{"id":288,"date":"2023-08-03T02:21:11","date_gmt":"2023-08-03T02:21:11","guid":{"rendered":"https:\/\/statorials.org\/tr\/ornekleme-dagilimi-1\/"},"modified":"2023-08-03T02:21:11","modified_gmt":"2023-08-03T02:21:11","slug":"ornekleme-dagilimi-1","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/ornekleme-dagilimi-1\/","title":{"rendered":"\u00d6rnekleme da\u011f\u0131l\u0131m\u0131"},"content":{"rendered":"<p>Bu makalede istatistikte \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n ne oldu\u011fu ve ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. B\u00f6ylece \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n anlam\u0131n\u0131, \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n somut bir \u00f6rne\u011fini ve ayr\u0131ca en yayg\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131 t\u00fcrlerine ili\u015fkin form\u00fclleri bulacaks\u0131n\u0131z. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-muestral\"><\/span> \u00d6rnekleme da\u011f\u0131l\u0131m\u0131 nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u00d6rnekleme da\u011f\u0131l\u0131m\u0131<\/strong> veya <strong>\u00f6rnekleme da\u011f\u0131l\u0131m\u0131<\/strong> , bir pop\u00fclasyondaki olas\u0131 t\u00fcm \u00f6rneklerin dikkate al\u0131nmas\u0131ndan kaynaklanan da\u011f\u0131l\u0131md\u0131r. Ba\u015fka bir deyi\u015fle \u00f6rnekleme da\u011f\u0131l\u0131m\u0131, bir evrenden al\u0131nabilecek t\u00fcm \u00f6rneklerin \u00f6rnekleme parametresinin hesaplanmas\u0131yla elde edilen da\u011f\u0131l\u0131md\u0131r.<\/p>\n<p> \u00d6rne\u011fin, istatistiksel bir pop\u00fclasyondan olas\u0131 t\u00fcm \u00f6rnekleri \u00e7\u0131kar\u0131rsak ve her \u00f6rne\u011fin ortalamas\u0131n\u0131 hesaplarsak, \u00f6rnek ortalamalar\u0131 k\u00fcmesi bir \u00f6rnekleme da\u011f\u0131l\u0131m\u0131 olu\u015fturur. Daha do\u011frusu hesaplanan parametre aritmetik ortalama oldu\u011fundan ortalaman\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131d\u0131r.<\/p>\n<p> \u0130statistikte \u00f6rnekleme da\u011f\u0131l\u0131m\u0131, tek bir \u00f6rnek \u00fczerinde \u00e7al\u0131\u015f\u0131l\u0131rken ana k\u00fctle parametresinin de\u011ferine yakla\u015fma olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in kullan\u0131l\u0131r. Benzer \u015fekilde \u00f6rnekleme da\u011f\u0131l\u0131m\u0131, belirli bir \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc i\u00e7in \u00f6rnekleme hatas\u0131n\u0131 tahmin etmemizi sa\u011flar. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-la-distribucion-muestral\"><\/span> \u00d6rnekleme Da\u011f\u0131t\u0131m\u0131 \u00d6rne\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Art\u0131k \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n tan\u0131m\u0131n\u0131 bildi\u011fimize g\u00f6re, kavram\u0131 tam olarak anlamak i\u00e7in basit bir \u00f6rne\u011fe bakal\u0131m.<\/p>\n<ul>\n<li> Bir kutuya \u00fc\u00e7 top koyuyoruz ve her birinde birden \u00fc\u00e7e kadar yaz\u0131lm\u0131\u015f bir say\u0131 var, b\u00f6ylece bir topun numaras\u0131 1, di\u011fer topun numaras\u0131 2 ve son topun numaras\u0131 da 3 numarad\u0131r. n boyutunda bir \u00f6rnek i\u00e7in = 2, de\u011fi\u015ftirilen \u00f6rneklerin se\u00e7ilmesi durumunda ortalaman\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n olas\u0131l\u0131klar\u0131n\u0131 hesaplar.<\/li>\n<\/ul>\n<p> Numuneler de\u011fi\u015ftirilerek se\u00e7ilir, yani numunenin ilk eleman\u0131n\u0131 se\u00e7mek i\u00e7in al\u0131nan top kutuya geri g\u00f6nderilir ve ikinci ekstraksiyon s\u0131ras\u0131nda tekrar se\u00e7ilebilir. Bu nedenle pop\u00fclasyondan al\u0131nabilecek t\u00fcm \u00f6rnekler \u015funlard\u0131r:<\/p>\n<p class=\"has-text-align-center\"> 1,1 1,2 1,3<br \/> 2,1 2,2 2,3<br \/> 3,1 3,2 3,3<\/p>\n<p> B\u00f6ylece olas\u0131 her \u00f6rne\u011fin aritmetik ortalamas\u0131n\u0131 hesapl\u0131yoruz: <\/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-36b3a1e0bbb1be6eddc1a5d9899c5643_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(1,1) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\overline{x}_{11}=\\cfrac{1+1}{2}=1\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"295\" style=\"vertical-align: -12px;\"><\/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-ff446066e6102f75d2d5435ad9dc46d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(1,2) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\overline{x}_{12}=\\cfrac{1+2}{2}=1,5\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"311\" style=\"vertical-align: -12px;\"><\/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-904c1ee161fd7214c2c20ef15a038ea2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(1,3) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\overline{x}_{13}=\\cfrac{1+3}{2}=2\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"295\" style=\"vertical-align: -12px;\"><\/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-4669b3b3d3ca07f035456cc50110134f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(2,1) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\overline{x}_{21}=\\cfrac{2+1}{2}=1,5\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"311\" style=\"vertical-align: -12px;\"><\/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-9fae1b39671fce31802b9ff66c8c1b9e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(2,2) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\overline{x}_{22}=\\cfrac{2+2}{2}=2\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"295\" style=\"vertical-align: -12px;\"><\/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-fb036db8580a0d7389daddf6a938c541_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(2,3) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\overline{x}_{23}=\\cfrac{2+3}{2}=2,5\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"311\" style=\"vertical-align: -12px;\"><\/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-7b77da5430a43732726cc62fb0fffe78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(3,1) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\overline{x}_{31}=\\cfrac{3+1}{2}=2\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"295\" style=\"vertical-align: -12px;\"><\/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-5edbfa4f2b8752676ceba5ad0cd34d6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(3,2) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\overline{x}_{32}=\\cfrac{3+2}{2}=2,5\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"311\" style=\"vertical-align: -12px;\"><\/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-bb60dfff5e3c5c090e019253ee84b198_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(3,3) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\overline{x}_{33}=\\cfrac{3+3}{2}=3\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"296\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Bu nedenle pop\u00fclasyondan rastgele bir \u00f6rnek se\u00e7ildi\u011finde \u00f6rnek ortalamas\u0131n\u0131n her bir de\u011ferinin elde edilme olas\u0131l\u0131klar\u0131 a\u015fa\u011f\u0131daki gibidir: <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/table-de-distribution-dechantillonnage.png\" alt=\"\u00f6rnek da\u011f\u0131t\u0131m tablosu \u00f6rne\u011fi\" class=\"wp-image-6145\" width=\"166\" height=\"195\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Yukar\u0131daki tabloda g\u00f6sterilen \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n olas\u0131l\u0131klar\u0131, s\u00f6z konusu ortalama de\u011fere sahip \u00f6rnek say\u0131s\u0131n\u0131n toplam olas\u0131 durum say\u0131s\u0131na b\u00f6l\u00fcnmesiyle hesaplanm\u0131\u015ft\u0131r. \u00d6rne\u011fin: m\u00fcmk\u00fcn olan dokuz durumdan ikisinde \u00f6rneklem ortalamas\u0131 1,5&#8217;tir, dolay\u0131s\u0131yla P(1,5)=2\/9. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"tipos-de-distribuciones-muestrales\"><\/span> \u00d6rnekleme da\u011f\u0131l\u0131m t\u00fcrleri<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u00d6rnekleme da\u011f\u0131l\u0131mlar\u0131 (veya \u00f6rnekleme da\u011f\u0131l\u0131mlar\u0131), elde edildikleri \u00f6rnekleme parametresine g\u00f6re s\u0131n\u0131fland\u0131r\u0131labilir. Dolay\u0131s\u0131yla, en yayg\u0131n da\u011f\u0131t\u0131m t\u00fcrleri a\u015fa\u011f\u0131daki gibidir:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:18px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Ortalaman\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131<\/strong> : Her \u00f6rne\u011fin aritmetik ortalamas\u0131n\u0131n hesaplanmas\u0131ndan kaynaklanan \u00f6rnekleme da\u011f\u0131l\u0131m\u0131d\u0131r.<\/span><\/li>\n<li style=\"margin-bottom:18px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Oranl\u0131 \u00d6rnekleme Da\u011f\u0131l\u0131m\u0131<\/strong> : T\u00fcm \u00f6rneklerin oranlar\u0131 hesaplanarak elde edilen \u00f6rnekleme da\u011f\u0131l\u0131m\u0131d\u0131r.<\/span><\/li>\n<li style=\"margin-bottom:18px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Varyans \u00f6rnekleme da\u011f\u0131l\u0131m\u0131<\/strong> : \u00d6rnekteki t\u00fcm varyanslar\u0131n k\u00fcmesini olu\u015fturan \u00f6rnekleme da\u011f\u0131l\u0131m\u0131d\u0131r.