Hipotez testi,<\/strong> istatistiksel bir hipotezi reddetmek veya reddetmek i\u00e7in kullan\u0131lan bir prosed\u00fcrd\u00fcr. Bir hipotez testinde, bir pop\u00fclasyon parametresinin de\u011ferinin, s\u00f6z konusu pop\u00fclasyonun bir \u00f6rne\u011finde g\u00f6zlemlenen de\u011ferle uyumlu olup olmad\u0131\u011f\u0131na karar veririz.<\/p>\n Yani hipotez testinde istatistiksel bir \u00f6rnek analiz edilir ve elde edilen sonu\u00e7lara g\u00f6re \u00f6nceden kurulmu\u015f bir hipotezin reddedilip kabul edilmeyece\u011fine karar verilir.<\/p>\n Genel olarak, hipotez testinden bir hipotezin do\u011fru veya yanl\u0131\u015f oldu\u011fu sonucunun kesin olarak \u00e7\u0131kar\u0131lamayaca\u011f\u0131n\u0131, ancak bir hipotezin basit\u00e7e reddedildi\u011fini veya elde edilen sonu\u00e7lara dayanmad\u0131\u011f\u0131n\u0131 unutmay\u0131n. Dolay\u0131s\u0131yla, bir hipotezi test ederken, verilen karar\u0131n en olas\u0131 karar oldu\u011funa dair istatistiksel kan\u0131t olsa bile yine de hata yap\u0131labilir.<\/p>\n \u0130statistikte hipotez testine hipotez testi<\/strong> , hipotez testi<\/strong> veya anlaml\u0131l\u0131k testi<\/strong> de denir.<\/p>\n Hipotez testi teorisi \u0130ngiliz istatistik\u00e7i Ronald Fisher taraf\u0131ndan olu\u015fturuldu ve Jerzy Neyman ve Egon Pearson taraf\u0131ndan daha da geli\u015ftirildi. <\/p>\n Bir hipotez testi iki t\u00fcr istatistiksel hipotezden olu\u015fur:<\/p>\n Uygulamada alternatif hipotez, s\u0131f\u0131r hipotezinden \u00f6nce form\u00fcle edilir, \u00e7\u00fcnk\u00fc bir veri \u00f6rne\u011finin istatistiksel analiziyle desteklenmesi ama\u00e7lanan hipotezdir. Daha sonra s\u0131f\u0131r hipotezi, alternatif hipotezin \u00e7eli\u015fmesiyle basit\u00e7e form\u00fcle edilir.<\/p>\n Hipotez testleri iki farkl\u0131 t\u00fcrde s\u0131n\u0131fland\u0131r\u0131labilir:<\/p>\n \u0130ki kuyruklu hipotez testi<\/strong> <\/p>\n<\/p>\n Tek kuyruklu hipotez testi (sa\u011f kuyruk)<\/strong> <\/p>\n<\/p>\n Tek kuyruklu hipotez testi (sol kuyruk)<\/strong><\/strong> <\/p>\n<\/p>\n A\u015fa\u011f\u0131da detayl\u0131 olarak g\u00f6rece\u011fimiz gibi hipotez testi, her hipotez testi t\u00fcr\u00fcne ait karakteristik bir de\u011ferin hesaplanmas\u0131ndan olu\u015fur, bu de\u011fere hipotez test istatistikleri denir. Dolay\u0131s\u0131yla kontrast istatisti\u011fi hesapland\u0131ktan sonra bir sonuca varmak i\u00e7in a\u015fa\u011f\u0131daki iki b\u00f6lgeden hangisinde bulundu\u011funu g\u00f6zlemlemek gerekir:<\/p>\n K\u0131saca, e\u011fer test istatisti\u011fi ret b\u00f6lgesi i\u00e7erisinde kal\u0131yorsa s\u0131f\u0131r hipotezi reddedilir ve alternatif hipotez kabul edilir. Aksine, e\u011fer test istatisti\u011fi kabul b\u00f6lgesi i\u00e7inde kal\u0131yorsa s\u0131f\u0131r hipotezi kabul edilir ve alternatif hipotez reddedilir. <\/p>\n Red b\u00f6lgesi ile kabul b\u00f6lgesinin s\u0131n\u0131rlar\u0131n\u0131 olu\u015fturan de\u011ferlere kritik de\u011ferler<\/strong> denir, benzer \u015fekilde red b\u00f6lgesini tan\u0131mlayan