Researcher conducts a study to decide whether support groupsimprove academic performance for at-risk high school students. Tensuch students are randomly selected to take part in the supportgroup for a semester, while the other 10 at-risk students serve asa control group. At the end of the semester, the improvement in GPAversus the previous semester is recorded for each student.
Support Group: 0.5, 0.8, 0.7, 0.7, -0.1, 0.2, 0.4, 0.4, 0.5,0.4
Control Group: -0.3, 0.0, -0.1, 0.2, -0.1, -0.2, -0.2, 0.0, -0.1,0.1

At the 10% level, use R to compare the two groups using apermutation test (with 100,000 randomly generated permutations).You need to write your hypotheses, the test statistic, the pvalue,and the decision/conclusion in the context of the problem.

R code for reference:

SupportGroup <- c(0.5, 0.8, 0.7, 0.7, -0.1, 0.2, 0.4, 0.4,0.5, 0.4)
ControlGroup <- c(-0.3, 0.0, -0.1, 0.2, -0.1, -0.2, -0.2, 0.0,-0.1, 0.1)

mean(SupportGroup);sd(SupportGroup)
mean(ControlGroup);sd(ControlGroup)

#permutation test on difference of means
choose(20,10)#number of possible permutations
new.dat <- c(SupportGroup,ControlGroup)
obs.mean.diff <- mean(SupportGroup) - mean(ControlGroup)
nsim <- 100000
sim.mean.diff <- rep(NA,length=nsim)
for (i in 1:nsim){
grps <- sample(c(rep(1,10),rep(2,10)),replace=FALSE)
sim.mean.diff[i] <- mean(new.dat[grps==1]) -mean(new.dat[grps==2])
}

hist(sim.mean.diff);abline(v=obs.mean.diff,col=\"red\",lty=2)
length(sim.mean.diff[sim.mean.diff<=obs.mean.diff])/nsim#estimated p-value