<\/span><\/li>\n<li style=\"margin-bottom:18px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Ortalama \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n fark\u0131<\/strong> : \u0130ki farkl\u0131 pop\u00fclasyondan m\u00fcmk\u00fcn olan t\u00fcm \u00f6rneklerin ortalamalar\u0131 aras\u0131ndaki fark\u0131n hesaplanmas\u0131ndan kaynaklanan \u00f6rnekleme da\u011f\u0131l\u0131m\u0131d\u0131r.<\/span><\/li>\n<li style=\"margin-bottom:18px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Oran Fark\u0131 \u00d6rnekleme Da\u011f\u0131l\u0131m\u0131<\/strong> : \u0130ki anak\u00fctleden olas\u0131 t\u00fcm \u00f6rnekleme oranlar\u0131n\u0131n \u00e7\u0131kar\u0131lmas\u0131yla elde edilen \u00f6rnekleme da\u011f\u0131l\u0131m\u0131d\u0131r.<\/span><\/li>\n<\/ul>\n<p> Her bir \u00f6rnekleme da\u011f\u0131l\u0131m\u0131 t\u00fcr\u00fc a\u015fa\u011f\u0131da daha ayr\u0131nt\u0131l\u0131 olarak a\u00e7\u0131klanmaktad\u0131r. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"distribucion-muestral-de-la-media\"><\/span> Ortalaman\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Ortalama ile normal bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131 takip eden bir pop\u00fclasyon g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda<\/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-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> ve standart sapma<\/p>\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> ve boyut \u00f6rnekleri \u00e7\u0131kar\u0131ld\u0131<\/p>\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> ortalaman\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131 a\u015fa\u011f\u0131daki \u00f6zelliklere sahip bir normal da\u011f\u0131l\u0131mla da tan\u0131mlanacakt\u0131r:<\/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-44571aa7337b095ab9c9fa1f746e93a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\mu_{\\overline{x}}=\\mu \\qquad \\sigma_{\\overline{x}}=\\cfrac{\\sigma}{\\sqrt{n}}\\\\[4ex]\\displaystyle N_{\\overline{x}}\\left(\\mu, \\frac{\\sigma}{\\sqrt{n}}\\right) \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"102\" width=\"159\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Alt\u0131n<\/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-8ed084decbdfb365889aae767cf63e81_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu_{\\overline{x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"20\" style=\"vertical-align: -4px;\"><\/p>\n<p> ortalaman\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n ortalamas\u0131d\u0131r ve<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-9067e28d896c7e5278763081c6cc40d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma_{\\overline{x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"19\" style=\"vertical-align: -3px;\"><\/p>\n<p> onun standart sapmas\u0131d\u0131r. \u00dcstelik,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7d78e2a2f2fae99a53eb087263cbb478_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{\\sigma}{\\sqrt{n}}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"26\" style=\"vertical-align: -16px;\"><\/p>\n<p> \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n standart hatas\u0131d\u0131r.<\/p>\n<p> <strong>Not:<\/strong> Pop\u00fclasyon normal bir da\u011f\u0131l\u0131m izlemiyorsa ancak \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc b\u00fcy\u00fckse (n&gt;30), ortalaman\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131, merkezi teorem limiti ile yukar\u0131daki normal da\u011f\u0131l\u0131ma da yakla\u015ft\u0131r\u0131labilir.<\/p>\n<p> Bu nedenle, ortalaman\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131 normal bir da\u011f\u0131l\u0131m izledi\u011finden, <strong>\u00f6rnek ortalamas\u0131na ili\u015fkin herhangi bir olas\u0131l\u0131\u011f\u0131 hesaplama form\u00fcl\u00fc<\/strong> \u015f\u00f6yledir:<\/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-ecd8bcb78b739c50d01b8bad563e5cb7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z=\\cfrac{\\overline{x}-\\mu}{\\displaystyle\\frac{\\sigma}{\\sqrt{n}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"81\" style=\"vertical-align: -34px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Alt\u0131n: <\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:5px\">\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> \u00f6rnek anlam\u0131na gelir.<\/li>\n<li style=\"margin-bottom:5px\">\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> Bu n\u00fcfus ortalamas\u0131d\u0131r.<\/li>\n<li style=\"margin-bottom:5px\">\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> n\u00fcfus standart sapmas\u0131d\u0131r.