###Q2(a)

t.test(datps$Final~datps$Tutor)


###Q2(c)

psmod1 <- glm(formula=Tutor~Sex+Year+Major+Participation+Midterm_out_of_40, family=binomial, data=datps)
datps$ps1 <- exp(fitted(psmod1))/(1+exp(fitted(psmod1)))

par(mfrow=c(1,2))
hist(datps$ps1[datps$Tutor==0])
hist(datps$ps1[datps$Tutor==1])


###Q2(d)

mod_match <- matchit(formula = Tutor ~ Midterm_out_of_40 + Year+Sex+Major+Participation, method="nearest",data=datps)
dat.m <- match.data(mod_match)
summary(mod_match)


###Q2(e)

with(dat.m, t.test(Final ~ Tutor))


###Q2(f)

par(mfrow=c(1,2))
hist(dat.m$Midterm_out_of_40[dat.m$Tutor==0])
hist(dat.m$Midterm_out_of_40[dat.m$Tutor==1])

par(mfrow=c(1,2))
hist(dat.m$Participation[dat.m$Tutor==0])
hist(dat.m$Participation[dat.m$Tutor==1])

table(dat.m$Sex,dat.m$Tutor)
table(dat.m$Year,dat.m$Tutor)
table(dat.m$Major,dat.m$Tutor)


###Q2(g)

plot(psmod1)

par(mfrow=c(1,1))
hist(residuals(psmod1))