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

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

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

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

Semester Pendek FMIPA UGM 2005 Distribusi X Rerata = µx = µ Deviasi Standar = x = (kesalahan standar)  n Semester Pendek FMIPA UGM 2005

Sampel Tanpa Pengembalian Rerata = µx = µ Deviasi Standar = x = • (kesalahan standar)  n N - n N - 1 Semester Pendek FMIPA UGM 2005

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

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

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

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

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

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

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

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

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

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