<\/li>\n<li style=\"margin-bottom:5px\">\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> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcd\u00fcr.<\/li>\n<li style=\"margin-bottom:5px\">\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> standart normal da\u011f\u0131l\u0131m N(0,1) taraf\u0131ndan tan\u0131mlanan bir de\u011fi\u015fkendir. <\/li>\n<\/ul>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Bak\u0131n\u0131z:<\/strong> <a href=\"https:\/\/statorials.org\/tr\/ortalamanin-ornekleme-dagilimi\/\">Ortalaman\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131na ili\u015fkin \u00e7\u00f6z\u00fclm\u00fc\u015f al\u0131\u015ft\u0131rma<\/a> <\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"distribucion-muestral-de-la-proporcion\"><\/span> Oran\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Asl\u0131nda bir \u00f6rneklemin belli bir k\u0131sm\u0131n\u0131 inceledi\u011fimizde ba\u015far\u0131 durumlar\u0131n\u0131 analiz etmi\u015f oluyoruz. Bu nedenle \u00e7al\u0131\u015fmadaki rastgele de\u011fi\u015fken binom olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131 izlemektedir.<\/p>\n<p> Merkezi limit teoremine g\u00f6re, b\u00fcy\u00fck boyutlar i\u00e7in (n&gt;30) binom da\u011f\u0131l\u0131m\u0131n\u0131 normal da\u011f\u0131l\u0131ma yakla\u015ft\u0131rabiliriz. Bu nedenle, <strong>oran\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131 a\u015fa\u011f\u0131daki parametrelerle normal da\u011f\u0131l\u0131ma yakla\u015fmaktad\u0131r:<\/strong><\/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-f3408076893f390bb65baecfe38e6eff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\displaystyle\\mu_{p}=p \\qquad \\sigma_{p}=\\sqrt{\\frac{pq}{n}}\\\\[4ex]\\displaystyle N_{p}\\left(p, \\sqrt{\\frac{pq}{n}}\\right) \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"109\" width=\"168\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Alt\u0131n<\/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-5faad0904f612a3fa5b27faafb8dc903_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p> ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 ve<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-420eca7b6df080cc5f01773d1978f44a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"q\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: -4px;\"><\/p>\n<p> ba\u015far\u0131s\u0131zl\u0131k olas\u0131l\u0131\u011f\u0131<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-e1d214c21abe0d79fa453d635a025865_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"q=1-p\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"72\" style=\"vertical-align: -4px;\"><\/p>\n<p> .<\/p>\n<p> <strong>Not:<\/strong> Bir binom da\u011f\u0131l\u0131m\u0131 ancak normal da\u011f\u0131l\u0131ma yakla\u015f\u0131k olarak \u015fu durumlarda verilebilir:<\/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-88e275a965c091eb810599a07b0f8d46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n>30&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;14&#8243; width=&#8221;52&#8243; style=&#8221;vertical-align: -2px;&#8221;><\/p>\n<p> ,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-41130f51ca4b83f1bf25b9dde90ecbfd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"np\\ge 5\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"51\" style=\"vertical-align: -4px;\"><\/p>\n<p> Ve<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0af2ac5b6eb874f65b406b3bc39f0c7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"nq\\ge 5\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"51\" style=\"vertical-align: -4px;\"><\/p>\n<p> .<\/p>\n<p> Bu nedenle, oran\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131 normal bir da\u011f\u0131l\u0131ma yak\u0131nla\u015ft\u0131r\u0131labildi\u011finden, <strong>bir numunenin oran\u0131na ili\u015fkin herhangi bir olas\u0131l\u0131\u011f\u0131n hesaplanmas\u0131na y\u00f6nelik form\u00fcl<\/strong> \u015fu \u015fekildedir:<\/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-5b7a4224240587268d0dd7865a33ac31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z=\\cfrac{\\widehat{p}-p}{\\displaystyle\\sqrt{\\frac{pq}{n}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"69\" width=\"78\" style=\"vertical-align: -41px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Alt\u0131n: <\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ecd29d136a62fc6b274e1181e064e20e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"12\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00f6rnek oran\u0131d\u0131r.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5faad0904f612a3fa5b27faafb8dc903_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p> n\u00fcfusa oran\u0131d\u0131r.