{"id":1031,"date":"2023-07-27T22:11:31","date_gmt":"2023-07-27T22:11:31","guid":{"rendered":"https:\/\/statorials.org\/tr\/basari-icin-basarisizlik-kosulu\/"},"modified":"2023-07-27T22:11:31","modified_gmt":"2023-07-27T22:11:31","slug":"basari-icin-basarisizlik-kosulu","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/basari-icin-basarisizlik-kosulu\/","title":{"rendered":"I\u0307statistiklerde ba\u015far\u0131l\u0131\/ba\u015far\u0131s\u0131z durumu nedir?"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Bir <strong>Bernoulli denemesi<\/strong> yaln\u0131zca iki olas\u0131 sonucu olan bir deneydir \u2013 \u201cba\u015far\u0131l\u0131\u201d veya \u201cba\u015far\u0131s\u0131z\u201d ve ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 deney her yap\u0131ld\u0131\u011f\u0131nda ayn\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bernoulli makalesinin bir \u00f6rne\u011fi yaz\u0131 tura atmakt\u0131r. Para yaln\u0131zca iki tura gelebilir (turalara &#8220;vuru\u015f&#8221;, yaz\u0131lara ise &#8220;ba\u015far\u0131s\u0131zl\u0131k&#8221; diyebiliriz) ve paran\u0131n adil oldu\u011funu varsayarsak, her at\u0131\u015fta ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 0,5&#8217;tir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0130statistikte genellikle birka\u00e7 Bernoulli denemesinden fazlas\u0131n\u0131 i\u00e7eren olas\u0131l\u0131klar\u0131 hesaplamak istedi\u011fimizde yakla\u015f\u0131kl\u0131k olarak normal da\u011f\u0131l\u0131m\u0131 kullan\u0131r\u0131z. Ancak bunu yapabilmek i\u00e7in <strong>ba\u015far\u0131l\u0131\/ba\u015far\u0131s\u0131z ko\u015fulunun<\/strong> kar\u015f\u0131lan\u0131p kar\u015f\u0131lanmad\u0131\u011f\u0131n\u0131 kontrol etmemiz gerekir:<\/span><\/p>\n<blockquote>\n<p> <span style=\"color: #000000;\"><strong>Ba\u015far\u0131l\u0131\/Ba\u015far\u0131s\u0131z Durumu:<\/strong> Normal da\u011f\u0131l\u0131m\u0131n yakla\u015f\u0131k olarak kullan\u0131labilmesi i\u00e7in bir numunede en az 10 beklenen ba\u015far\u0131 ve 10 beklenen ba\u015far\u0131s\u0131zl\u0131k olmal\u0131d\u0131r.<\/span><\/p>\n<\/blockquote>\n<p> <span style=\"color: #000000;\">G\u00f6sterimle yaz\u0131ld\u0131\u011f\u0131nda a\u015fa\u011f\u0131daki iki \u015feyi kontrol etmemiz gerekir:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Beklenen ba\u015far\u0131 say\u0131s\u0131 en az 10: <strong>np \u2265 10<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\">Beklenen ar\u0131za say\u0131s\u0131 en az 10&#8217;dur: <strong>n(1-p) \u2265 10<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">burada <em>n<\/em> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc ve <em>p<\/em> belirli bir deneme i\u00e7in ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><em><strong>Not:<\/strong> Baz\u0131 k\u0131lavuzlar normal yakla\u015f\u0131m\u0131 kullanmak i\u00e7in yaln\u0131zca 5 beklenen ba\u015far\u0131n\u0131n ve 5 beklenen ba\u015far\u0131s\u0131zl\u0131\u011f\u0131n gerekli oldu\u011funu s\u00f6yl\u00fcyor. Ancak 10 daha yayg\u0131n olarak kullan\u0131l\u0131r ve daha ihtiyatl\u0131 bir say\u0131d\u0131r. Bu nedenle bu derste bu say\u0131y\u0131 kullanaca\u011f\u0131z.<\/em><\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek: Ba\u015far\u0131l\u0131\/ba\u015far\u0131s\u0131z ko\u015fulunun kontrol edilmesi<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bir il\u00e7ede belirli bir yasay\u0131 destekleyen sakinlerin oran\u0131 i\u00e7in bir g\u00fcven aral\u0131\u011f\u0131 olu\u015fturmak istedi\u011fimizi varsayal\u0131m. 100 sakinden rastgele bir \u00f6rnek se\u00e7iyoruz ve onlara yasadaki konumlar\u0131n\u0131n ne oldu\u011funu soruyoruz. Sonu\u00e7lar burada:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc <strong>n = 100<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\">Kanun lehine oran <strong>p = 0,56<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">G\u00fcven aral\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanmak istiyoruz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>G\u00fcven aral\u0131\u011f\u0131 = p<\/strong> <strong>+\/- z*\u221a <span style=\"border-top: 1px solid black;\">p(1-p) \/ n<\/span><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>p:<\/strong> \u00f6rnek oran\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>z:<\/strong> normal da\u011f\u0131l\u0131ma kar\u015f\u0131l\u0131k gelen z de\u011feri<\/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;\">Bu form\u00fcl normal da\u011f\u0131l\u0131mdan az de\u011ferini kullan\u0131r. Dolay\u0131s\u0131yla bu form\u00fclde binom da\u011f\u0131l\u0131m\u0131na yakla\u015fmak i\u00e7in normal da\u011f\u0131l\u0131m\u0131 kullan\u0131yoruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ancak bunu yapabilmek i\u00e7in <strong>ba\u015far\u0131l\u0131\/ba\u015far\u0131s\u0131z ko\u015fulunun<\/strong> kar\u015f\u0131land\u0131\u011f\u0131n\u0131 do\u011frulamam\u0131z gerekir. \u00d6rnekteki ba\u015far\u0131l\u0131 ve ba\u015far\u0131s\u0131zl\u0131k say\u0131s\u0131n\u0131n en az 10 oldu\u011funu kontrol edelim:<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ba\u015far\u0131 say\u0131s\u0131: np = 100*.56 = <strong>56<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Ar\u0131za say\u0131s\u0131: n(1-p) = 100*(1-.56) = <strong>44<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Her iki say\u0131 da 10&#8217;a e\u015fit veya 10&#8217;dan b\u00fcy\u00fck oldu\u011fundan g\u00fcven aral\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in yukar\u0131daki form\u00fcl\u00fc kullanabiliriz.<\/span><\/p>\n<h3> <strong>Ek kaynaklar<\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Normal da\u011f\u0131l\u0131m\u0131n binom da\u011f\u0131l\u0131m\u0131na yakla\u015f\u0131m olarak kullan\u0131labilmesi i\u00e7in yerine getirilmesi gereken bir di\u011fer ko\u015ful da, \u00fczerinde \u00e7al\u0131\u015ft\u0131\u011f\u0131m\u0131z \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fcn evren b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fcn %10&#8217;unu ge\u00e7memesidir. Buna %10 ko\u015fulu denir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ayr\u0131ca iki oran ile \u00e7al\u0131\u015f\u0131yorsan\u0131z (\u00f6rne\u011fin <a href=\"https:\/\/statorials.org\/tr\/orantilarin-guven-araligi-farki\/\" target=\"_blank\" rel=\"noopener noreferrer\">oranlar aras\u0131ndaki fark i\u00e7in bir g\u00fcven aral\u0131\u011f\u0131 olu\u015fturmak<\/a> ), <em>iki<\/em> \u00f6rnekte beklenen ba\u015far\u0131 ve ba\u015far\u0131s\u0131zl\u0131k say\u0131s\u0131n\u0131n en az 10 oldu\u011funu kontrol etmeniz gerekti\u011fini unutmay\u0131n.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bir Bernoulli denemesi yaln\u0131zca iki olas\u0131 sonucu olan bir deneydir \u2013 \u201cba\u015far\u0131l\u0131\u201d veya \u201cba\u015far\u0131s\u0131z\u201d ve ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 deney her yap\u0131ld\u0131\u011f\u0131nda ayn\u0131d\u0131r. Bernoulli makalesinin bir \u00f6rne\u011fi yaz\u0131 tura atmakt\u0131r. Para yaln\u0131zca iki tura gelebilir (turalara &#8220;vuru\u015f&#8221;, yaz\u0131lara ise &#8220;ba\u015far\u0131s\u0131zl\u0131k&#8221; diyebiliriz) ve paran\u0131n adil oldu\u011funu varsayarsak, her at\u0131\u015fta ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 0,5&#8217;tir. \u0130statistikte genellikle birka\u00e7 Bernoulli denemesinden fazlas\u0131n\u0131 [&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-1031","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>\u0130statistiklerde ba\u015far\u0131l\u0131\/ba\u015far\u0131s\u0131z durumu nedir? - Statoryaller<\/title>\n<meta name=\"description\" content=\"Bir tan\u0131m ve \u00e7e\u015fitli \u00f6rnekler de dahil olmak \u00fczere istatistiklerdeki ba\u015far\u0131l\u0131-ba\u015far\u0131s\u0131z ko\u015fulunun basit bir a\u00e7\u0131klamas\u0131.\" \/>\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\/basari-icin-basarisizlik-kosulu\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0130statistiklerde ba\u015far\u0131l\u0131\/ba\u015far\u0131s\u0131z durumu nedir? 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