# Lab 10 20 maggio 21 IS

# Es. 1

dati=c(63, 65, 94, 37, 83, 95, 70, 96, 47, 29, 52, 38, 47, 79, 66, 25, 48, 80, 52, 49)
n=length(dati)

# (a)
t.test(dati)$conf.int

# (b)  

t.test(dati, alternative = "two.sided", conf.level = 0.95, mu=70)
# 
t.oss=-1.8948
2*pt(-abs(t.oss),n-1)

2*(1-pt(abs(t.oss),n-1))

# (e)
var(dati)

x.med=60.75
theta.0=70
t.oss=t.test(dati, alternative = "two.sided", conf.level = 0.95, mu=70)$statistic
S.n=sqrt(n)*(x.med-theta.0)/t.oss
S.n^2

t.test(dati, alternative = "two.sided", conf.level = 0.95, mu=70)$statistic

# (g)

t.test(dati, alternative = "less", conf.level = 0.99, mu=70)


# Es. 2

x.a=c(100,125,135,128,140,142,128,137,156,142,134,122,100,98,101)
x.b=c(95,87,100,75,110,85,95,98,96,100,107)
n.a=length(x.a)
n.b=length(x.b)
n.a+n.b-2

# (f)
t.test(x.a,x.b)$conf.int
t.test(x.a,x.b, var.equal=TRUE)

t.test(x.a,x.b, mu=40, var.equal=TRUE)

t.test(x.a,x.b, mu=45, alternative="less", var.equal=TRUE)


# Es. 3
data(women)
women
attach(women)
height
weight
data()