© 1999 Prentice-Hall, Inc. Chap. 6 - 1
Sampling Distributions
(Distribusi Penarikan Contoh)
•Sebaran (Distribusi) Peluang teoritis
• Peubah Acak : Statistik Sample , misal
Rata-rata dan proporsi sample
• Hasil semua kemungkinan Sample dg ukuran yg sama
•Sampling Distribution: Distribusi peluang yang menyatakan peluang nilai-nilai yang mungking bagi suatu statistik contoh
© 1999 Prentice-Hall, Inc. Chap. 6 - 2
Ukuran Populasi, N = 4
Peubah Acak, X, adalah
Umur individu
Nilai-nilai X: 18, 20, 22, 24
diukur dalam tahun
© 1984-1994 T/Maker Co.
Ilustrasi Sampling Distributions
A
B C
D
Misalkan ada suatu
populasi……
© 1999 Prentice-Hall, Inc. Chap. 6 - 3
2362
214
24222018
1
2
1
.N
X
N
X
N
ii
N
ii
Karakteristik Populasi
Ukuran Ringkas
(Summary) Distribusi Populasi
.3
.2
.1
0 A B C D
(18) (20) (22) (24)
Distribusi Seragam
P(X)
X
© 1999 Prentice-Hall, Inc. Chap. 6 - 4
1st
2nd
Observation
Obs 18 20 22 24
18 18,18 18,20 18,22 18,24
20 20,18 20,20 20,22 20,24
22 22,18 22,20 22,22 22,24
24 24,18 24,20 24,22 24,24
16 Kemungkinan Sample
Diambil dengan cara
Pengembalian (with replacement)
16 Rataan Sample
Semua kemungkinan Sample
berukuran n = 2
1st 2nd Observation
Obs 18 20 22 24
18 18 19 20 21
20 19 20 21 22
22 20 21 22 23
24 21 22 23 24
1st 2nd Observation
Obs 18 20 22 24
18 18 19 20 21
20 19 20 21 22
22 20 21 22 23
24 21 22 23 24
© 1999 Prentice-Hall, Inc. Chap. 6 - 5
1st 2nd Observation
Obs 18 20 22 24
18 18 19 20 21
20 19 20 21 22
22 20 21 22 23
24 21 22 23 24
1st 2nd Observation
Obs 18 20 22 24
18 18 19 20 21
20 19 20 21 22
22 20 21 22 23
24 21 22 23 2418 19 20 21 22 23 24
0
.1
.2
.3
P(X)
X
Distribusi Rataan
Sample
16 Rataan Sample
Distribusi Sampling dari Semua
kemungkinan rataan Sample
# in sample = 2, # in Sampling Distribution = 16
_
© 1999 Prentice-Hall, Inc. Chap. 6 - 6
2116
241919181
N
XN
ii
x
581
16
212421192118222
1
2
.
N
XN
ixi
x
Ukuran Ringkas untuk
Distribusi Sampling
© 1999 Prentice-Hall, Inc. Chap. 6 - 7
18 19 20 21 22 23 24 0
.1
.2
.3 P(X)
X
Distribusi Rataan Sample n = 2
Membandingkan Populasi dgn
Distribusi Sampling-nya
A B C D
(18) (20) (22) (24)
0
.1
.2
.3
Populasi
N = 4 = 21, = 2.236
P(X)
X
21x 581.x
_
© 1999 Prentice-Hall, Inc. Chap. 6 - 8
• Nilai tengah Populasi sama dgn nilai
harapan dugaanya
• Standar deviasi dugaan (dari distribusi
sampling) kurang dari Standar Deviasi
populasi
• Formula (sampling with replacement):
Sifat-Sifat dari Rataan Contoh
(dugaan Rataan Populasi)
x
As n naik, turun x =
x n
_ _
© 1999 Prentice-Hall, Inc. Chap. 6 - 9
Unbiasedness (Tidak Bias)
Nilai harapan (rata-rata dari semua
kemungkinan) dugaan sama dgn nilai
sebenarnya (rataan populasi)
Efficiency (efisien)
Rataan contoh variasinya lebih kecil dari
penduga tak-bias lainnya
Consistency (Konsisten)
Jika ukuran sample naik, variasi rataan sample
dari rataan populasi turun
Sifat dari rataan contoh
(Dugaan Rataan Populasi)
© 1999 Prentice-Hall, Inc. Chap. 6 - 11
Efficiency
Sampling
Distribution
of Median Sampling
Distribution of
Mean
X
P(X)
© 1999 Prentice-Hall, Inc. Chap. 6 - 12
Larger
sample size
Smaller
sample size
Consistency
X
P(X)
A
B
© 1999 Prentice-Hall, Inc. Chap. 6 - 13
= 50
= 10
X = 50
= 10
X
X
= 50- XX
= 50- X
n =16 `X = 2.5
n = 4 `X = 5
Jika Populasi Menyebar Normal
Central Tendency
Variation
Sampling dgn
pengembalian
Population Distribution
Sampling Distributions
x
=
x = n
_
_
© 1999 Prentice-Hall, Inc. Chap. 6 - 14
XX
Central Limit Theorem
(Dalil Limit Pusat)
Jika
Sample
Size
Cukup
Besar
Distribusi
Sampling
Mendekati
Distribusi
Normal, Tdk
tergantung
bentuk
distribusi
populasi
© 1999 Prentice-Hall, Inc. Chap. 6 - 15
nx
x
n =30 `X = 1.8 n = 4
`X = 5
When The Population is
Not Normal
Central Tendency
Variation
Sampling with
Replacement
Population Distribution
Sampling Distributions
= 50
= 10
X
X50X
© 1999 Prentice-Hall, Inc. Chap. 6 - 16
Example: Sampling Distribution
Sampling
Distribution
Standardized
Normal Distribution
.1915
50252
887.
/
.
n/
XZ
4.X
7.8 8 8.2 = 0 Z
= 1
.3830
.1915
50252
828.
/
.
n/
XZ
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