Impact of Significance Level on Type I and II Errors

In a hypothesis testing scenario, a researcher is testing a new medication to see if it is more effective than the current standard treatment. The null hypothesis ($H_0$) states that the new medication is just as effective as the current treatment, while the alternative hypothesis ($H_a$) states that the new medication is more effective. The researcher sets a significance level ($eta$) of 0.05 for the test.

In this context:

- A Type I error occurs if the researcher rejects the null hypothesis ($H_0$) when it is actually true, implying that the new medication is more effective when it is not.

- A Type II error occurs if the researcher fails to reject the null hypothesis ($H_0$) when it is false, implying that the new medication is not recognized as more effective when it actually is.

Given these definitions, if the researcher decides to lower the significance level to 0.01 in order to be more stringent about claiming the medication's effectiveness, which of the following statements is true regarding the impacts on Type I and Type II errors?