{"id":248,"date":"2023-08-03T16:05:59","date_gmt":"2023-08-03T16:05:59","guid":{"rendered":"https:\/\/statorials.org\/tr\/oranti-icin-guven-araligi\/"},"modified":"2023-08-03T16:05:59","modified_gmt":"2023-08-03T16:05:59","slug":"oranti-icin-guven-araligi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/oranti-icin-guven-araligi\/","title":{"rendered":"Orant\u0131 i\u00e7in g\u00fcven aral\u0131\u011f\u0131"},"content":{"rendered":"<p>Bu makalede orant\u0131 i\u00e7in g\u00fcven aral\u0131\u011f\u0131n\u0131n ne oldu\u011fu ve istatistikte ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. Benzer \u015fekilde, oran\u0131n g\u00fcven aral\u0131\u011f\u0131n\u0131 nas\u0131l hesaplayaca\u011f\u0131n\u0131z\u0131 ve kavram\u0131 daha iyi anlamak i\u00e7in \u00e7\u00f6z\u00fcml\u00fc bir al\u0131\u015ft\u0131rmay\u0131 ke\u015ffedeceksiniz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-el-intervalo-de-confianza-para-la-proporcion\"><\/span> Oran\u0131n g\u00fcven aral\u0131\u011f\u0131 nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Oran i\u00e7in g\u00fcven aral\u0131\u011f\u0131,<\/strong> bir pop\u00fclasyonun oran\u0131 i\u00e7in bir dizi kabul edilebilir de\u011fer sa\u011flayan bir aral\u0131kt\u0131r. Yani orana ili\u015fkin g\u00fcven aral\u0131\u011f\u0131, n\u00fcfus oran\u0131n\u0131n bir hata pay\u0131 ile bu de\u011ferler aras\u0131nda yer ald\u0131\u011f\u0131 bir maksimum de\u011feri ve bir minimum de\u011feri belirtir.<\/p>\n<p> \u00d6rne\u011fin g\u00fcven d\u00fczeyi %95 olan bir pop\u00fclasyonun oran\u0131na ili\u015fkin g\u00fcven aral\u0131\u011f\u0131 (0,73, 0,81) ise bu, bir pop\u00fclasyonun oran\u0131n\u0131n %95 olas\u0131l\u0131kla %73 ile %81 aras\u0131nda oldu\u011fu anlam\u0131na gelir.<\/p>\n<p> Bu nedenle oran\u0131n g\u00fcven aral\u0131\u011f\u0131, belirli \u00f6zellikleri kar\u015f\u0131layan bir pop\u00fclasyonun oran\u0131n\u0131n de\u011ferini tahmin etmek i\u00e7in kullan\u0131l\u0131r.<\/p>\n<p> Bir sonraki b\u00f6l\u00fcmde g\u00f6rece\u011fimiz gibi orana ili\u015fkin g\u00fcven aral\u0131\u011f\u0131 \u00f6rneklem oran\u0131na ve \u00f6rneklemdeki g\u00f6zlem say\u0131s\u0131na ba\u011fl\u0131d\u0131r. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-del-intervalo-de-confianza-para-la-proporcion\"><\/span> Oran i\u00e7in g\u00fcven aral\u0131\u011f\u0131 form\u00fcl\u00fc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Oran\u0131n g\u00fcven aral\u0131\u011f\u0131, Z <sub>\u03b1\/2<\/sub> de\u011ferinin \u00f6rnek oran\u0131n\u0131n karek\u00f6k\u00fcyle (p) \u00e7arp\u0131lmas\u0131, 1-p ile \u00e7arp\u0131lmas\u0131 ve \u00f6rnek b\u00fcy\u00fckl\u00fc\u011f\u00fcne (n) b\u00f6l\u00fcnmesiyle \u00f6rnek oran\u0131na eklenip \u00e7\u0131kar\u0131larak hesaplan\u0131r. Bu nedenle <strong>orana ili\u015fkin g\u00fcven aral\u0131\u011f\u0131n\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-a328986eaa330c075c7fb85780df6411_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(p-Z_{\\alpha\/2}\\sqrt{\\frac{p(1-p)}{n}}\\ , \\ p+Z_{\\alpha\/2}\\sqrt{\\frac{p(1-p)}{n}}\\right) \" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"339\" style=\"vertical-align: -23px;\"><\/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-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> \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-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:7px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-6f8ee37ecf97c2a7c7d6dbe8fddddc27_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z_{\\alpha\/2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"34\" style=\"vertical-align: -8px;\"><\/p>\n<p> \u03b1\/2 olas\u0131l\u0131\u011f\u0131na kar\u015f\u0131l\u0131k gelen standart normal da\u011f\u0131l\u0131m\u0131n niceli\u011fidir. B\u00fcy\u00fck \u00f6rneklem b\u00fcy\u00fckl\u00fckleri ve %95 g\u00fcven d\u00fczeyi i\u00e7in genellikle 1,96&#8217;ya, %99 g\u00fcven d\u00fczeyi i\u00e7in ise genellikle 2,576&#8217;ya yak\u0131nd\u0131r. <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-del-calculo-de-un-intervalo-de-confianza-para-la-proporcion\"><\/span> Oran i\u00e7in g\u00fcven aral\u0131\u011f\u0131 hesaplama \u00f6rne\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Oran i\u00e7in g\u00fcven aral\u0131\u011f\u0131n\u0131n nas\u0131l hesapland\u0131\u011f\u0131n\u0131 g\u00f6rebilmeniz i\u00e7in sizi ad\u0131m ad\u0131m somut bir \u00f6rnekle a\u015fa\u011f\u0131da b\u0131rak\u0131yoruz.<\/p>\n<ul>\n<li> Bir sigorta \u015firketi pazar ara\u015ft\u0131rmas\u0131 yaparak bir \u00fclkede ka\u00e7 ki\u015finin hayat sigortas\u0131na sahip oldu\u011funu belirlemek istiyor. Bunun i\u00e7in rastgele 700 ki\u015filik bir \u00f6rneklem analiz ediliyor ve \u00f6rneklemin %40&#8217;\u0131n\u0131n hayat sigortas\u0131 oldu\u011fu sonucuna ula\u015f\u0131yoruz. \u00dclke n\u00fcfusunun oran\u0131 i\u00e7in %95 g\u00fcven d\u00fczeyinde g\u00fcven aral\u0131\u011f\u0131 nedir?