{"id":261,"date":"2023-08-03T11:26:47","date_gmt":"2023-08-03T11:26:47","guid":{"rendered":"https:\/\/statorials.org\/id\/uji-hipotesis-untuk-mean\/"},"modified":"2023-08-03T11:26:47","modified_gmt":"2023-08-03T11:26:47","slug":"uji-hipotesis-untuk-mean","status":"publish","type":"post","link":"https:\/\/statorials.org\/id\/uji-hipotesis-untuk-mean\/","title":{"rendered":"Pengujian hipotesis untuk mean"},"content":{"rendered":"<p>Artikel ini menjelaskan apa yang dimaksud dengan pengujian hipotesis untuk mean dalam statistik. Dengan demikian, Anda akan menemukan rumus uji hipotesis untuk rata-rata dan, sebagai tambahan, latihan yang diselesaikan langkah demi langkah. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-prueba-de-hipotesis-para-la-media\"><\/span> Apa yang dimaksud dengan pengujian hipotesis?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Pengujian hipotesis mean<\/strong> merupakan metode statistik yang digunakan untuk menolak atau menolak hipotesis nol suatu mean populasi.<\/p>\n<p> Lebih khusus lagi, pengujian hipotesis untuk mean melibatkan penghitungan statistik uji dan membandingkannya dengan nilai kritis untuk menolak hipotesis nol atau tidak.<\/p>\n<p> Perlu dicatat bahwa uji hipotesis memiliki nama yang berbeda; dalam statistik, mereka juga disebut kontras hipotesis, uji hipotesis, atau uji signifikansi. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-prueba-de-hipotesis-para-la-media\"><\/span> Rumus Pengujian Hipotesis Mean<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Selanjutnya kita akan melihat bagaimana statistik uji hipotesis untuk mean dihitung. Namun, rumusnya sedikit berbeda tergantung apakah variansnya diketahui atau tidak, jadi pertama-tama kita akan melihat cara melakukannya ketika varians diketahui dan kemudian ketika varians tidak diketahui.<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"con-varianza-conocida\"><\/span> Dengan penyimpangan yang diketahui<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>Rumus pengujian hipotesis untuk mean dengan varians yang diketahui<\/strong> adalah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-fdf1817a07bfb8c1eda9a8d8ccd8c828_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Z=\\frac{\\overline{x}-\\mu}{\\displaystyle \\frac{\\sigma}{\\sqrt{n}}} \" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"81\" style=\"vertical-align: -34px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Emas:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0be116875001706f29a24434bd0d91c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah statistik uji hipotesis untuk mean.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a39858a792fb4fe9a3173e004701f2a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah sarana sampel.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-05d9eae892416bd34247a25207f8b718_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"11\" style=\"vertical-align: -4px;\"><\/p>\n<p> adalah nilai rata-rata yang diusulkan.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-eaaf379fee5e67946f3fedf5631047b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah simpangan baku populasi.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ec4217f4fa5fcd92a9edceba0e708cf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah ukuran sampel.<\/li>\n<\/ul>\n<p> Setelah statistik uji hipotesis untuk mean dihitung, hasilnya harus diinterpretasikan untuk menolak atau menolak hipotesis nol:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Jika uji hipotesis mean adalah dua sisi, hipotesis nol ditolak jika nilai absolut statistik lebih besar dari nilai kritis Z <sub>\u03b1\/2<\/sub> .<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Jika uji hipotesis untuk mean cocok dengan ekor kanan, hipotesis nol ditolak jika statistik lebih besar dari nilai kritis Z <sub>\u03b1<\/sub> .<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Jika uji hipotesis untuk mean cocok dengan ekor kiri, hipotesis nol ditolak jika statistiknya kurang dari nilai kritis -Z <sub>\u03b1<\/sub> .<\/span><\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0e2ccadfc369eb7543b8f86dfccc528e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}H_1: \\mu\\neq \\mu_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } |Z|>Z_{\\alpha\/2} \\text{ se rechaza } H_0\\\\[3ex]H_1: \\mu> \\mu_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } Z>Z_{\\alpha} \\text{ se rechaza } H_0\\\\[3ex]H_1: \\mu< \\mu_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } Z<-Z_{\\alpha} \\text{ se rechaza } H_0\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"440\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Dalam hal ini, nilai kritis diperoleh dari <a href=\"https:\/\/statorials.org\/id\/tabel-distribusi-normal\/\">tabel distribusi normal terstandar<\/a> .<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"con-varianza-desconocida\"><\/span> Dengan varian yang tidak diketahui<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>Rumus pengujian hipotesis untuk mean yang variansinya tidak diketahui<\/strong> adalah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f8277d83b2d28325f25f5d118486200f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle t=\\frac{\\overline{x}-\\mu}{\\displaystyle \\frac{s}{\\sqrt{n}}} \" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"75\" style=\"vertical-align: -34px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Emas:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-fd9cb27edab3f0a8a249bc80cc9c6ee2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah statistik pengujian hipotesis untuk mean, yang ditentukan oleh <a href=\"https:\/\/statorials.org\/id\/distribusi-siswa\/\">distribusi t Student<\/a> .