{"id":2448,"date":"2023-07-22T05:54:51","date_gmt":"2023-07-22T05:54:51","guid":{"rendered":"https:\/\/statorials.org\/tr\/tek-tarafli-guven-araligi\/"},"modified":"2023-07-22T05:54:51","modified_gmt":"2023-07-22T05:54:51","slug":"tek-tarafli-guven-araligi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/tek-tarafli-guven-araligi\/","title":{"rendered":"Tek tarafl\u0131 g\u00fcven aral\u0131klar\u0131 nas\u0131l olu\u015fturulur: \u00f6rneklerle"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Bir ortalama i\u00e7in g\u00fcven aral\u0131\u011f\u0131,<\/strong> belirli bir g\u00fcven d\u00fczeyine sahip bir pop\u00fclasyon ortalamas\u0131n\u0131 i\u00e7ermesi muhtemel bir de\u011fer aral\u0131\u011f\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u015fekilde hesaplan\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>G\u00fcven aral\u0131\u011f\u0131 =<\/strong> <strong><span style=\"text-decoration: overline;\">x<\/span> +\/- t <sub>\u03b1\/2, n-1<\/sub> *(s\/\u221a <span style=\"border-top: 1px solid black;\">n<\/span> )<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong><span style=\"text-decoration: overline;\">x<\/span> :<\/strong> \u00f6rnek ortalama<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>t <sub>\u03b1\/2, n-1<\/sub> :<\/strong> n-1 serbestlik derecesine sahip \u03b1\/2&#8217;ye kar\u015f\u0131l\u0131k gelen t de\u011feri<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>s:<\/strong> numune standart sapmas\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;\">Yukar\u0131daki form\u00fcl, tipik bir <strong>iki tarafl\u0131 g\u00fcven aral\u0131\u011f\u0131n\u0131n<\/strong> nas\u0131l olu\u015fturulaca\u011f\u0131n\u0131 a\u00e7\u0131klamaktad\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ancak baz\u0131 senaryolarda yaln\u0131zca <strong>tek tarafl\u0131 g\u00fcven aral\u0131klar\u0131<\/strong> olu\u015fturmak istiyoruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bunu yapmak i\u00e7in a\u015fa\u011f\u0131daki form\u00fclleri kullanabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Alt tek tarafl\u0131 g\u00fcven aral\u0131\u011f\u0131<\/strong> = [-\u221e, <span style=\"text-decoration: overline;\">x<\/span> + t <sub>\u03b1, n-1<\/sub> *(s\/\u221a <span style=\"border-top: 1px solid black;\">n<\/span> )]<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00dcst tek tarafl\u0131 g\u00fcven aral\u0131\u011f\u0131<\/strong> = [ <span style=\"text-decoration: overline;\">x<\/span> \u2013 t <sub>\u03b1, n-1<\/sub> *(s\/\u221a <span style=\"border-top: 1px solid black;\">n<\/span> ), \u221e ]<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnekler uygulamada alt ve \u00fcst tek tarafl\u0131 g\u00fcven aral\u0131klar\u0131n\u0131n nas\u0131l olu\u015fturulaca\u011f\u0131n\u0131 g\u00f6stermektedir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 1: Daha d\u00fc\u015f\u00fck tek tarafl\u0131 bir g\u00fcven aral\u0131\u011f\u0131 olu\u015fturun<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bir \u00f6rnek i\u00e7in a\u015fa\u011f\u0131daki bilgileri toplad\u0131\u011f\u0131m\u0131z bir pop\u00fclasyon ortalamas\u0131 i\u00e7in daha d\u00fc\u015f\u00fck tek tarafl\u0131 %95 g\u00fcven aral\u0131\u011f\u0131 olu\u015fturmak istedi\u011fimizi varsayal\u0131m:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong><span style=\"text-decoration: overline;\">x<\/span> :<\/strong> 20,5<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>s:<\/strong> 3.2<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>say\u0131:<\/strong> 18<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Ters t da\u011f\u0131l\u0131m\u0131 hesaplay\u0131c\u0131s\u0131na g\u00f6re n-1 = 17 serbestlik derecesi ile tek tarafl\u0131 %95 g\u00fcven aral\u0131\u011f\u0131 i\u00e7in kullanmam\u0131z gereken t de\u011feri 1,7396&#8217;d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Daha sonra tek tarafl\u0131 daha d\u00fc\u015f\u00fck bir g\u00fcven aral\u0131\u011f\u0131 i\u00e7in bu de\u011ferlerin her birini form\u00fcle ekleyebiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>Alt tek tarafl\u0131 g\u00fcven aral\u0131\u011f\u0131<\/strong> = [-\u221e, <span style=\"text-decoration: overline;\">x<\/span> + t <sub>\u03b1, n-1<\/sub> *(s\/\u221a <span style=\"border-top: 1px solid black;\">n<\/span> )]<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>D\u00fc\u015f\u00fck tek tarafl\u0131 g\u00fcven aral\u0131\u011f\u0131<\/strong> = [-\u221e, 20,5 + 1,7396*(3,2\/\u221a <span style=\"border-top: 1px solid black;\">18<\/span> )]<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>D\u00fc\u015f\u00fck tek tarafl\u0131 g\u00fcven aral\u0131\u011f\u0131<\/strong> = [-\u221e, 21,812 ]<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu aral\u0131\u011f\u0131 \u015fu \u015fekilde yorumlayabiliriz: Ger\u00e7ek n\u00fcfus ortalamas\u0131n\u0131n <strong>21.812&#8217;ye<\/strong> e\u015fit veya daha k\u00fc\u00e7\u00fck oldu\u011fundan %95 eminiz.