I need help solving for e. I think the probability of a type 2 error is possible, but I need an explanation as to why

1. (15 pts) A Randomized Clinical Trial was designed to compare the effectiveness of two different antiretroviral (ARV) drugs in patients co-infected with TB and HIV in Korea. A sample size of 485 per group was chosen to have 90% power to detect a difference in mean CD4 at 1 year of 25 based on an estimated standard deviation of 120. a. Which of the following is an accurate interpretation of the 90% power of this study? (circle 1) 1. We will have a 90% chance of finding a significant difference if the observed means of the two treatment groups differ by 25 and the standard deviation is 120. 2. We will have a 90% chance of finding a significant difference if the true means of the two groups differ by 25 and the standard deviation is 120. 3. There is a 90% chance that the observed difference will be 25 or more if the standard deviation is 120. 4. At the end of the study, if the standard deviation is 120 then on average 90% of the data will be contained in a 90% confidence interval b. If the true standard deviation in this population is 110, will the study have more or less power than expected? This study will have greater power, because as the standard deviation decreases, power increases. C. All participants will be observed for exactly one year, at which point their CD4 count is measured. Once the study is over, what type of test can be used to compare the observed differences in CD4 count between the two groups? A prospective Cohort Study many be used to compare the CD4 counts between both groups. d. The investigators are considering adding a third and fourth group who would receive two other ARVs. If they do so, what test would you use to simultaneously compare the four ARVs with respect to CD4? The four ARV's can simultaneously be compared using Single Factor One-Way ANOVA test. e. What is the problem with comparing all four ARVs two-at-a-time, using a t-test at alpha=0.05 for each