 97 \end{aligned}

$β$ depends on the choice of $α$ , sample size, the true value of the parameter, etc
the greater the value of $α$ or $β$ , the higher the probability that the other test errors occur
type 1 errors are worst case scenario, so we normally choose a small value for $α$ and let $β$ be