<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a39858a792fb4fe9a3173e004701f2a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah sarana sampel.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-05d9eae892416bd34247a25207f8b718_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"11\" style=\"vertical-align: -4px;\"><\/p>\n<p> adalah nilai rata-rata yang diusulkan.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-1edc883862ceed1a21913f60358e31d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah deviasi standar sampel.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ec4217f4fa5fcd92a9edceba0e708cf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah ukuran sampel.<\/li>\n<\/ul>\n<p> Seperti sebelumnya, hasil perhitungan statistik uji harus diinterpretasikan dengan nilai kritis untuk menolak atau tidak hipotesis nol:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Jika uji hipotesis mean adalah dua sisi, hipotesis nol ditolak jika nilai absolut statistik lebih besar dari nilai kritis t <sub>\u03b1\/2|n-1<\/sub> .<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Jika uji hipotesis untuk mean cocok dengan ekor kanan, hipotesis nol ditolak jika statistik lebih besar dari nilai kritis t <sub>\u03b1|n-1<\/sub> .<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Jika uji hipotesis untuk mean cocok dengan ekor kiri, hipotesis nol ditolak jika statistiknya kurang dari nilai kritis -t <sub>\u03b1|n-1<\/sub> .<\/span><\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-31fb206b75a47181c7c673f54ba28ee8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}H_1: \\mu\\neq \\mu_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } |t|>t_{\\alpha\/2|n-1} \\text{ se rechaza } H_0\\\\[3ex]H_1: \\mu> \\mu_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } t>t_{\\alpha|n-1} \\text{ se rechaza } H_0\\\\[3ex]H_1: \\mu< \\mu_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } t<-t_{\\alpha|n-1} \\text{ se rechaza } H_0\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"112\" width=\"457\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Apabila variansinya tidak diketahui maka nilai uji kritis diperoleh dari tabel distribusi Student. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-resuelto-de-la-prueba-de-hipotesis-para-la-media\"><\/span> Contoh Pengujian Hipotesis Mean di Dunia Nyata<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Untuk memahami sepenuhnya konsep pengujian hipotesis untuk mean populasi, Anda dapat melihat contoh nyata dari jenis pengujian hipotesis ini di bawah.<\/p>\n<ul>\n<li> Sebuah perusahaan teknologi mengklaim baterai laptop yang dijualnya mampu bertahan hingga 6 jam. Kita memeriksa apakah hipotesis ini salah dengan melakukan uji hipotesis dengan tingkat signifikansi \u03b1 = 0,05. Untuk melakukan ini, diputuskan untuk membeli 20 unit dan mengamati masa pakai baterai setiap komputer (nilai dinyatakan dalam jam):<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"> 5.2 5.9 7.1 4.2 6.5<br \/> 8,5 4,6 6,8 6,9 5,8<br \/> 5.1 6.5 7.0 5.3 6.2<br \/> 5.7 6.6 7.5 5.1 6.1<\/p>\n<p> Dalam hal ini, hipotesis <a href=\"https:\/\/statorials.org\/id\/hipotesis-nol-dan-alternatif\/\">nol dan hipotesis alternatif<\/a> dari uji hipotesis tentang mean adalah sebagai berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-329ffe392783b8bee1eef642d1a45f53_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases}H_0: \\mu=6\\\\[2ex] H_1:\\mu\\neq 6 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"93\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Untuk menentukan statistik uji, pertama-tama kita perlu menghitung mean sampel dan deviasi standar sampel:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ef07dbee8f95fc767bc069bd738bb493_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x}=6,13 \\qquad s=1,05\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"169\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Karena varians populasi tidak diketahui, untuk mendapatkan statistik uji kita perlu menerapkan rumus pengujian hipotesis untuk mean dengan varians yang tidak diketahui: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f8277d83b2d28325f25f5d118486200f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle t=\\frac{\\overline{x}-\\mu}{\\displaystyle \\frac{s}{\\sqrt{n}}} \" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"75\" style=\"vertical-align: -34px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-447879c9f526afed74796d347fd69c97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle t=\\frac{6,13-6}{\\displaystyle \\frac{1,05}{\\sqrt{20}}} \" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"98\" style=\"vertical-align: -38px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-e0e63621349c12eec107c43152b5213c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle t=0,68\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"65\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Sekarang kita perlu mencari nilai kritis uji hipotesis, jadi kita lihat <a href=\"https:\/\/statorials.org\/id\/tabel-distribusi-t-siswa\/\">tabel distribusi t Student<\/a> untuk nilai yang sesuai. Derajat kebebasan t Student kurang satu dari ukuran sampel (20-1=19) dan, sebaliknya, probabilitas yang bersesuaian adalah setengah tingkat signifikansi (0,05\/2= 0,025) karena ini adalah dua sisi pengujian hipotesis.