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Distribusi Sampling

Distribusi Sampling. Materi Kuliah Metstat #3 Sekolah Tinggi Ilmu Statistik. Usman Bustaman, S.Si, MSE, M.Sc. Makna Probabilita. klasik (eksak): P(event E) = N e /N cth: melempar 2 koin 1 kali frekuensi relatif: P(event E)  n e /n cth: melempar 2 koin banyak kali

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Distribusi Sampling

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  1. Distribusi Sampling Materi Kuliah Metstat #3 Sekolah Tinggi Ilmu Statistik Usman Bustaman, S.Si, MSE, M.Sc.

  2. Makna Probabilita • klasik (eksak): P(event E) = Ne/N cth:melempar 2 koin 1 kali • frekuensi relatif: P(event E)  ne/n cth:melempar 2 koin banyak kali • Subjektif: P(event E)  (suka)2 cth: tidak melempar 2 koin  !!

  3. eksak • P (tepat 0 H) = ¼ • P (tepat 1 H) = 2/4 • P (tepat 2 H) = ¼

  4. relatif

  5. Pengambilan Sampel Acak(Random Sampling) • Syarat: Masing-2 elemen dlm populasi memiliki probabilita yg sama utk terpilih If Xi ~ f(x)  f(x1,x2,…,xn)=f(x1)f(x2)…f(xn) i i d r v

  6. Pengambilan Sampel Acak(Random Sampling) • Cara (Sampling Technique): • membuat sampling frame • menarik sampel secara random • Contoh: Ott & Longnecker (2010) p. 195: Survey (polling) yang dilakukan oleh Literary Digest vs Goerge Gallup  pemenang pilpres AS (Landon vs Roosevelt) th 1936

  7. Contoh • Pemilihan 2 kota dari 10 kota All Possible Sample Bgm dgn populasi yg besar?? • Buat Sampling frame • Tarik angka random sebanyak n

  8. Distribusi Sampling • 7an pengambilan sampel  memperoleh/menduga karakteristik populasi statistik  parameter • Distribusi sampling  distribusi probabilita dari (sebuah) statistik. • Example 4.22 (Ott & Longnecker p. 182) Montgomery, p.197 Walpole, p.231

  9. Distribusi sampling dari rata-2 sampel • Example 4.22 (Ott & Longnecker p. 182) • Teorema Limit Pusat Tugas: Buktikan

  10. ContohAplikasi Montgomery, p. 241, exercise 7.14 • Misal X memilikidistribusipeluang uniform: • Jikadiambilsebanyak 40 sampeldari X, tentukandistribusi sampling untuk rata-ratanya. Hint: tent. E(X) danVar(X), lalugunakan CLT

  11. Distribusi sampling dari varians sampel Bagi dengan dan substitusi i = 1 Dist. Chi-square dgn df = n Dist. Chi-square dgn df = 1

  12. Normal  chi-square • Tabel Chi-square

  13. Distribusi sampling dari proporsi sampel • P = X/n  binomial(n,p)

  14. Contoh Montgomeri example 4.17, 4.18, p. 119-120 • Dengan pendekatan dist. normal

  15. Queez • Apa yang dimaksud dengan Distribusi Probabilita? • Apa yang dimaksud dengan Distribusi Sampling? • Apakah Distribusi Probabilita = Distribusi Sampling: • Secara makna? (Ya/tidak), jelaskan! • Secara realita/interpretasi? (Ya/tidak), jelaskan! • Jelaskan pengertian dari teorema limit pusat (central limit theorem)

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