Minggu 14 - Distribusi-distribusi statistik sampling 1.pdf

Minggu 14 - Distribusi-distribusi statistik sampling 1.pdf...

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DISTRIBUSI-DISTRIBUSI STATISTIK SAMPLING TI2102 TEORI PROBABILITAS MINGGU KE-14
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Pengertian statistik & distribusi sampling n Statistika vs statistik n Statistik adalah variabel random yang merupakan fungsi dari karakteristik (nilai) sampel yang diambil n Contoh statistik: n rataan sampel: n simpangan baku sampel: s n Karena statistik adalah variabel random maka statistik memiliki distribusi probabilitas. n Biasanya distribusi ini disebut dengan distribusi sampel dari (nama statistiknya) atau sampling distribution of … X
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Gambaran Central Limit Theorem Sampel 1 Sampel 2 Sampel 3 Sampel n ... 1 x 2 x 3 x n x μ σ
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Central Limit Theorem Jika merupakan rataan dari sebuah sampel berukuran n yang diambil secara random dari sembarang populasi dengan rataan μ dan variansi terbatas ( finite ) σ 2 , maka bentuk limit dari distribusi saat n à , adalah distribusi normal n ( z ; 0,1) X n X Z / σ μ =
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Contoh Penggunaan CLT (1) Sebuah mesin mengisi minuman dalam botol dengan volume yang tidak diketahui distribusinya tetapi memiliki rataan 221 ml dan variansi 20 ml. Berapa probabilitas dari satu krat (24 botol) minuman, didapatkan isi rata-rata botol-botol dalam krat tersebut kurang dari 220 ml?
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Contoh Penggunaan CLT (2) Jawab: Berdasarkan dalil limit sentral akan mendekati distribusi normal baku manakala n sangat besar. Di sini angka n = 24 kita anggap cukup besar sehingga z dapat dianggap berdistribusi normal baku. Maka: Jadi probabilitas didapatkan rataan isi suatu krat kurang dari 220 ml adalah 0.137 n X Z / σ μ = P ( x 220) = P ( z 220 221 20 / 24 ) = P ( z 1 0.91 ) = P ( z ≤ − 1.095) = 0.137
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Teorema: Sifat Merampat Distribusi Normal Jika X 1 , X 2 , …, X n adalah variabel-variabel random yang saling bebas (independen) dan berdistribusi normal dengan rataan μ 1 , μ 2 , …, μ n dan deviasi standar σ 1 , σ 2 , …, σ n Maka variabel random:
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