{"id":738,"date":"2023-07-28T22:31:50","date_gmt":"2023-07-28T22:31:50","guid":{"rendered":"https:\/\/statorials.org\/tr\/guven-araligi-standart-sapmasi\/"},"modified":"2023-07-28T22:31:50","modified_gmt":"2023-07-28T22:31:50","slug":"guven-araligi-standart-sapmasi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/guven-araligi-standart-sapmasi\/","title":{"rendered":"Bir standart sapma i\u00e7in g\u00fcven aral\u0131\u011f\u0131"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Standart sapma i\u00e7in g\u00fcven aral\u0131\u011f\u0131,<\/strong> belirli bir g\u00fcven d\u00fczeyine sahip bir pop\u00fclasyon standart sapmas\u0131n\u0131 i\u00e7ermesi muhtemel bir de\u011fer aral\u0131\u011f\u0131d\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;\">Bu g\u00fcven aral\u0131\u011f\u0131n\u0131 yaratma motivasyonu.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Bu g\u00fcven aral\u0131\u011f\u0131n\u0131 olu\u015fturman\u0131n form\u00fcl\u00fc.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Bu g\u00fcven aral\u0131\u011f\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131na dair bir \u00f6rnek.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Bu g\u00fcven aral\u0131\u011f\u0131 nas\u0131l yorumlan\u0131r?<\/span><\/li>\n<\/ul>\n<h3> <span style=\"color: #000000;\"><strong>Bir standart sapma i\u00e7in g\u00fcven aral\u0131\u011f\u0131: motivasyon<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Standart sapma i\u00e7in bir g\u00fcven aral\u0131\u011f\u0131 olu\u015fturmam\u0131z\u0131n nedeni, pop\u00fclasyon standart sapmas\u0131n\u0131 tahmin ederken belirsizli\u011fimizi yakalamak istememizdir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, Florida&#8217;daki belirli bir kaplumba\u011fa t\u00fcr\u00fcn\u00fcn a\u011f\u0131rl\u0131\u011f\u0131n\u0131n standart sapmas\u0131n\u0131 tahmin etmek istedi\u011fimizi varsayal\u0131m. Florida&#8217;da binlerce kaplumba\u011fa oldu\u011fundan, etrafta dola\u015f\u0131p her kaplumba\u011fay\u0131 ayr\u0131 ayr\u0131 tartmak son derece zaman al\u0131c\u0131 ve pahal\u0131 olacakt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bunun yerine, 50 kaplumba\u011fadan olu\u015fan <a href=\"https:\/\/statorials.org\/tr\/ornekleme-yontemleri\/\" target=\"_blank\" rel=\"noopener\">basit bir rastgele \u00f6rnek<\/a> alabilir ve ger\u00e7ek pop\u00fclasyon standart sapmas\u0131n\u0131 tahmin etmek i\u00e7in bu \u00f6rnekteki kaplumba\u011falar\u0131n a\u011f\u0131rl\u0131\u011f\u0131n\u0131n standart sapmas\u0131n\u0131 kullanabiliriz:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-7353 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/cimoyenne1.png\" alt=\"\u00d6rnek bir pop\u00fclasyon \u00f6rne\u011fi\" width=\"405\" height=\"270\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Sorun, \u00f6rneklem standart sapmas\u0131n\u0131n t\u00fcm pop\u00fclasyonun standart sapmas\u0131na tam olarak uymas\u0131n\u0131n garanti edilememesidir. Dolay\u0131s\u0131yla, bu belirsizli\u011fi yakalamak i\u00e7in ger\u00e7ek pop\u00fclasyon standart sapmas\u0131n\u0131 i\u00e7ermesi muhtemel bir dizi de\u011fer i\u00e7eren bir g\u00fcven aral\u0131\u011f\u0131 olu\u015fturabiliriz.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Bir standart sapma i\u00e7in g\u00fcven aral\u0131\u011f\u0131: form\u00fcl<\/strong><\/span><\/h3>\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 = [\u221a(n-1)s <sup>2<\/sup> \/X <sup>2<\/sup> <sub>\u03b1\/2<\/sub> , \u221a(n-1)s <sup>2<\/sup> \/X <sup>2<\/sup> <sub>1-\u03b1\/2<\/sub> ]<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n:<\/strong> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc<\/span><\/li>\n<li> <strong>s:<\/strong> numune standart sapmas\u0131<\/li>\n<li> <span style=\"color: #000000;\"><strong>X <sup>2<\/sup> :<\/strong> n-1 serbestlik derecesine sahip Ki karenin kritik de\u011feri.