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DISTRIBUSISAMPLING
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Distribusi Sampling
Sampling Error
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Bahasan
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Distribusi Sampling
Distribusi Sampling adalah distribusidari besaran-besaran statistik, sepertirata-rata, simpangan baku, proporsi(persentase) yang mungkin muncul darisampel-sampel. Distribusi rata-rata sampel
Distribusi proporsi sampel
Distribusi beda dua rata-rata
Distribusi beda dua proporsi
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Population
Sample-5
Mean-5
Sample-6
Mean-6
Sample-8
Mean-8
Sample-4
Mean-4
Sample-9
Mean-9
Sample-2
Mean-2
Sample-1
Mean-1 Sample-3
Mean-3
Sample-7
Mean-7
Sample-10
Mean-10
Ilustrasi
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Distribusi Sampling Rata-Rata
Contoh 1: Populasi beranggotakan 6 dengan ukuran
masing: 2,3,5,6,8,9
Diambil sampel ukuran 2, pengambilansampel dilakukan tanpa pengembalian
Buat distribusi sampling rata-ratanya
Banyaknya sampel:
15
)!26(!2
!662
C
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Distribusi Sampling Rata-Rata
Sampel 1 : 2,3, rata-rata: 2.5
Sampel 2 : 2,5, rata-rata: 3.5
Sampel 3 : 2,6, rata-rata: 4
Sampel 4 : 2,8, rata-rata: 5
Sampel 5 : 2,9, rata-rata: 5.5
Sampel 6 : 3,5, rata-rata: 4 Sampel 7 : 3,6, rata-rata: 4.5
Sampel 8 : 3,8, rata-rata: 5,5
Sampel 9 : 3,9, rata-rata: 6
Sampel 10: 5,6, rata-rata: 5,5
Sampel 11: 5,8, rata-rata: 6.5 Sampel 12: 5,9, rata-rata: 7
Sampel 13: 6,8, rata-rata: 7
Sampel 14: 6,9, rata-rata: 7.5
Sampel 15: 8,9, rata-rata: 8.5
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Distribusi Sampling Rata-Rata
Frekuensi (f)
2.5 1
3.5 1
4 2
4.5 1
5 1
5.5 3
6 1
6.5 1
7 2
7.5 1
8.5 1
Jumlah 15
Chart Title
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Distribusi Sampling
Teorema Limit Pusat
Terlepas dari bentuk distribusi dataindividual dalam populasi, jika ukuran
sampel semakin besar ( ), distribusisampling dari mean dapat didekatidengan distribusi normal.
n
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Teorema Limit Pusat
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Contoh 2:
Tabel di sampingadalah hasilpengambilan20sampel denganukuran n=15,dipilih daripopulasiberukuran 200.Diketahui rata-ratapopulasinya
69.637 danstandar deviasinya10.411.
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Contoh 2:
Dari contoh 2, dapat diamati beberapa halberikut:
Statistics sample berbeda dari sample 1dan yang lainnya. Mean sample berkisarantara 64.65 75.80. Standar deviasiberkisar 7.62 14.42. Median sample64.10 77.10, dan range sample dari26.70 48.70.
Beberapa mean sample lebih tinggi danada yang lebih rendah dari rata-ratapopulasi. Begitu juga dengan standar
deviasi, variasi dan range. Dengan demikian, dapat disimpulkan
bahwa statistics sample hampir selalubervariasi dari sample ke sample.Variasi/keheterogenan ini dinamakandengan sampling error.
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Sampling Error
Ada beberapa sumber kesalahan dalamsampling. Salah satu diantaranyaadalah samplingerror.
Sampling error mencerminkan
keheterogenan atau peluangmunculnya perbedaan dari satu sampledengan sample yang lain.
Sampling error dapat diperkecil dengan
memperbesar ukuran sampel.
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Latihan
01. The sampling distribution of the
mean can be approximated bythe normal distribution:
a. As the number of samples getslarge enough
b. As the sample size (number ofobservations in each sample)gets large enough.
c. As the size of the population
standard deviation increases.d. As the size of the sample
standard deviation decreases.
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Latihan
02. The sampling distribution of the meanrequires ________ sample size toreach a normal distribution if thepopulation is skewed than if thepopulation is symmetrical.
a. The same
b. A smaller
c. A largerd. The distribution cannot be
compared.
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Latihan
03. Which of the following is true regardingthe sampling distribution of the mean fora larger sample size?
a. It has the same shape and mean as
the population.b. It has a normal distribution with the
same mean from the population.
c. It has a normal distribution with a
different mean from the population.
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Latihan
04. For samples of n=30, for mostpopulations, the sampling distribution ofthe mean will be approximately normallydistributed:
a. Regardless of the shape of thepopulation
b. If the shape of the population issymmetrical
c. If the standard deviation of the meanis known.
d. If the population is normallydistributed.
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Latihan
05. For samples of n=1, the samplingdistribution of the mean will be normallydistributed:
a. Regardless of the shape of thepopulation
b. If the shape of the population issymmetrical
c. If the standard deviation of the meanis known.
d. If the population is normallydistributed.