Type I and II Errors in Hypothesis Testing

In a hypothesis test, a researcher is evaluating whether a new drug is more effective than a placebo. The null hypothesis (H₀) states that the new drug has no effect (i.e., the mean difference $ar{X} - ar{Y} = 0$), while the alternative hypothesis (H₁) suggests that the drug is effective (i.e., the mean difference $ar{X} - ar{Y} > 0$).

The researcher conducts the test and decides on a significance level ($eta$) of 0.05, which means that there is a 5% risk of rejecting the null hypothesis when it is actually true (Type I error). However, the researcher learns that they failed to detect a true effect when the drug was indeed effective, which indicates the presence of a Type II error.

Based on this scenario, which of the following statements correctly describes the errors committed?