{"id":279,"date":"2023-08-03T05:14:26","date_gmt":"2023-08-03T05:14:26","guid":{"rendered":"https:\/\/statorials.org\/tr\/ornekleme-orani-dagilimi\/"},"modified":"2023-08-03T05:14:26","modified_gmt":"2023-08-03T05:14:26","slug":"ornekleme-orani-dagilimi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/ornekleme-orani-dagilimi\/","title":{"rendered":"Oran\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131"},"content":{"rendered":"<p>Bu makalede istatistikte orant\u0131 \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n ne oldu\u011fu a\u00e7\u0131klanmaktad\u0131r. Benzer \u015fekilde, orant\u0131 \u00f6rnekleme da\u011f\u0131t\u0131m form\u00fcl\u00fcn\u00fc ve ayr\u0131ca ad\u0131m ad\u0131m \u00e7\u00f6z\u00fclm\u00fc\u015f bir al\u0131\u015ft\u0131rmay\u0131 bulacaks\u0131n\u0131z. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-muestral-de-la-proporcion\"><\/span> Oran\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131 nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Oran\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131<\/strong> (veya <strong>oranlar\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131<\/strong> ), bir pop\u00fclasyondaki olas\u0131 her \u00f6rne\u011fin oran\u0131n\u0131n hesaplanmas\u0131ndan kaynaklanan da\u011f\u0131l\u0131md\u0131r. Yani, bir evrendeki olas\u0131 t\u00fcm \u00f6rneklerin <a href=\"https:\/\/statorials.org\/tr\/numunenin-orani\/\">\u00f6rnekleme oranlar\u0131,<\/a> oran\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131 olu\u015fturur.<\/p>\n<p> Ba\u015fka bir deyi\u015fle orant\u0131sal \u00f6rnekleme da\u011f\u0131l\u0131m\u0131, bir evrenden se\u00e7ilebilecek t\u00fcm \u00f6rneklerin incelenmesi ve her \u00f6rne\u011fin \u00f6rnekleme oran\u0131n\u0131n t\u00fcretilmesiyle elde edilir. B\u00f6ylece hesaplanan \u00f6rneklem oranlar\u0131 k\u00fcmesi, oran\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131 olu\u015fturur.<\/p>\n<p> Oran\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n ne i\u015fe yarad\u0131\u011f\u0131n\u0131 merak ediyorsan\u0131z istatistiklerde, tek bir \u00f6rnek analiz edilirken n\u00fcfus oran\u0131n\u0131n de\u011ferine yakla\u015fma olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in kullan\u0131l\u0131r. <\/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\/ortalamanin-ornekleme-dagilimi\/\">Ortalaman\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-distribucion-muestral-de-la-proporcion\"><\/span> Orant\u0131l\u0131 \u00d6rnekleme Da\u011f\u0131t\u0131m Form\u00fcl\u00fc<span class=\"ez-toc-section-end\"><\/span><\/h2>\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 <a href=\"https:\/\/statorials.org\/tr\/binom-dagilimi-1\/\">binom olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131<\/a> 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<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\/normal-dagilim\/\">Normal da\u011f\u0131l\u0131m \u00f6rnekleri<\/a><\/div>\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<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-resuelto-de-la-distribucion-muestral-de-la-proporcion\"><\/span> Orant\u0131l\u0131 \u00d6rnekleme Da\u011f\u0131t\u0131m\u0131n\u0131n Somut \u00d6rne\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Oranl\u0131 \u00d6rnekleme Da\u011f\u0131t\u0131m\u0131n\u0131n tan\u0131m\u0131n\u0131 ve ilgili form\u00fcllerinin neler oldu\u011funu g\u00f6rd\u00fckten sonra, kavram\u0131 tam olarak anlamak i\u00e7in a\u015fa\u011f\u0131da ad\u0131m ad\u0131m \u00e7\u00f6z\u00fcml\u00fc bir \u00f6rnek verilmi\u015ftir.<\/p>\n<ul>\n<li> Bir sanayi \u015firketi, par\u00e7alar\u0131 yaln\u0131zca %3 hatal\u0131 par\u00e7ayla \u00fcretti\u011fini iddia eden bir fabrikadan partiler halinde par\u00e7a sat\u0131n al\u0131yor. Bunu kontrol etmek i\u00e7in \u015firket 500 par\u00e7al\u0131k bir sipari\u015fi analiz etmeye karar verir. Numunede %5&#8217;ten fazla kusurlu par\u00e7a bulma olas\u0131l\u0131\u011f\u0131 nedir?