CD4 cells are a component of the human immune system that are destroyed by the HIV virus. Antiretroviral therapy (ART) is designed to inhibit the ability of the HIV virus to reproduce. Therefore, we might expect to see lower viral load levels and higher CD4 levels in those individuals taking ART. In this exercise, we will carry out a hypothesis test to compare the CD4 and HIV viral load levels between individuals taking ART and those not taking ART. The dataset hiv.csv contains data from a study of men infected with HIV-1 Source: Coombs et al., Association between Culturable Human Immunodeficiency Virus Type 1 (HIV-1) in Semen and HIV-1 RNA Levels in Semen and Blood: Evidence for Compartmentalization of HIV-1 between Semen and Blood. JID 177:320-330, 1997. The following variables are included in the dataset: Variable Description id subject id number blood HIV-1 viral load level in subject's blood (copies/ml) cd4 CD4 level in subject's blood (cells/l) (CD4 cells are part of the immune system and loss of CD4 cells is a hallmark of HIV-1 infection) art Is the subject taking antiretroviral therapy? (0 = no, 1 = yes) a. We want to compare the mean CD4 levels of individuals taking ART versus those not taking ART. Translate this scientific aim into a null hypothesis and a two-sided alternative hypothesis. b. Test the null hypothesis you wrote in (a) using a t-test and significance level = 0.05. Provide a point estimate and 95% confidence interval for the difference in mean CD4 count between those receiving ART and those not receiving ART. Report the p-value for the test and state your scientific conclusion. (Hint: see Lab 8, Question 1) Note: The data file doesn't have a header row. This code will read in the data file and assign column names to name the variables. # read in data dat <- read.csv("hiv.csv", # specify variable names since file had no header row col.names=c("id","blood","cd4","art")) c. Does this tell us about the causal effect of taking ART on CD4 counts? (Why or why not?)

Question 4 Suppose we now design a new study and collect similar data from 500 patients