Type I vs Type II error

Donated blood is tested for infectious diseases and other contaminants. Since most donated blood is safe, it saves time and money to test batches of donated blood rather than test individual samples. A certain test is performed to see if a certain toxin is present, and the entire batch is discarded if the toxin is detected. This is similar to using a null and an alternative hypothesis to determine whether to discard or keep the batch. The hypotheses being tested could be stated as:

$H_0:$H, start subscript, 0, end subscript, colon The batch does not contain the toxin.
$H_\text{a}:$H, start subscript, start text, a, end text, end subscript, colon The batch contains the toxin.