<\/li>\n<\/ul>\n<p> Bu durumda, incelemek istedi\u011fimiz pop\u00fclasyonun oran\u0131 0,03&#8217;t\u00fcr, dolay\u0131s\u0131yla q parametresi 0,97&#8217;ye e\u015fde\u011ferdir.<\/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-f4354c268853ec7b592bcacd23f3b214_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}p=0,03\\\\[2ex]q=1-p=0,97\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"130\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Dolay\u0131s\u0131yla bize sorduklar\u0131 olas\u0131l\u0131\u011f\u0131 bulmak i\u00e7in, \u00f6nceki b\u00f6l\u00fcmde g\u00f6rd\u00fc\u011f\u00fcm\u00fcz form\u00fcl\u00fc uygulayarak ilgili istatisti\u011fi hesaplamal\u0131y\u0131z:<\/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-647d67d275bb8a7fbeb60f7ae464c0fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z=\\cfrac{\\widehat{p}-p}{\\displaystyle\\sqrt{\\frac{pq}{n}}}=\\cfrac{0,05-0,03}{\\displaystyle\\sqrt{\\frac{0,03\\cdot 0,97}{500}}}=2,62\" title=\"Rendered by QuickLaTeX.com\" height=\"69\" width=\"264\" style=\"vertical-align: -41px;\"><\/p>\n<\/p>\n<p> Dolay\u0131s\u0131yla %5&#8217;ten fazla hatal\u0131 par\u00e7a elde etme olas\u0131l\u0131\u011f\u0131 a\u015fa\u011f\u0131daki olas\u0131l\u0131\u011fa e\u015fde\u011ferdir:<\/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-a5e5cff61f2cc97762df561b3e35a7ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P\\left[\\widehat{p}>0,05\\right]=P[Z>2,62]=1-P[Z\\leq 2,62]&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;19&#8243; width=&#8221;360&#8243; style=&#8221;vertical-align: -5px;&#8221;><\/p>\n<\/p>\n<p> Son olarak <a href=\"https:\/\/statorials.org\/tr\/normal-dagilim-tablosu\/\">Z da\u011f\u0131l\u0131m tablosunda<\/a> P[Z\u22642.62] olas\u0131l\u0131\u011f\u0131n\u0131 ar\u0131yoruz ve problemin bize sorma olas\u0131l\u0131\u011f\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-812f9b97c53e15da88b0cb7149f254c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}P\\left[\\widehat{p}>0,05\\right]=\\\\[2ex]=P[Z>2,62]=\\\\[2ex]=1-P[Z\\leq 2,62]=\\\\[2ex]=1-0,9956=\\\\[2ex]=0,0044\\end{array}&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;167&#8243; width=&#8221;162&#8243; style=&#8221;vertical-align: 0px;&#8221;><\/p>\n<\/p>\n<p> Sonu\u00e7 olarak, analiz edilen numunede %5&#8217;ten fazla hatal\u0131 par\u00e7a bulunma olas\u0131l\u0131\u011f\u0131 %0,44&#8217;t\u00fcr.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bu makalede istatistikte orant\u0131 \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n ne oldu\u011fu a\u00e7\u0131klanmaktad\u0131r. Benzer \u015fekilde, orant\u0131 \u00f6rnekleme da\u011f\u0131t\u0131m form\u00fcl\u00fcn\u00fc ve ayr\u0131ca ad\u0131m ad\u0131m \u00e7\u00f6z\u00fclm\u00fc\u015f bir al\u0131\u015ft\u0131rmay\u0131 bulacaks\u0131n\u0131z. Oran\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131 nedir? Oran\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131 (veya oranlar\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131 ), bir pop\u00fclasyondaki olas\u0131 her \u00f6rne\u011fin oran\u0131n\u0131n hesaplanmas\u0131ndan kaynaklanan da\u011f\u0131l\u0131md\u0131r. Yani, bir evrendeki olas\u0131 t\u00fcm \u00f6rneklerin \u00f6rnekleme oranlar\u0131, oran\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131 [&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-279","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>\u25b7 Oranl\u0131 \u00f6rnekleme da\u011f\u0131l\u0131m\u0131<\/title>\n<meta name=\"description\" content=\"Burada orant\u0131 \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n ne oldu\u011funu, form\u00fcl\u00fcn\u00fc ve orant\u0131 \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n somut bir \u00f6rne\u011fini bulacaks\u0131n\u0131z.\" \/>\n<meta name=\"robots\" content=\"index, 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