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-420eca7b6df080cc5f01773d1978f44a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"q\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: -4px;\"><\/p>\n<p> pop\u00fclasyonun ba\u015far\u0131s\u0131z olma olas\u0131l\u0131\u011f\u0131d\u0131r,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-e1d214c21abe0d79fa453d635a025865_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"q=1-p\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"72\" style=\"vertical-align: -4px;\"><\/p>\n<p> .<\/li>\n<li style=\"margin-bottom:5px\">\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> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcd\u00fcr.<\/li>\n<li style=\"margin-bottom:5px\">\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> standart normal da\u011f\u0131l\u0131m N(0,1) taraf\u0131ndan tan\u0131mlanan bir de\u011fi\u015fkendir. <\/li>\n<\/ul>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Bak\u0131n\u0131z:<\/strong> <a href=\"https:\/\/statorials.org\/tr\/ornekleme-orani-dagilimi\/\">Oran\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131na ili\u015fkin \u00e7\u00f6z\u00fclm\u00fc\u015f al\u0131\u015ft\u0131rma<\/a> <\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"distribucion-muestral-de-la-varianza\"><\/span> Varyans\u0131n \u00d6rnekleme Da\u011f\u0131l\u0131m\u0131<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Varyans\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131 ki-kare olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131 ile tan\u0131mlan\u0131r. Bu nedenle, <strong>\u00f6rnekleme varyans da\u011f\u0131l\u0131m\u0131 istatisti\u011finin form\u00fcl\u00fc<\/strong> \u015f\u00f6yledir:<\/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-3917636d4c911eeaad1a005195204d08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\chi^2=\\cfrac{(n-1)s^2}{\\sigma^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"115\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Alt\u0131n:<\/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-984dc78529fc235b078a9f3b62d0f0c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\chi^2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"18\" style=\"vertical-align: -4px;\"><\/p>\n<p> ki-kare da\u011f\u0131l\u0131m\u0131n\u0131 takip eden varyans\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n istatisti\u011fidir.<\/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> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcd\u00fcr.<\/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-3ab572e85f9cb7cb6f495387f2a6ab0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00f6rnek varyans\u0131d\u0131r.<\/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-c6d52162ef1ec2e8130fb00687aca707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"18\" style=\"vertical-align: 0px;\"><\/p>\n<p> n\u00fcfus varyans\u0131d\u0131r. <\/li>\n<\/ul>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Bak\u0131n\u0131z:<\/strong> <a href=\"https:\/\/statorials.org\/tr\/ornekleme-varyans-dagilimi\/\">Varyans\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131na ili\u015fkin \u00e7\u00f6z\u00fclm\u00fc\u015f al\u0131\u015ft\u0131rma<\/a> <\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"distribucion-muestral-de-la-diferencia-de-medias\"><\/span> Ortalamalar fark\u0131n\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> \u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc yeterince b\u00fcy\u00fckse (n <sub>1<\/sub> \u226530 ve n <sub>2<\/sub> \u226530), ortalama fark\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131 normal bir da\u011f\u0131l\u0131m izler. Daha do\u011frusu s\u00f6z konusu da\u011f\u0131l\u0131m\u0131n parametreleri \u015fu \u015fekilde hesaplan\u0131r:<\/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-90c67b74b4e9326b7869d641a59725d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\displaystyle \\mu_{\\overline{x_1}-\\overline{x_2}}=\\mu_1-\\mu_2 \\qquad \\sigma_{\\overline{x_1}-\\overline{x_2}}=\\sqrt{\\frac{\\sigma_1^2}{n_1}+\\frac{\\sigma_2^2}{n_2}}\\\\[6ex]\\displaystyle N_{\\overline{x_1}-\\overline{x_2}}\\left(\\mu_1-\\mu_2, \\sqrt{\\frac{\\sigma_1^2}{n_1}+\\frac{\\sigma_2^2}{n_2}}\\right) \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"151\" width=\"328\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> <strong>Not:<\/strong> Her iki pop\u00fclasyon da normal da\u011f\u0131l\u0131ma sahipse, ortalamalardaki fark\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131, \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcnden ba\u011f\u0131ms\u0131z olarak normal bir da\u011f\u0131l\u0131m izler.