Suppose that X1, . . . , Xn is a sample from a distribution whose variance 2 is unknown. Suppose we are planning to estimate 2 by the sample variance S2 _ = ni =1(Xi X)2/(n1), and we want to use the bootstrap technique to estimate Var(S2). (a) If n = 2 and X1 = 1 and X2 = 3, what is the bootstrap estimate of Var(S2)? (b) If n = 15, and the data values are 5, 4, 9, 6, 21, 17, 11, 20, 7, 10, 21, 15, 13, 8, 6 use simulation to obtain the bootstrap estimate of Var(S2).

Groups Randomize control group Split individuals into two groups separately Control vs. treatment Compare the two averages correlation between the groups (Measure the strength before and after to get the experiment) Matching Observed and match into pairs with two treatments (Longitudinal and measures) Each group has their own control group within Find the change between...