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Semester Pendek FMIPA UGM 2005
Sampel Acak Sederhana Semua obyek populasi mempunyai probabilitas yang sama untuk terpilih Populasi Berhingga: Untuk yakin bahwa sampel acak sederhana diambil dari suatu populasi berhingga, semua obyek populasi diberi nomor dari 1 s.d N Hampir semua prosedur/teknik statistik mensyaratkan sampel diambil secara acak Semester Pendek FMIPA UGM 2005
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Semester Pendek FMIPA UGM 2005
Estimasi Populasi adalah himpunan semua obyek yang menjadi perhatian Rerata populasi dengan notasi µ biasanya tidak diketahui Sampel diambil secara acak dari populasi Pengambilan sampel dapat dengan pengembalian, tanpa pengembalian atau sekaligus Semester Pendek FMIPA UGM 2005
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Semester Pendek FMIPA UGM 2005
Teorema Limit Pusat Jika suatu sampel dengan ukuran cukup besar (n > 30) diambil dari populasi, maka rerata sampel X berdistribusi mendekati distribusi normal Artinya jika suatu sampel acak diambil dari populasi X, maka X berdistribusi mendekati normal dengan rerata µ dan deviasi standar ( kesalahan standar) x = n Semester Pendek FMIPA UGM 2005
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Semester Pendek FMIPA UGM 2005
Distribusi X = 50 µ = 400 Populasi X x = = 11.18 50 20 µx = 400 (n = 10) x = = 15.81 50 10 X X µx = 400 (n = 20) x = = 7.07 50 x = = 5 50 100 X X µx = 400 (n = 50) µx = 400 (n = 100) Semester Pendek FMIPA UGM 2005
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Semester Pendek FMIPA UGM 2005
Distribusi X Rerata = µx = µ Deviasi Standar = x = (kesalahan standar) n Semester Pendek FMIPA UGM 2005
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Sampel Tanpa Pengembalian
Rerata = µx = µ Deviasi Standar = x = • (kesalahan standar) n N - n N - 1 Semester Pendek FMIPA UGM 2005
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Prosedur Sampling Lain
Population: the collection of all items about which we are interested Sampling Unit: a collection of elements selected from the population Cluster: a sampling unit that is a group of elements from the population, such as all adults in a particular city block Sampling frame: a list of population elements Semester Pendek FMIPA UGM 2005
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Prosedur Sampling Lain
Strata: are nonoverlapping subpopulations Sampling design: specifies the manner in which the sampling units are to be selected Semester Pendek FMIPA UGM 2005
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Simple Random Sampling
Population mean: µ Estimator: Estimated standard error of X: Approximate confidence interval: X = ∑x n N - n N - 1 sx = • X ± Z/2sx Semester Pendek FMIPA UGM 2005
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Semester Pendek FMIPA UGM 2005
Sampling Sistematik The sampling frame consists of N records The sample of n is obtained by sampling every kth record, where k is an integer approximately equal N/n The sampling frame should be ordered randomly Semester Pendek FMIPA UGM 2005
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Semester Pendek FMIPA UGM 2005
Sampling Strata Stratified sampling obtains more information due to the homogenous nature of each strata Stratified sampling obtains a cross section of the entire population Obtain a mean within each strata as well as an estimate of Semester Pendek FMIPA UGM 2005
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Semester Pendek FMIPA UGM 2005
Sampling Strata Gunakan notasi berikut: ni = ukuran sampel dalam stratum i Ni = banyaknya elemen dalam stratum i N = ukuran populasi = ∑Ni n = ukuran sampel = ∑ni Xi = rerata sampel dalam stratum i si = deviasi standar sampel dalam stratum i Semester Pendek FMIPA UGM 2005
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Semester Pendek FMIPA UGM 2005
Sampling Strata Rerata Populasi: µ Estimator: Estimasi kesalahan standar X: Aproksimasi interval interval: Xst = ∑NiXi N sx = ∑ st Ni 2 Ni - ni si ni Xst ± Z/2sx Semester Pendek FMIPA UGM 2005
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Semester Pendek FMIPA UGM 2005
Sampling Klaster Single-stage cluster sampling: randomly select a set of clusters for sampling Include all elements in the cluster in your sample Two-stage cluster sampling: randomly select a set of clusters for sampling Randomly select elements from each sampled cluster Semester Pendek FMIPA UGM 2005
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Semester Pendek FMIPA UGM 2005
Sampling Klaster Rerata Populasi: µ Estimator: Estimasi kesalahan standar Xc: Aproksimasi interval konfidensi: Xc = ∑Ti ∑ni Xc ± Z/2sx c sx = M - m mMN2 ∑(Ti - Xcni)2 m - 1 Semester Pendek FMIPA UGM 2005
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Interval Konfidensi Konstruksi suatu Interval Konfidensi untuk Rerata Populasi diketahui Tak diket Gunakan Tabel z Gunakan Tabel t Dapat menggunakan Tabel z Untuk mendapatkan aproksimasi interval konfidensi jika n > 30 Semester Pendek FMIPA UGM 2005
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