© 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 - 10

Unbiasedness

Biased Unbiased

P(X)

X

© 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

© 1999 Prentice-Hall, Inc. Chap. 6 - 17

© 1999 Prentice-Hall, Inc. Chap. 6 - 18