Would you recommend using a z-test, a t-test, or an ANOVA for the analysis?

Below is the discussion question for my class.  I believe that the ANOVA testing is best for this study because you are able to test multiple populations. I chose this test because you can study the current medication on the market against the new test.  I am not sure if I am answer the questions correctly. Please help

In this discussion, you will evaluate a research question and determine how that question might best be analyzed.  To do this, you will need to identify the appropriate application of course specified statistical tests, examine assumptions and limitations of course specified statistical tests, and communicate in writing critiques of statistical tests.

A researcher wishes to study the effect of a new drug on blood pressure.  Consider and discuss the following questions as you respond:

• Would you recommend using a z-test, a t-test, or an ANOVA for the analysis?  Explain your answer.
• What would your choice of test depend on?  For the test you select, explain your design and your comparison groups.
• Would the hypothesis be directional or non-directional?
• Would the test be one-tailed or two-tailed?
• What would be the null and what would be the alternative hypothesis?