## Exercise 1
alpha <- 1 - c(.7,.8,.9)

zcrit <- qnorm(1-alpha/2) ## get the coefficient
2 * pnorm(zcrit, lower.tail=FALSE) ## Check if they are right!

## Exercise 2
# \bar{X} = \mathcal{N}(\mu, \sigma^2/n)
n <- 9
sigma <- 6/sqrt(9)
kk <- qnorm(0.1,mean=110,sd=2)
2 * pnorm(kk, mean=110, sd=2, lower.tail=TRUE)

## Exercise 3 same as 2 with sigma = s

# Exercise 4
bt <- read.table("BodyTemperature.txt", header=TRUE)
str(bt)
mh <- mean(bt$HeartRate)
sh <- sd(bt$HeartRate)/sqrt(nrow(bt))
alpha <- 0.22
kk <- qnorm((1-alpha/2),mean=mh, sd=sh)
pnorm(kk, mean=mh, sd=sh, lower.tail=FALSE)
k <- (kk - mh)/sh
ci <- c(mh-k*sh, mh+k*sh)


## Exercise 5
n <- 2000
ns <- 320
p <- ns/n
s2 <- sqrt(p * (1-p))/sqrt(n)
alpha <- 1 - 0.9

kk <- qnorm(0.95,mean=p, sd=s2)
pnorm(kk, mean=p, sd=s2)
k <- (kk - p)/s2
ci <- c(p - k * s2,p + k * s2)

## Exercise 6
data(Pima.tr, package="MASS")
idx <- sample(200,100)

## Manual computation
mi <- mean(Pima.tr$bmi[idx])
si <- sd(Pima.tr$bmi[idx])/sqrt(length(idx))
t <- (mi - 30) / si
pt(t,df=100-1, lower.tail=FALSE)

## R
t.test(Pima.tr$bmi[idx], alternative="greater", mu=30)


## Exercise 7
t.test(bp~type, data=Pima.tr, var.equal=TRUE)

## Exercise 7
t.test(npreg~type, data=Pima.tr, var.equal=TRUE)
t.test(bmi~type, data=Pima.tr, var.equal=TRUE)

## Exercise 8
bw <- read.table("birthwt.txt", header=TRUE)
str(bw)
t.test(ht~low, data=bw, var.equal=TRUE)

## Exercise 9
t.test(bwt~smoke, data=bw, var.equal=TRUE)