{"id":4912,"date":"2023-07-06T13:07:19","date_gmt":"2023-07-06T13:07:19","guid":{"rendered":"https:\/\/statorials.org\/tr\/guven-araligi-ornek-problemleri\/"},"modified":"2023-07-06T13:07:19","modified_gmt":"2023-07-06T13:07:19","slug":"guven-araligi-ornek-problemleri","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/guven-araligi-ornek-problemleri\/","title":{"rendered":"G\u00fcven aral\u0131klar\u0131 nas\u0131l hesaplan\u0131r: 3 \u00f6rnek problem"},"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 <a href=\"https:\/\/statorials.org\/tr\/populasyon-ortalamasiyla-karsilastirildiginda-ornek-ortalamasi\/\" target=\"_blank\" rel=\"noopener\">pop\u00fclasyon ortalamas\u0131n\u0131<\/a> i\u00e7ermesi muhtemel bir de\u011fer aral\u0131\u011f\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bir ortalaman\u0131n g\u00fcven aral\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullan\u0131r\u0131z:<\/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*(s\/\u221a <span style=\"text-decoration: overline;\">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:<\/strong> t&#8217;nin kritik 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;\"><strong>Not<\/strong> : Pop\u00fclasyon standart sapmas\u0131 (\u03c3) biliniyorsa <em>ve<\/em> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc 30&#8217;dan b\u00fcy\u00fckse, form\u00fclde kritik de\u011feri az kritik de\u011fer ile de\u011fi\u015ftiririz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnekler, \u00fc\u00e7 farkl\u0131 senaryoda ortalama i\u00e7in g\u00fcven aral\u0131\u011f\u0131n\u0131n nas\u0131l olu\u015fturulaca\u011f\u0131n\u0131 g\u00f6sterir:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">N\u00fcfus standart sapmas\u0131 (\u03c3) bilinmiyor<\/span><\/li>\n<li> <span style=\"color: #000000;\">Pop\u00fclasyon standart sapmas\u0131 (\u03c3) biliniyor ancak n \u2264 30<\/span><\/li>\n<li> <span style=\"color: #000000;\">Pop\u00fclasyon standart sapmas\u0131 (\u03c3) biliniyor ve n &gt; 30<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Hadi gidelim!<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>\u00d6rnek 1: \u03c3 bilinmedi\u011finde g\u00fcven aral\u0131\u011f\u0131<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Belirli bir bitki t\u00fcr\u00fcn\u00fcn ortalama y\u00fcksekli\u011fi (in\u00e7 cinsinden) i\u00e7in %95&#8217;lik bir g\u00fcven aral\u0131\u011f\u0131 hesaplamak istedi\u011fimizi varsayal\u0131m.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki bilgileri i\u00e7eren basit bir rastgele \u00f6rnek toplad\u0131\u011f\u0131m\u0131z\u0131 varsayal\u0131m:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u00f6rnek ortalamas\u0131 ( <span style=\"text-decoration: overline;\">x<\/span> ) = 12<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc (n) = 19<\/span><\/li>\n<li> <span style=\"color: #000000;\">numune standart sapmas\u0131 (s) = 6,3<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu g\u00fcven aral\u0131\u011f\u0131n\u0131 olu\u015fturmak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">%95 GA = <span style=\"text-decoration: overline;\">x<\/span> +\/- t*(s\/\u221a <span style=\"text-decoration: overline;\">n<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">%95 GA = 12 +\/- t <sub>n-1, \u03b1\/2<\/sub> *(6,3\/\u221a <span style=\"text-decoration: overline;\">19<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">%95 GA = 12 +\/- t <sub>18,025<\/sub> *(6,3\/\u221a <span style=\"text-decoration: overline;\">19<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">%95 GA = 12 +\/- 2,1009*(6,3\/\u221a <span style=\"text-decoration: overline;\">19<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">%95 