<\/li>\n<\/ul>\n<p> Pop\u00fclasyon oran\u0131n\u0131n g\u00fcven aral\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in yukar\u0131da g\u00f6rd\u00fc\u011f\u00fcm\u00fcz form\u00fcl\u00fc kullanmam\u0131z gerekiyor:<\/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-a328986eaa330c075c7fb85780df6411_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(p-Z_{\\alpha\/2}\\sqrt{\\frac{p(1-p)}{n}}\\ , \\ p+Z_{\\alpha\/2}\\sqrt{\\frac{p(1-p)}{n}}\\right) \" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"339\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p> Bu durumda g\u00fcven aral\u0131\u011f\u0131n\u0131n g\u00fcven d\u00fczeyinin %95 olmas\u0131n\u0131 istiyoruz yani almam\u0131z gereken Z <sub>\u03b1\/2<\/sub> de\u011feri 1,96 olsun.<\/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-776a555edd1d064cf29a3a354caa5325_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1-\\alpha=0,95 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\alpha=0,05 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black}\\ \\alpha\/2=0,025\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"534\" 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-54dda39d0da5b29f2d25728b89565859_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}Z_{\\alpha\/2}= \\ \\color{orange}\\bm{?}\\\\[4ex]Z_{0,025}=1,96\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"71\" width=\"127\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Sorun ifadesi zaten bize \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fcn n=700 oldu\u011funu ve \u00f6rneklemde g\u00f6zlemlenen oran\u0131n p=0,40 oldu\u011funu s\u00f6yl\u00fcyor, bu nedenle verileri oran i\u00e7in g\u00fcven aral\u0131\u011f\u0131 form\u00fcl\u00fcne yerle\u015ftiriyoruz ve aral\u0131\u011f\u0131n s\u0131n\u0131rlar\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-a328986eaa330c075c7fb85780df6411_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(p-Z_{\\alpha\/2}\\sqrt{\\frac{p(1-p)}{n}}\\ , \\ p+Z_{\\alpha\/2}\\sqrt{\\frac{p(1-p)}{n}}\\right) \" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"339\" style=\"vertical-align: -23px;\"><\/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-19482f8505723187c6106d6a1ab9ebb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(0,40-1,96\\cdot \\sqrt{\\frac{0,40\\cdot (1-0,40)}{700}}\\ , \\ 0,40+1,96\\cdot \\sqrt{\\frac{0,40\\cdot (1-0,40)}{700}\\right) \" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"542\" style=\"vertical-align: -23px;\"><\/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-bc0b3de3cfa91d76192cb5cd5778aef6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(0,36 \\ , \\ 0,44\\right) \" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"101\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Sonu\u00e7 olarak, incelenen pop\u00fclasyonun oran\u0131 %95 g\u00fcven d\u00fczeyiyle %36 ila %44 aras\u0131ndad\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\/ortalama-icin-guven-araligi\/\">Ortalama i\u00e7in g\u00fcven aral\u0131\u011f\u0131<\/a><br \/> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Bak\u0131n\u0131z:<\/strong> <a href=\"https:\/\/statorials.org\/tr\/varyans-icin-guven-araligi\/\">Varyans i\u00e7in g\u00fcven aral\u0131\u011f\u0131<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Bu makalede orant\u0131 i\u00e7in g\u00fcven aral\u0131\u011f\u0131n\u0131n ne oldu\u011fu ve istatistikte ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. Benzer \u015fekilde, oran\u0131n g\u00fcven aral\u0131\u011f\u0131n\u0131 nas\u0131l hesaplayaca\u011f\u0131n\u0131z\u0131 ve kavram\u0131 daha iyi anlamak i\u00e7in \u00e7\u00f6z\u00fcml\u00fc bir al\u0131\u015ft\u0131rmay\u0131 ke\u015ffedeceksiniz. Oran\u0131n g\u00fcven aral\u0131\u011f\u0131 nedir? Oran i\u00e7in g\u00fcven aral\u0131\u011f\u0131, bir pop\u00fclasyonun oran\u0131 i\u00e7in bir dizi kabul edilebilir de\u011fer sa\u011flayan bir aral\u0131kt\u0131r. Yani orana ili\u015fkin g\u00fcven [&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-248","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 Orant\u0131 i\u00e7in g\u00fcven aral\u0131\u011f\u0131<\/title>\n<meta name=\"description\" content=\"Burada oran\u0131n g\u00fcven aral\u0131\u011f\u0131n\u0131n ne oldu\u011funu, nas\u0131l hesapland\u0131\u011f\u0131n\u0131 (form\u00fcl) ve ad\u0131m ad\u0131m somut bir \u00f6rne\u011fi bulacaks\u0131n\u0131z.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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