{"id":751,"date":"2023-07-28T21:26:47","date_gmt":"2023-07-28T21:26:47","guid":{"rendered":"https:\/\/statorials.org\/tr\/oranti-z-testi\/"},"modified":"2023-07-28T21:26:47","modified_gmt":"2023-07-28T21:26:47","slug":"oranti-z-testi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/oranti-z-testi\/","title":{"rendered":"Tek oranl\u0131 z testi: tan\u0131m, form\u00fcl ve \u00f6rnek"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">G\u00f6zlenen bir oran\u0131 teorik bir oranla kar\u015f\u0131la\u015ft\u0131rmak i\u00e7in <strong>tek oranl\u0131 z testi<\/strong> kullan\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu e\u011fitimde a\u015fa\u011f\u0131dakiler a\u00e7\u0131klanmaktad\u0131r:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Belirli bir oranda z testi ger\u00e7ekle\u015ftirme motivasyonu.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Tek oranl\u0131 z testi ger\u00e7ekle\u015ftirme form\u00fcl\u00fc.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Tek oranl\u0131 z testinin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fine bir \u00f6rnek.<\/span><\/li>\n<\/ul>\n<h3> <span style=\"color: #000000;\"><strong>Tek oranl\u0131 Z testi: motivasyon<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Belirli bir il\u00e7ede belirli bir yasay\u0131 destekleyen insanlar\u0131n oran\u0131n\u0131n %60&#8217;a e\u015fit olup olmad\u0131\u011f\u0131n\u0131 bilmek istedi\u011fimizi varsayal\u0131m. \u0130l\u00e7ede binlerce sakin bulundu\u011fundan, etrafta dola\u015f\u0131p her sakine kanunla ilgili g\u00f6r\u00fc\u015flerini sormak \u00e7ok maliyetli ve zaman al\u0131c\u0131 olacakt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bunun yerine, sakinlerden <a href=\"https:\/\/statorials.org\/tr\/ornekleme-yontemleri\/\" target=\"_blank\" rel=\"noopener\">basit ve rastgele bir \u00f6rneklem<\/a> se\u00e7ip her birine yasay\u0131 destekleyip desteklemediklerini sorabiliriz:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-7603\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/ciprop1.png\" sizes=\"auto, \" srcset=\"\" alt=\"N\u00fcfus oran\u0131n\u0131 tahmin etme \u00f6rne\u011fi\" width=\"429\" height=\"400\"><\/p>\n<p> <span style=\"color: #000000;\">Bununla birlikte, \u00f6rneklemde yasay\u0131 destekleyen sakinlerin oran\u0131n\u0131n genel n\u00fcfusta yasay\u0131 destekleyen sakinlerin oran\u0131ndan en az\u0131ndan bir miktar farkl\u0131 olaca\u011f\u0131 neredeyse garantidir. <strong>Soru, bu fark\u0131n istatistiksel olarak anlaml\u0131 olup olmad\u0131\u011f\u0131d\u0131r<\/strong> . Neyse ki tek oranl\u0131 z testi bu soruyu yan\u0131tlamam\u0131za olanak tan\u0131yor.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Tek oranl\u0131 Z testi:<\/strong><\/span> <span style=\"color: #000000;\"><strong>form\u00fcl<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Tek oranl\u0131 z testi her zaman a\u015fa\u011f\u0131daki bo\u015f hipotezi kullan\u0131r:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> :<\/strong> p = p <sub>0<\/sub> (n\u00fcfus oran\u0131 varsay\u0131msal bir n\u00fcfus oran\u0131na e\u015fittir p <sub>0<\/sub> )<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Alternatif hipotez iki tarafl\u0131, sol veya sa\u011f olabilir:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>H <sub>1<\/sub> (iki kuyruklu):<\/strong> p \u2260 p <sub>0<\/sub> (n\u00fcfus oran\u0131 varsay\u0131msal bir p <sub>0<\/sub> de\u011ferine e\u015fit de\u011fildir)<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>H <sub>1<\/sub> (solda):<\/strong> p &lt; p <sub>0<\/sub> (n\u00fcfus oran\u0131 varsay\u0131msal bir p <sub>0<\/sub> de\u011ferinden azd\u0131r)<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>H <sub>1<\/sub> (sa\u011f):<\/strong> p &gt; p <sub>0<\/sub> (n\u00fcfus oran\u0131 varsay\u0131msal bir de\u011fer olan p <sub>0&#8217;dan<\/sub> b\u00fcy\u00fckt\u00fcr)<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Z testi istatisti\u011fini hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullan\u0131r\u0131z:<\/span><\/p>\n<p> <span style=\"color: #000000;\">z = (pp <sub>0<\/sub> ) \/ \u221a <span style=\"border-top: 1px solid black;\">p <sub>0<\/sub> (1-p <sub>0<\/sub> )\/n<\/span><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>p:<\/strong> g\u00f6zlemlenen \u00f6rnek oran\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>p <sub>0<\/sub> :<\/strong> n\u00fcfusun varsay\u0131msal oran\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>n:<\/strong> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Z testi istatisti\u011fine kar\u015f\u0131l\u0131k gelen p de\u011feri se\u00e7ilen anlaml\u0131l\u0131k seviyesinden k\u00fc\u00e7\u00fckse (ortak se\u00e7enekler 0,10, 0,05 ve 0,01&#8217;dir), o zaman s\u0131f\u0131r hipotezini reddedebilirsiniz.