GA = <strong>(8,964, 15,037)<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu \u00f6zel bitki t\u00fcr\u00fcn\u00fcn ortalama pop\u00fclasyon y\u00fcksekli\u011fine ili\u015fkin %95 g\u00fcven aral\u0131\u011f\u0131 <strong>(8,964 in\u00e7, 15,037 in\u00e7)<\/strong> \u015feklindedir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Not #1<\/strong> : 18 serbestlik derecesi ve 0,95 g\u00fcven d\u00fczeyi ile ili\u015fkili kritik t de\u011ferini bulmak i\u00e7in ters t da\u011f\u0131l\u0131m\u0131 hesaplay\u0131c\u0131s\u0131n\u0131 kulland\u0131k.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Not #2<\/strong> : Pop\u00fclasyon standart sapmas\u0131 (\u03c3) bilinmedi\u011finden g\u00fcven aral\u0131\u011f\u0131n\u0131 hesaplarken kritik t de\u011ferini kulland\u0131k.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>\u00d6rnek 2:<\/strong><\/span> <span style=\"color: #000000;\"><strong>\u03c3 bilindi\u011fi halde n \u2264 30 oldu\u011funda g\u00fcven aral\u0131\u011f\u0131<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Belirli bir \u00fcniversiteye giri\u015f s\u0131nav\u0131n\u0131n ortalama puan\u0131 i\u00e7in %99&#8217;luk bir g\u00fcven aral\u0131\u011f\u0131 hesaplamak istedi\u011fimizi varsayal\u0131m.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki bilgileri i\u00e7eren basit bir rastgele \u00f6rnek toplad\u0131\u011f\u0131m\u0131z\u0131 varsayal\u0131m:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u00f6rnek ortalamas\u0131 ( <span style=\"text-decoration: overline;\">x<\/span> ) = 85<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc (n) = 25<\/span><\/li>\n<li> <span style=\"color: #000000;\">pop\u00fclasyon standart sapmas\u0131 (\u03c3) = 3,5<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu g\u00fcven aral\u0131\u011f\u0131n\u0131 olu\u015fturmak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">%99 GA = <span style=\"text-decoration: overline;\">x<\/span> +\/- t*(s\/\u221a <span style=\"text-decoration: overline;\">n<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">%99 GA = 85 +\/- t <sub>n-1, \u03b1\/2<\/sub> *(3,5\/\u221a <span style=\"text-decoration: overline;\">25<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">%99 GA = 85 +\/- t <sub>24,005<\/sub> *(3,5\/\u221a <span style=\"text-decoration: overline;\">25<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">%99 GA = 85 +\/- 2,7969*(3,5\/\u221a <span style=\"text-decoration: overline;\">25<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">%99 GA = <strong>(83.042, 86.958)<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">N\u00fcfusun bu \u00fcniversiteye giri\u015f s\u0131nav\u0131ndaki ortalama puan\u0131 i\u00e7in %99 g\u00fcven aral\u0131\u011f\u0131 <strong>(83.042, 86.958)&#8217;<\/strong> dir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Not #1<\/strong> : 24 serbestlik derecesi ve 0,99 g\u00fcven d\u00fczeyi ile ili\u015fkili kritik t de\u011ferini bulmak i\u00e7in ters t da\u011f\u0131l\u0131m\u0131 hesaplay\u0131c\u0131s\u0131n\u0131 kulland\u0131k.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Not #2<\/strong> : Pop\u00fclasyon standart sapmas\u0131 (\u03c3) bilindi\u011fi halde \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc (n) 30&#8217;dan k\u00fc\u00e7\u00fck oldu\u011fundan, g\u00fcven aral\u0131\u011f\u0131n\u0131 hesaplarken kritik de\u011fer t&#8217;yi kulland\u0131k.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>\u00d6rnek 3:<\/strong><\/span> <span style=\"color: #000000;\"><strong>\u03c3 bilindi\u011finde ve n &gt; 30 oldu\u011funda g\u00fcven aral\u0131\u011f\u0131<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Belirli bir kaplumba\u011fa t\u00fcr\u00fcn\u00fcn ortalama a\u011f\u0131rl\u0131\u011f\u0131 i\u00e7in %90&#8217;l\u0131k bir g\u00fcven aral\u0131\u011f\u0131 hesaplamak istedi\u011fimizi varsayal\u0131m.