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-8154fa6e5bfee35698c6dc26928cd98c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha=0,05 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black}\\ \\alpha\/2=0,025\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"300\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-e85692dfb2fb2522025566dc205b8117_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}t_{\\alpha\/2| n-1}= \\ \\color{orange}\\bm{?}\\\\[4ex]t_{0,025| 19}=2,093\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"72\" width=\"152\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Kesimpulannya, karena ini adalah uji hipotesis dua sisi dan nilai absolut statistik uji lebih kecil dari nilai kritis, maka hipotesis nol tidak ditolak, namun hipotesis alternatif ditolak. <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0e46ceecc8ebcda6dd88ec4d3771c285_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"0,68<2,093 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Se rechaza } H_1\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"345\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prueba-de-hipotesis-para-la-diferencia-de-medias\"><\/span> Pengujian hipotesis untuk perbedaan rata-rata<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Uji hipotesis perbedaan mean<\/strong> digunakan untuk menolak atau menerima hipotesis nol yang menyatakan mean dua populasi adalah sama.<\/p>\n<p> Jadi hipotesis nol dari uji hipotesis untuk selisih dua mean selalu sebagai berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-2945a64bf97e1c02ac7fb56bbf1f215b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"H_0: \\mu_1=\\mu_2\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"97\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Sedangkan hipotesis alternatifnya dapat berupa salah satu dari tiga hal berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c612ac7651faad9faa195f37fdf6edef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}H_1:\\mu_1\\neq \\mu_2\\\\[2ex]H_1:\\mu_1>\\mu_2\\\\[2ex]H_1:\\mu_1<\\mu_2\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"92\" width=\"97\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Maka <strong>rumus untuk menghitung statistik uji hipotesis selisih mean ketika varians diketahui<\/strong> adalah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-83c9d3ddf8c2ff8b9cf2b0fa4ac8082e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Z=\\frac{\\displaystyle \\overline{x_1}-\\overline{x_2}}{\\displaystyle\\sqrt{\\frac{\\sigma_1^2}{n_1}+\\frac{\\sigma_2^2}{n_2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"75\" width=\"123\" style=\"vertical-align: -52px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Emas:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0be116875001706f29a24434bd0d91c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah statistik pengujian hipotesis untuk perbedaan dua mean dengan varians yang diketahui, yang mengikuti distribusi normal standar.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-1436bb55d331d1efe559fd1e55245851_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x_1}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"18\" style=\"vertical-align: -3px;\"><\/p>\n<p> adalah rata-rata sampel 1.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f06b28a75570ecb4df1371dea2d9f2b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x_2}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"18\" style=\"vertical-align: -3px;\"><\/p>\n<p> adalah rata-rata sampel 2.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c2e8ce841b1fc1e199b133e6f24f6f51_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma_1^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"18\" style=\"vertical-align: -5px;\"><\/p>\n<p> adalah varian populasi 1.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d5fd430c9ff19057933c215e683ace41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma_2^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"18\" style=\"vertical-align: -5px;\"><\/p>\n<p> adalah varians populasi 2.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-cebc0a013985f2695aeb53ded9e7afb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_1\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"><\/p>\n<p> adalah ukuran sampel 1.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-bf1e42c248eee22a0911c24c95fe28f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_2\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"18\" style=\"vertical-align: -3px;\"><\/p>\n<p> adalah ukuran sampel 2.<\/li>\n<\/ul>\n<p> Sedangkan <strong>rumus menghitung statistik uji hipotesis selisih mean ketika varians tidak diketahui<\/strong> adalah sebagai berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-e9fbc7bf6d5bbaeb18a3992a3f373a55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle t=\\frac{\\displaystyle \\overline{x_1}-\\overline{x_2}}{\\displaystyle\\sqrt{\\frac{(n_1-1)s_1^2+(n_2-1)s_2^2}{n_1+n_2-2}}\\sqrt{\\frac{1}{n_1}+\\frac{1}{n_2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"75\" width=\"317\" style=\"vertical-align: -52px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Emas:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-fd9cb27edab3f0a8a249bc80cc9c6ee2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah statistik pengujian hipotesis untuk selisih dua mean yang variansnya tidak diketahui, yang mengikuti distribusi t Student.