TEKNIK PENGAMBILAN SAMPEL

Simple Random Sampling

—4.14—

n1=30
N1=300
sigma_yi_1=25

p1=sigma_yi_1/n1
q1=1-p1
B1=2*sqrt((1-n1/N1)*(p1*q1/(n1-1)))

p1
## [1] 0.8333333
B1
## [1] 0.1313064

—4.19—

cavities=c(0,4,2,3,2,0,3,4,1,1)
n2=length(cavities)
N2=1000
sigma_yi_2=sum(cavities)

miu2=sigma_yi_2/n2
sigma2_2=var(cavities)
B2=2*sqrt((1-n2/N2)*sigma2_2/n2)

miu2
## [1] 2
B2
## [1] 0.9380832

—4.25—

N3=621
n3=60
sigma_yi_3=11
#------------------------------
p3=sigma_yi_3/n3
q3=1-p3
B3=2*sqrt((1-n3/N3)*(p3*q3/(n3-1)))
#------------------------------
p3
## [1] 0.1833333
B3
## [1] 0.09575969

—4.26—

B4=0.08
p4=0.2
N4=N3
#------------------------------
q4=1-p4
D4=B4^2/4
n4=(N4*p4*q4)/((N4-1)*D4+p4*q4)
#------------------------------
n4
## [1] 86.25
n4_int=ceiling(n4)
n4_int
## [1] 87

Systematic Sampling

—7.4—

n1=200
N1=2000
sigma_yi_1=132

p1=sigma_yi_1/n1
q1=1-p1
B1=2*sqrt((1-n1/N1)*(p1*q1/(n1-1)))

p1
## [1] 0.66
B1
## [1] 0.06371419

—7.5—

N2=N1
sigma_yi_2=sigma_yi_1
B2=0.01
p2=p1
#------------------------------
q2=1-p2
D2=B2^2/4
n2=(N2*p2*q2)/((N2-1)*D2+p2*q2)
#------------------------------
n2
## [1] 1635.718
n2_int=ceiling(n2)
n2_int
## [1] 1636

—7.6—

# Create the vector
Amount_of_fill <- c(12.00, 11.91, 11.87, 12.05, 11.75, 11.85, 11.97, 11.98, 12.01, 11.87, 11.93,11.98, 12.01, 12.03, 11.98, 11.91, 11.95, 11.87, 12.03, 11.98,11.87, 11.93, 11.97, 12.05, 12.01, 12.00, 11.90, 11.94, 11.93, 12.02, 11.80, 11.83, 11.88, 11.89, 12.05, 12.04)

yi_3 = data.frame(Amount_of_fill)
N3=1800
n3=36
sigma_yi_3=sum(yi_3)
#------------------------------
miu3=sigma_yi_3/n3
var_3=var(yi_3)
B3=2*sqrt((1-n3/N3)*var_3/n3)
#------------------------------
miu3
## [1] 11.94556
B3
##                Amount_of_fill
## Amount_of_fill     0.02514864

Stratified Sampling

—5.1—

N=c(65, 42, 93, 25)
N_Tot = sum(N)
n = c (14, 9, 21,6)
delinquent = c(4, 2, 8, 1) 

p=vector(,4)
Np =vector (,4)
sum_Np = 0

for ( i in 1 : 4){
  p[i]=delinquent[i]/n[i]
  Np [i]=N[i]*p[i]
  sum_Np=sum_Np+Np[i]
  }
p_st=(1/N_Tot)*sum_Np 

p
## [1] 0.2857143 0.2222222 0.3809524 0.1666667
sum_Np
## [1] 67.5
p_st
## [1] 0.3
sum_pst = 0
pst=vector (,4)

for (i in 1:4){
  pst[i]=N[i]^2*(1-n[i]/N[i])*((p[i]*(1-p[i]))/(n[i]-1))
  sum_pst=sum_pst+pst[i]
  }

V_pst=(1/N_Tot^2)*sum_pst
B=2*sqrt(V_pst)
B
## [1] 0.1172979

—5.10—

stratum1=c(97,42,25,105,27,45,53,67,125,92,86,43,59,21)
M1=86
m1=14
var1=var(stratum1)
stratum2=c(125,67,256,310,220,142,155,96,47,236,352,190)
M2=72
m2=12
var2=var(stratum2)
stratum3=c(142,310,495,320,196,256,440,510,396)
M3=52
m3=9
var3=var(stratum3)
stratum4=c(167,220,780,655,540)
M4=30
m4=5
var4=var(stratum4)

tau=M1*sum(stratum1)/m1+M2*sum(stratum2)/m2+M3*sum(stratum3)/m3+M4*sum(stratum4)/m4
V_Nybarst=M1^2*(1-m1/M1)*(var1/m1)+M2^2*(1-m2/M2)*(var2/m2)+M3^2*(1-m3/M3)*(var3/m3)+M4^2*(1-m4/M4)*(var4/m4)
V_Nybarst
## [1] 18762431
B_=2*sqrt(V_Nybarst)
tau
## [1] 50505.6
B_
## [1] 8663.124

Cluster Sampling

—8.2—

m=c(3,7,11,9,2,12,14,3,5,9,8,6,3,2,1,4,12,6,5,8)
y=c(50,110,230,140,60,280,240,45,60,230,140,130,70,50,10,60,280,150,110,120)
n=20
N=96

sum_yi=sum(y)
sum_mi=sum(m)
y_bar=sum_yi/sum_mi
y_bar
## [1] 19.73077
mbar=mean(m)
yyi2=vector(,n)
sum_yyi2=0
for (i in 1:n){
  yyi2[i]=(y[i]-y_bar*m[i])^2
  sum_yyi2=sum_yyi2+yyi2[i]
}
sr2=1/(n-1)*sum_yyi2
V_ybar=(1-n/N)*(sr2/(n*mbar^2))
B=2*sqrt(V_ybar)
B
## [1] 1.780103

—8.3—

M=N*mbar
tau=M*y_bar
tau
## [1] 12312
#------------
y_bart=mean(y)
var_t=var(y)
V_Nybart=N^2*(1-n/N)*var_t/n
B_=2*sqrt(V_Nybart)
B_
## [1] 3175.068

—8.14—

#dont have the data M6-Exercise 8_14.txt bruh

—8.15—

#same issue with the previous one hehe, check ppt