# IS 1 luglio 21 SOLUZIONI

# ES. 1

rm(list = ls())

n=30
s=20
d.mv=s/n
alpha=0.15
z=qnorm(1-0.15/2)
z
L=d.mv-z*d.mv/sqrt(n)
U=d.mv+z*d.mv/sqrt(n)
L   # 0.49
U   # 0.84



# Es. 2

rm(list = ls())

n=30
s=10
m=s/n
z=qnorm(1-0.1/2)
z
smv=m/(1-m)
L=smv-z*sqrt(smv/n)
U=smv+z*sqrt(smv/n)
L   # 0.29
U   # 0.71





# Es. 3

rm(list = ls())

n=30
S2=0.9
th.0=0.6
s=12
m=s/n
W=sqrt(n)*(m-th.0)/sqrt(S2)
W
alpha=0.05
t.al=qt(alpha,df=n-1)
t.al
# Rif se W< t.al
W<t.al    # FALSE --> accetto H0




# Es. 4

rm(list = ls())

NUM=64
n=25
th.0=2

w.oss=NUM/th.0
w.oss

p.val=1-pchisq(w.oss,df=n-1)
p.val



# Es. 5

pnorm(0.5)
# 0.69

# PARTE B

# Es. 7

rm(list = ls())

x=c(1,4,2,3,5,6,2,5,7,8)
n=length(x)
n
m=mean(x)
m    # 4.3
max(x)   # 8
th.mom=3/2*m
th.mom

L=th.mom-1.96*th.mom/sqrt(8*n)
U=th.mom+1.96*th.mom/sqrt(8*n)
L
U

q=0.147
L.v=max(x)
U.v=(q^(-1/(20)))*max(x)
L.v
U.v