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki bilgileri i\u00e7eren basit bir rastgele \u00f6rnek toplad\u0131\u011f\u0131m\u0131z\u0131 varsayal\u0131m:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u00f6rnek ortalama ( <span style=\"text-decoration: overline;\">x<\/span> ) = 300<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc (n) = 40<\/span><\/li>\n<li> <span style=\"color: #000000;\">pop\u00fclasyon standart sapmas\u0131 (\u03c3) = 15<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu g\u00fcven aral\u0131\u011f\u0131n\u0131 olu\u015fturmak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">%90 GA = <span style=\"text-decoration: overline;\">x<\/span> +\/- z*(\u03c3\/\u221a <span style=\"text-decoration: overline;\">n<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">%90 GA = 300 +\/- 1,645*(15\/\u221a <span style=\"text-decoration: overline;\">40<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">%90 GA = <strong>(296.099, 303.901)<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu kaplumba\u011fa t\u00fcr\u00fcn\u00fcn ortalama pop\u00fclasyon a\u011f\u0131rl\u0131\u011f\u0131 i\u00e7in %90 g\u00fcven aral\u0131\u011f\u0131 <strong>(83.042, 86.958)&#8217;<\/strong> dir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Not #1<\/strong> : 0,1 anlaml\u0131l\u0131k d\u00fczeyiyle ili\u015fkili kritik z de\u011ferini bulmak i\u00e7in Kritik Z De\u011feri Hesaplay\u0131c\u0131s\u0131n\u0131 kulland\u0131k.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Not #2<\/strong> : Pop\u00fclasyon standart sapmas\u0131 (\u03c3) bilindi\u011finden ve \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc (n) 30&#8217;dan b\u00fcy\u00fck oldu\u011fundan g\u00fcven aral\u0131\u011f\u0131n\u0131 hesaplarken kritik z de\u011ferini kulland\u0131k.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h2>\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> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/guven-araligi-gercek-ornegi\/\" target=\"_blank\" rel=\"noopener\">Ger\u00e7ek Hayattan 4 G\u00fcven Aral\u0131\u011f\u0131 \u00d6rne\u011fi<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/guven-araligi-sonucu-nasil-yazilir\/\" target=\"_blank\" rel=\"noopener\">G\u00fcven Aral\u0131\u011f\u0131 Sonucu Nas\u0131l Yaz\u0131l\u0131r<\/a><br \/> Kontrol edilecek 6 g\u00fcven aral\u0131\u011f\u0131 hipotezi<\/span><\/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. Bir ortalaman\u0131n g\u00fcven aral\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullan\u0131r\u0131z: G\u00fcven aral\u0131\u011f\u0131 = x +\/- t*(s\/\u221a n ) Alt\u0131n: x : \u00f6rnek ortalama t: t&#8217;nin kritik de\u011feri s: numune standart sapmas\u0131 n: \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc Not : Pop\u00fclasyon standart [&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-4912","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>G\u00fcven aral\u0131klar\u0131 nas\u0131l hesaplan\u0131r: 3 \u00f6rnek problem - Statorials<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde, g\u00fcven aral\u0131klar\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131na ili\u015fkin ad\u0131m ad\u0131m \u00e7\u00f6z\u00fcmler i\u00e7eren birka\u00e7 \u00f6rnek sunulmaktad\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\/guven-araligi-ornek-problemleri\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"G\u00fcven aral\u0131klar\u0131 nas\u0131l hesaplan\u0131r: 3 \u00f6rnek problem - 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