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 2: Tek tarafl\u0131 bir \u00fcst g\u00fcven aral\u0131\u011f\u0131 olu\u015fturun<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bir \u00f6rnek i\u00e7in a\u015fa\u011f\u0131daki bilgileri toplad\u0131\u011f\u0131m\u0131z bir pop\u00fclasyon ortalamas\u0131 i\u00e7in \u00fcst tek tarafl\u0131 %95 g\u00fcven aral\u0131\u011f\u0131 olu\u015fturmak istedi\u011fimizi varsayal\u0131m:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong><span style=\"text-decoration: overline;\">x<\/span> :<\/strong> 40<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>s:<\/strong> 6.7<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>say\u0131:<\/strong> 25<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Ters t da\u011f\u0131l\u0131m\u0131 hesaplay\u0131c\u0131s\u0131na g\u00f6re n-1 = 24 serbestlik derecesi ile tek tarafl\u0131 %95 g\u00fcven aral\u0131\u011f\u0131 i\u00e7in kullanmam\u0131z gereken t de\u011feri 1,7109&#8217;dur.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Daha sonra bu de\u011ferlerin her birini \u00fcst tek tarafl\u0131 g\u00fcven aral\u0131\u011f\u0131 form\u00fcl\u00fcne ekleyebiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u00dcst tek tarafl\u0131 g\u00fcven aral\u0131\u011f\u0131<\/strong> = [ <span style=\"text-decoration: overline;\">x<\/span> \u2013 t <sub>\u03b1, n-1<\/sub> *(s\/\u221a <span style=\"border-top: 1px solid black;\">n<\/span> ), \u221e ]<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>D\u00fc\u015f\u00fck tek tarafl\u0131 g\u00fcven aral\u0131\u011f\u0131<\/strong> = [ 40 \u2013 1,7109*(6,7\/\u221a <span style=\"border-top: 1px solid black;\">25<\/span> ), \u221e ]<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Daha d\u00fc\u015f\u00fck tek tarafl\u0131 g\u00fcven aral\u0131\u011f\u0131<\/strong> = [37,707, \u221e]<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu aral\u0131\u011f\u0131 \u015fu \u015fekilde yorumlayabiliriz: Ger\u00e7ek n\u00fcfus ortalamas\u0131n\u0131n <strong>37.707&#8217;den<\/strong> b\u00fcy\u00fck veya ona e\u015fit oldu\u011fundan %95 eminiz.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki e\u011fitimler g\u00fcven aral\u0131klar\u0131 hakk\u0131nda ek bilgi sa\u011flar:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/tr\/guvenilirlik-araligi\/\" target=\"_blank\" rel=\"noopener\">G\u00fcven Aral\u0131klar\u0131na Giri\u015f<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/guven-araliklari-nasil-raporlanir\/\" target=\"_blank\" rel=\"noopener\">G\u00fcven aral\u0131klar\u0131 nas\u0131l raporlan\u0131r?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/guven-araligi-sifir-iceriyor\/\" target=\"_blank\" rel=\"noopener\">S\u0131f\u0131r i\u00e7eren bir g\u00fcven aral\u0131\u011f\u0131 nas\u0131l yorumlan\u0131r?<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bir ortalama i\u00e7in g\u00fcven aral\u0131\u011f\u0131, belirli bir g\u00fcven d\u00fczeyine sahip bir pop\u00fclasyon ortalamas\u0131n\u0131 i\u00e7ermesi muhtemel bir de\u011fer aral\u0131\u011f\u0131d\u0131r. A\u015fa\u011f\u0131daki \u015fekilde hesaplan\u0131r: G\u00fcven aral\u0131\u011f\u0131 = x +\/- t \u03b1\/2, n-1 *(s\/\u221a n ) Alt\u0131n: x : \u00f6rnek ortalama t \u03b1\/2, n-1 : n-1 serbestlik derecesine sahip \u03b1\/2&#8217;ye kar\u015f\u0131l\u0131k gelen t de\u011feri s: numune standart sapmas\u0131 n: [&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-2448","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>Tek Tarafl\u0131 G\u00fcven Aral\u0131klar\u0131 Nas\u0131l Olu\u015fturulur (\u00d6rneklerle) - Statorials<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde, tek tarafl\u0131 bir g\u00fcven aral\u0131\u011f\u0131n\u0131n nas\u0131l olu\u015fturulaca\u011f\u0131 birka\u00e7 \u00f6rnekle a\u00e7\u0131klanmaktad\u0131r.\" \/>\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\/tek-tarafli-guven-araligi\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Tek Tarafl\u0131 G\u00fcven Aral\u0131klar\u0131 Nas\u0131l Olu\u015fturulur (\u00d6rneklerle) - 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