but they're not actually equivalent, in spite of tables like this [0]. type ii error is a false negative result in the context of a test, where you have to understand which hypothesis is which and exactly what you are accepting or rejecting (hypotheses are not always as simple as hotdog/not-hotdog); if your listener doesn't know what statistical tests mean or wasn't following the setup, they have to stop you and ask.

[0] https://en.wikipedia.org/wiki/Type_I_and_type_II_errors#Tabl...