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-1436bb55d331d1efe559fd1e55245851_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x_1}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"18\" style=\"vertical-align: -3px;\"><\/p>\n<p> adalah rata-rata sampel 1.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f06b28a75570ecb4df1371dea2d9f2b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x_2}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"18\" style=\"vertical-align: -3px;\"><\/p>\n<p> adalah rata-rata sampel 2.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-59ae3c411ec80f65d56e397f87d29753_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s_1^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"15\" style=\"vertical-align: -5px;\"><\/p>\n<p> adalah varians sampel 1.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c785df8c080b6984c6205f881426fb10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s_2^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"15\" style=\"vertical-align: -5px;\"><\/p>\n<p> adalah varians sampel 2.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-cebc0a013985f2695aeb53ded9e7afb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_1\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"><\/p>\n<p> adalah ukuran sampel 1.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-bf1e42c248eee22a0911c24c95fe28f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_2\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"18\" style=\"vertical-align: -3px;\"><\/p>\n<p> adalah ukuran sampel 2.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Artikel ini menjelaskan apa yang dimaksud dengan pengujian hipotesis untuk mean dalam statistik. Dengan demikian, Anda akan menemukan rumus uji hipotesis untuk rata-rata dan, sebagai tambahan, latihan yang diselesaikan langkah demi langkah. Apa yang dimaksud dengan pengujian hipotesis? Pengujian hipotesis mean merupakan metode statistik yang digunakan untuk menolak atau menolak hipotesis nol suatu mean populasi. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[14],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Pengujian hipotesis untuk mean<\/title>\n<meta name=\"description\" content=\"Di sini Anda akan menemukan apa itu uji hipotesis mean, rumusnya dan contoh nyata uji hipotesis mean.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/id\/uji-hipotesis-untuk-mean\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Pengujian hipotesis untuk mean\" \/>\n<meta property=\"og:description\" content=\"Di sini Anda akan menemukan apa itu uji hipotesis mean, rumusnya dan contoh nyata uji hipotesis mean.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/id\/uji-hipotesis-untuk-mean\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-03T11:26:47+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-fdf1817a07bfb8c1eda9a8d8ccd8c828_l3.png\" \/>\n<meta name=\"author\" content=\"Benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Ditulis oleh\" \/>\n\t<meta name=\"twitter:data1\" content=\"Benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimasi waktu membaca\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/id\/uji-hipotesis-untuk-mean\/\",\"url\":\"https:\/\/statorials.org\/id\/uji-hipotesis-untuk-mean\/\",\"name\":\"\u25b7 Pengujian hipotesis untuk mean\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/id\/#website\"},\"datePublished\":\"2023-08-03T11:26:47+00:00\",\"dateModified\":\"2023-08-03T11:26:47+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/3d17a1160dd2d052b7c78e502cb9ec81\"},\"description\":\"Di sini Anda akan menemukan apa itu uji hipotesis mean, rumusnya dan contoh nyata uji hipotesis mean.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/id\/uji-hipotesis-untuk-mean\/#breadcrumb\"},\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/id\/uji-hipotesis-untuk-mean\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/id\/uji-hipotesis-untuk-mean\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/statorials.org\/id\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Pengujian hipotesis untuk mean\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/id\/#website\",\"url\":\"https:\/\/statorials.org\/id\/\",\"name\":\"Statorials\",\"description\":\"Panduan anda untuk kompetensi statistik!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/id\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"id\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/3d17a1160dd2d052b7c78e502cb9ec81\",\"name\":\"Benjamin anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"id\",\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/image\/\",\"url\":\"http:\/\/statorials.org\/id\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"http:\/\/statorials.org\/id\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Benjamin anderson\"},\"description\":\"Halo, saya Benjamin, pensiunan profesor statistika yang menjadi guru Statorial yang berdedikasi. 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