<\/span><\/li>\n<\/ul>\n<h3> <span style=\"color: #000000;\"><strong>Standart sapma i\u00e7in g\u00fcven aral\u0131\u011f\u0131: \u00f6rnek<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki bilgileri i\u00e7eren rastgele bir kaplumba\u011fa \u00f6rne\u011fi toplad\u0131\u011f\u0131m\u0131z\u0131 varsayal\u0131m:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc <strong>n = 27<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\">\u00d6rneklem standart sapmas\u0131 <strong>s = 6,43<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Ger\u00e7ek pop\u00fclasyon standart sapmas\u0131 i\u00e7in farkl\u0131 g\u00fcven aral\u0131klar\u0131n\u0131 nas\u0131l bulaca\u011f\u0131n\u0131z a\u015fa\u011f\u0131da a\u00e7\u0131klanm\u0131\u015ft\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>%90 g\u00fcven aral\u0131\u011f\u0131:<\/strong> [ <strong>\u221a<\/strong> (27-1)*6,43 <sup>2<\/sup> \/38,885, <strong>\u221a<\/strong> (27-1)*6,43 <sup>2 \/<\/sup> 15,379) = <strong>[5,258, 8,361]<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>%95 g\u00fcven aral\u0131\u011f\u0131:<\/strong> [ <strong>\u221a<\/strong> (27-1)*6,43 <sup>2<\/sup> \/41,923, <strong>\u221a<\/strong> (27-1)*6,43 <sup>2 \/<\/sup> 13,844) = <strong>[5,064, 8,812]<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>%99 g\u00fcven aral\u0131\u011f\u0131:<\/strong> [ <strong>\u221a<\/strong> (27-1)*6,43 <sup>2<\/sup> \/48,289, <strong>\u221a<\/strong> (27-1)*6,43 <sup>2 \/<\/sup> 11,160) = <strong>[4,718, 9,814]<\/strong><\/span><\/p>\n<p> <em><span style=\"color: #000000;\"><strong>Not:<\/strong> Bu g\u00fcven aral\u0131klar\u0131n\u0131 <a href=\"https:\/\/statorials.org\/tr\" target=\"_blank\" rel=\"noopener\">Standart Sapma Hesaplay\u0131c\u0131s\u0131 i\u00e7in G\u00fcven Aral\u0131\u011f\u0131&#8217;n\u0131<\/a> kullanarak da bulabilirsiniz.<\/span><\/em><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Bir standart sapma i\u00e7in g\u00fcven aral\u0131\u011f\u0131: yorumlama<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bir g\u00fcven aral\u0131\u011f\u0131n\u0131 yorumlama \u015feklimiz \u015fu \u015fekildedir:<\/span><\/p>\n<blockquote>\n<p> <span style=\"color: #000000;\">[5,064, 8,812] g\u00fcven aral\u0131\u011f\u0131n\u0131n ger\u00e7ek pop\u00fclasyon standart sapmas\u0131n\u0131 i\u00e7erme olas\u0131l\u0131\u011f\u0131 %95&#8217;tir.<\/span><\/p>\n<\/blockquote>\n<p> <span style=\"color: #000000;\">Ayn\u0131 \u015feyi s\u00f6ylemenin ba\u015fka bir yolu da, ger\u00e7ek pop\u00fclasyon standart sapmas\u0131n\u0131n %95 g\u00fcven aral\u0131\u011f\u0131n\u0131n d\u0131\u015f\u0131nda olma ihtimalinin yaln\u0131zca %5 oldu\u011fudur. Yani, ger\u00e7ek pop\u00fclasyon standart sapmas\u0131n\u0131n 8.812&#8217;den b\u00fcy\u00fck veya 5.064&#8217;ten k\u00fc\u00e7\u00fck olma ihtimali yaln\u0131zca %5&#8217;tir.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Standart sapma i\u00e7in g\u00fcven aral\u0131\u011f\u0131, belirli bir g\u00fcven d\u00fczeyine sahip bir pop\u00fclasyon standart sapmas\u0131n\u0131 i\u00e7ermesi muhtemel bir de\u011fer aral\u0131\u011f\u0131d\u0131r. Bu e\u011fitimde a\u015fa\u011f\u0131dakiler a\u00e7\u0131klanmaktad\u0131r: Bu g\u00fcven aral\u0131\u011f\u0131n\u0131 yaratma motivasyonu. Bu g\u00fcven aral\u0131\u011f\u0131n\u0131 olu\u015fturman\u0131n form\u00fcl\u00fc. Bu g\u00fcven aral\u0131\u011f\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131na dair bir \u00f6rnek. Bu g\u00fcven aral\u0131\u011f\u0131 nas\u0131l yorumlan\u0131r? Bir standart sapma i\u00e7in g\u00fcven aral\u0131\u011f\u0131: motivasyon Standart sapma [&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-738","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 standart sapma i\u00e7in g\u00fcven aral\u0131\u011f\u0131 \u2013 Statorials<\/title>\n<meta name=\"description\" content=\"Ad\u0131m ad\u0131m \u00f6rnekler de dahil olmak \u00fczere, standart sapma i\u00e7in g\u00fcven aral\u0131\u011f\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131na 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\" 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