10 - distribusi sampling

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    DISTRIBUSISAMPLING

    yenirokhayati

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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.