<\/p>\n<p> Bu nedenle, ortalamalardaki fark\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131 normal bir da\u011f\u0131l\u0131mla tan\u0131mland\u0131\u011f\u0131ndan, <strong>ortalamalardaki fark\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n istatisti\u011fini hesaplamak i\u00e7in form\u00fcl<\/strong> \u015fu \u015fekildedir:<\/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-767964a3f07b303178ee08ec191eef43_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z=\\cfrac{(\\overline{x_1}-\\overline{x_2})-(\\mu_1-\\mu_2)}{\\displaystyle\\sqrt{\\frac{\\sigma_1^2}{n_1}+\\frac{\\sigma_2^2}{n_2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"80\" width=\"203\" style=\"vertical-align: -52px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Alt\u0131n: <\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a4071a38558726a684ed069430c89fe2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x_i}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00f6rnek i&#8217;nin ortalamas\u0131d\u0131r.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-78e04dacbf6a47efcbdcc0417020dcbb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu_i\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: -4px;\"><\/p>\n<p> n\u00fcfusun ortalamas\u0131d\u0131r i.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-dc8c8f782c0ed8b7925012b60e174fa3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"><\/p>\n<p> pop\u00fclasyonun standart sapmas\u0131 i&#8217;dir.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5f087375b50e0b49186779714206626b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc i&#8217;dir.<\/li>\n<li style=\"margin-bottom:5px\">\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> standart normal da\u011f\u0131l\u0131m N(0,1) taraf\u0131ndan tan\u0131mlanan bir de\u011fi\u015fkendir.<\/li>\n<\/ul>\n<p> Farkl\u0131 pop\u00fclasyonlardan al\u0131nan numunelerin farkl\u0131 numune boyutlar\u0131na sahip olabilece\u011fini unutmay\u0131n. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Bak\u0131n\u0131z:<\/strong> <a href=\"https:\/\/statorials.org\/tr\/ortalamalar-farkinin-ornekleme-dagilimi\/\">Ortalamalar fark\u0131n\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131na ili\u015fkin \u00e7\u00f6z\u00fclm\u00fc\u015f al\u0131\u015ft\u0131rma<\/a> <\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"distribucion-muestral-de-la-diferencia-de-proporciones\"><\/span> Oranlardaki fark\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Orant\u0131 \u00f6rnekleme da\u011f\u0131l\u0131m\u0131ndaki fark i\u00e7in se\u00e7ilen \u00f6rnekler binom da\u011f\u0131l\u0131mlar\u0131yla tan\u0131mlan\u0131r, \u00e7\u00fcnk\u00fc pratik ama\u00e7lar i\u00e7in oran, ba\u015far\u0131 durumlar\u0131n\u0131n toplam g\u00f6zlem say\u0131s\u0131na oran\u0131d\u0131r.<\/p>\n<p> Ancak merkezi limit teoremi nedeniyle binom da\u011f\u0131l\u0131mlar\u0131 normal olas\u0131l\u0131k da\u011f\u0131l\u0131mlar\u0131na yakla\u015ft\u0131r\u0131labilir. Bu nedenle oranlardaki fark\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131, a\u015fa\u011f\u0131daki \u00f6zelliklerle normal bir da\u011f\u0131l\u0131ma yakla\u015ft\u0131r\u0131labilir:<\/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-a1ce359b5dd6d80f8d27b0b9a1034bed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\displaystyle\\mu_{\\widehat{p_1}-\\widehat{p_2}}=p_1-p_2 \\qquad \\sigma_{\\widehat{p_1}-\\widehat{p_2}}=\\sqrt{\\frac{p_1q_1}{n_1}+\\frac{p_2q_2}{n_2}}\\\\[6ex]\\displaystyle N_{p}\\left(p_1-p_2, \\sqrt{\\frac{p_1q_1}{n_1}+\\frac{p_2q_2}{n_2}}\\right) \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"122\" width=\"348\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> <strong>Not:<\/strong> Oranlardaki fark\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131 ancak a\u015fa\u011f\u0131daki durumlarda normal da\u011f\u0131l\u0131ma yakla\u015fabilir:<\/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-6a7ebccb76a4ee9bbf44bb0f41ffee53_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_1\\geq30\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"60\" style=\"vertical-align: -3px;\"><\/p>\n<p> ,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-93c3febf2679c77d41d7b319e262f298_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_2\\geq 30\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"60\" style=\"vertical-align: -3px;\"><\/p>\n<p> ,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-19a35b2095afa5133c32d92de163adaf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_1p_1\\geq5\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"67\" style=\"vertical-align: -4px;\"><\/p>\n<p> ,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a89c44bd89266e2fba37bf5211a6e30e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_2p_2\\geq5\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"67\" style=\"vertical-align: -4px;\"><\/p>\n<p> ,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-08c0b04a830a0062f4e7f25801c45fa9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_1q_1\\geq5\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"66\" style=\"vertical-align: -4px;\"><\/p>\n<p> Ve<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-789e8bfde9b6a18c7ff9b1390feca142_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_2q_2\\geq5\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"66\" style=\"vertical-align: -4px;\"><\/p>\n<p> .<\/p>\n<p> Bu nedenle, oranlardaki fark\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131 normal bir da\u011f\u0131l\u0131ma yak\u0131nla\u015ft\u0131r\u0131labilece\u011finden, <strong>oranlardaki fark\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n istatisti\u011fini hesaplama form\u00fcl\u00fc<\/strong> a\u015fa\u011f\u0131daki gibidir:<\/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-a6b74dafd0599052a453e77646e5a77a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z=\\cfrac{(\\widehat{p_1}-\\widehat{p_2})-(p_1-p_2)}{\\displaystyle\\sqrt{\\frac{p_1q_1}{n_1}+\\frac{p_2q_2}{n_2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"69\" width=\"198\" style=\"vertical-align: -41px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Alt\u0131n: <\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ad10d8ae9a51401d94ca9742249d6d15_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p_i}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"15\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00f6rnek oran\u0131 i&#8217;dir.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a5db80b23c0dc6e4f21c509cb298856a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p_i\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"15\" style=\"vertical-align: -4px;\"><\/p>\n<p> i n\u00fcfus oran\u0131d\u0131r.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-4b2d0075b0f4fd8e4e14194b33ed0fe8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"q_i\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: -4px;\"><\/p>\n<p> i pop\u00fclasyonunun ba\u015far\u0131s\u0131zl\u0131k olas\u0131l\u0131\u011f\u0131d\u0131r,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-917f2422b9b0d7d99ec3de548cc6bba3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"q_i=1-p_i\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\"><\/p>\n<p> .<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5f087375b50e0b49186779714206626b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc i&#8217;dir.<\/li>\n<li style=\"margin-bottom:5px\">\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> standart normal da\u011f\u0131l\u0131m N(0,1) taraf\u0131ndan tan\u0131mlanan bir de\u011fi\u015fkendir. <\/li>\n<\/ul>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Bak\u0131n\u0131z:<\/strong> <a href=\"https:\/\/statorials.org\/tr\/oranlar-farkinin-ornekleme-dagilimi\/\">Oranlar fark\u0131n\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131na ili\u015fkin \u00e7\u00f6z\u00fclm\u00fc\u015f al\u0131\u015ft\u0131rma<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Bu makalede istatistikte \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n ne oldu\u011fu ve ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. B\u00f6ylece \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n anlam\u0131n\u0131, \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n somut bir \u00f6rne\u011fini ve ayr\u0131ca en yayg\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131 t\u00fcrlerine ili\u015fkin form\u00fclleri bulacaks\u0131n\u0131z. \u00d6rnekleme da\u011f\u0131l\u0131m\u0131 nedir? \u00d6rnekleme da\u011f\u0131l\u0131m\u0131 veya \u00f6rnekleme da\u011f\u0131l\u0131m\u0131 , bir pop\u00fclasyondaki olas\u0131 t\u00fcm \u00f6rneklerin dikkate al\u0131nmas\u0131ndan kaynaklanan da\u011f\u0131l\u0131md\u0131r. Ba\u015fka bir deyi\u015fle \u00f6rnekleme da\u011f\u0131l\u0131m\u0131, bir [&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":[],"class_list":["post-288","post","type-post","status-publish","format-standard","hentry","category-istatistik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u00d6rnekleme da\u011f\u0131l\u0131m\u0131 nedir? 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