I understand that a Type II error that arises from a hypothesis test indicates a failure to reject the null hypothesis $H_0$ when $H_a$ in reality is true. But when I try to interpret a Type II error in the context of an actual problem, I have a question on the wording I can use.
Suppose I conduct a study to see if mean systolic blood pressure of patients receiving a treatment ($\mu_T$) is lower than that of patients taking a placebo, ($\mu_P$). I would have:
$$ H_0: \mu_T = \mu_P \\ H_a: \mu_T < \mu_P $$
In this context, I would say that a Type II error involves "believing the treatment does not lower means systolic blood pressure even though in reality it does". But is this, in effect, saying I accept $H_0$ instead of failing to reject $H_0$? Is it better to say a Type II error is "failing to find any evidence the treatment lowers mean systolic blood pressure even though in reality it does"?