Researchers at a medical school want to determine if a new procedure helps patients recover faster than a standard procedure. During your consultation they discuss with you the following ideas that they have for pursuing this study. Explain why you might NOT suggest these procedures.

a. The researchers inform you that they have come up with the following hypotheses (in context, not formal): Null hyp. Our procedure performs better. Alternative: The procedures are the same. Explain why this is not the correct structure for hypotheses to the researchers.

b. The current data set that the researchers show you contains 5 patients who underwent the old procedure and 3 who underwent the new procedure. For each patient, the recovery time is noted in days. The researchers inform you that this is a pilot study in order to obtain a grant. They feel that a two-sample t-test is the best approach to show significant differences. Explain to them why this may NOT be the best approach.

c. The researchers tell you that they plan on collecting additional data pending grant funding. They ask you for a quick estimate on how many subjects they may need in order to be able to use two-sample t-tests to test their claim. What sample size might you suggest for each sample (new procedure, old procedure) in order for the t-test to be appropriate. (No need for a calculation, give an "off-the-cuff" estimate).