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Tek oranl\u0131 Z testi<\/strong><\/span> <span style=\"color: #000000;\"><strong>: \u00f6rnek<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Belirli bir il\u00e7ede belirli bir yasay\u0131 destekleyen sakinlerin oran\u0131n\u0131n %60&#8217;a e\u015fit olup olmad\u0131\u011f\u0131n\u0131 bilmek istedi\u011fimizi varsayal\u0131m. Bunu test etmek i\u00e7in a\u015fa\u011f\u0131daki ad\u0131mlar\u0131 kullanarak \u03b1 = 0,05 anlaml\u0131l\u0131k d\u00fczeyinde tek oranl\u0131 bir z testi ger\u00e7ekle\u015ftirece\u011fiz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 1: \u00d6rnek verileri toplay\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Rastgele bir b\u00f6lge sakini \u00f6rne\u011fini ara\u015ft\u0131rd\u0131\u011f\u0131m\u0131z\u0131 ve a\u015fa\u011f\u0131daki bilgileri elde etti\u011fimizi<\/span> <span style=\"color: #000000;\">varsayal\u0131m<\/span> :<\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>p:<\/strong> g\u00f6zlemlenen \u00f6rnek oran\u0131 = 0,64<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>p <sub>0<\/sub> :<\/strong> n\u00fcfusun varsay\u0131msal oran\u0131 = 0,60<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>n:<\/strong> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc = 100<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 2: Varsay\u0131mlar\u0131 tan\u0131mlay\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Tek \u00f6rnek t-testini a\u015fa\u011f\u0131daki hipotezlerle ger\u00e7ekle\u015ftirece\u011fiz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> :<\/strong> p = 0,60 (n\u00fcfus oran\u0131 0,60&#8217;a e\u015fittir)<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>H <sub>1<\/sub> :<\/strong> p \u2260 0,60 (n\u00fcfus oran\u0131 0,60&#8217;a e\u015fit de\u011fildir)<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 3: <em>z<\/em> testi istatisti\u011fini hesaplay\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>z<\/strong> = (pp <sub>0<\/sub> ) \/ \u221a <span style=\"border-top: 1px solid black;\">p <sub>0<\/sub> (1-p <sub>0<\/sub> )\/n<\/span> = (.64-.6) \/ \u221a <span style=\"border-top: 1px solid black;\">.6(1-.6)\/100<\/span> = <strong>0.816<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 4: <em>z<\/em> testi istatisti\u011finin p de\u011ferini hesaplay\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Z puan\u0131 &#8211; P De\u011feri hesaplay\u0131c\u0131s\u0131na g\u00f6re, z = 0,816 ile ili\u015fkili iki kuyruklu p de\u011feri <strong>0,4145&#8217;tir<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 5: Bir sonu\u00e7 \u00e7\u0131kar\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu p de\u011feri bizim anlaml\u0131l\u0131k d\u00fczeyimiz olan \u03b1 = 0,05&#8217;ten d\u00fc\u015f\u00fck olmad\u0131\u011f\u0131 i\u00e7in s\u0131f\u0131r hipotezini reddedemiyoruz. Yasay\u0131 destekleyenlerin oran\u0131n\u0131n 0,60&#8217;tan farkl\u0131 oldu\u011funu s\u00f6yleyecek yeterli kan\u0131t\u0131m\u0131z yok.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><em><strong>Not:<\/strong> Bu tek oranl\u0131 z testinin tamam\u0131n\u0131 <a href=\"https:\/\/statorials.org\/tr\/a-z-testi-oranti-hesaplayicisi\/\" target=\"_blank\" rel=\"noopener\">tek oranl\u0131 Z testi hesaplay\u0131c\u0131s\u0131n\u0131<\/a> kullanarak da ger\u00e7ekle\u015ftirebilirsiniz.<\/em><\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/tr\/oranti-z-testi-excel\/\" target=\"_blank\" rel=\"noopener\">Excel&#8217;de Tek Oranl\u0131 Z Testi Nas\u0131l Yap\u0131l\u0131r<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/a-z-testi-oranti-hesaplayicisi\/\" target=\"_blank\" rel=\"noopener\">Tek Oranl\u0131 Z Testi Hesaplay\u0131c\u0131s\u0131<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>G\u00f6zlenen bir oran\u0131 teorik bir oranla kar\u015f\u0131la\u015ft\u0131rmak i\u00e7in tek oranl\u0131 z testi kullan\u0131l\u0131r. Bu e\u011fitimde a\u015fa\u011f\u0131dakiler a\u00e7\u0131klanmaktad\u0131r: Belirli bir oranda z testi ger\u00e7ekle\u015ftirme motivasyonu. Tek oranl\u0131 z testi ger\u00e7ekle\u015ftirme form\u00fcl\u00fc. Tek oranl\u0131 z testinin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fine bir \u00f6rnek. Tek oranl\u0131 Z testi: motivasyon Belirli bir il\u00e7ede belirli bir yasay\u0131 destekleyen insanlar\u0131n oran\u0131n\u0131n %60&#8217;a e\u015fit olup [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-751","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Bir Oran Z Testi: Tan\u0131m, Form\u00fcl ve \u00d6rnek - Statoryaller<\/title>\n<meta name=\"description\" content=\"Ad\u0131m ad\u0131m \u00f6rnek de dahil olmak \u00fczere tek oranl\u0131 z testinin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fine ili\u015fkin basit bir a\u00e7\u0131klama.\" \/>\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\/tr\/oranti-z-testi\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Bir Oran Z Testi: Tan\u0131m, Form\u00fcl ve \u00d6rnek - 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