Understanding Type I and Type II Errors

In the context of hypothesis testing, a researcher is testing a new drug to determine if it is more effective than the current benchmark. The null hypothesis ($H_0$) states that the new drug is not more effective than the benchmark, while the alternative hypothesis ($H_a$) posits that the new drug is indeed more effective. The researcher sets a significance level ($eta$) of 0.05 for the test. If the researcher rejects $H_0$ when it is actually true, a Type I error occurs. Conversely, if the researcher fails to reject $H_0$ when it is false, a Type II error is made. Based on this scenario, which of the following statements about these errors is true?