de\u011fer aral\u0131\u011f\u0131na da g\u00fcven aral\u0131\u011f\u0131<\/strong> denir. Ve her iki de\u011fer de se\u00e7ilen \u00f6nem d\u00fczeyine<\/strong> ba\u011fl\u0131d\u0131r. <\/p>\n \u00d6te yandan, s\u0131f\u0131r hipotezini reddetme veya kabul etme karar\u0131, hipotez testinden elde edilen p de\u011ferinin<\/strong> (veya p de\u011ferinin) se\u00e7ilen anlaml\u0131l\u0131k d\u00fczeyiyle kar\u015f\u0131la\u015ft\u0131r\u0131lmas\u0131 yoluyla da verilebilir. <\/p>\n Hipotez testi ger\u00e7ekle\u015ftirmek i\u00e7in a\u015fa\u011f\u0131daki ad\u0131mlar izlenmelidir:<\/p>\n Hipotez testinde, bir hipotezi reddedip di\u011fer test hipotezini kabul ederken iki hatadan biri yap\u0131labilir:<\/p>\n \u00d6te yandan her bir hata t\u00fcr\u00fcn\u00fcn yap\u0131lma olas\u0131l\u0131\u011f\u0131 \u015fu \u015fekilde adland\u0131r\u0131l\u0131r:<\/p>\n Benzer \u015fekilde hipotez testinin g\u00fcc\u00fc<\/strong> , bo\u015f hipotezin (H 0<\/sub> ) yanl\u0131\u015f olmas\u0131 durumunda reddedilme olas\u0131l\u0131\u011f\u0131, ba\u015fka bir deyi\u015fle, do\u011fru oldu\u011funda alternatif hipotezin (H 1<\/sub> ) se\u00e7ilmesi olas\u0131l\u0131\u011f\u0131 olarak tan\u0131mlanmaktad\u0131r. Dolay\u0131s\u0131yla hipotez testinin g\u00fcc\u00fc 1-\u03b2’ya e\u015fittir. <\/p>\n Bir hipotez testinin istatisti\u011fi,<\/strong> s\u0131f\u0131r hipotezinin reddedilip reddedilmedi\u011fini belirlemek i\u00e7in kullan\u0131lan hipotez testi referans da\u011f\u0131l\u0131m\u0131n\u0131n de\u011feridir. Test istatisti\u011fi ret b\u00f6lgesine d\u00fc\u015ferse s\u0131f\u0131r hipotezi reddedilir (ve alternatif hipotez kabul edilir), di\u011fer taraftan, test istatisti\u011fi kabul b\u00f6lgesine d\u00fc\u015ferse s\u0131f\u0131r hipotezi kabul edilir (ve alternatif hipotez kabul edilir) reddedildi).alternatif hipotez).<\/p>\n Hipotez testi istatisti\u011finin hesaplanmas\u0131 testin t\u00fcr\u00fcne ba\u011fl\u0131d\u0131r. Bu nedenle, her bir hipotez testi t\u00fcr\u00fc i\u00e7in istatisti\u011fi hesaplama form\u00fcl\u00fc a\u015fa\u011f\u0131da g\u00f6sterilmi\u015ftir. <\/p>\n Bilinen varyansl\u0131 ortalamaya ili\u015fkin hipotez testi istatisti\u011finin form\u00fcl\u00fc<\/strong> \u015f\u00f6yledir:<\/p>\n<\/p>\n Alt\u0131n:<\/p>\n ortalama i\u00e7in hipotez kontrast istatisti\u011fidir.<\/li>\n \u00f6rnek anlam\u0131na gelir.<\/li>\n \u00f6nerilen ortalama de\u011ferdir.<\/li>\n n\u00fcfus standart sapmas\u0131d\u0131r.<\/li>\n \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcd\u00fcr.<\/li>\n<\/ul>\n Ortalama i\u00e7in hipotez testi istatisti\u011fi hesapland\u0131ktan sonra, sonu\u00e7 s\u0131f\u0131r hipotezini reddedip reddetmeyecek \u015fekilde yorumlanmal\u0131d\u0131r:<\/p>\n Bu durumda kritik de\u011ferler standartla\u015ft\u0131r\u0131lm\u0131\u015f normal da\u011f\u0131l\u0131m tablosundan elde edilir.<\/p>\n \u00d6te yandan bilinmeyen varyansl\u0131 ortalamaya ili\u015fkin hipotez testi istatisti\u011finin form\u00fcl\u00fc<\/strong> \u015f\u00f6yledir:<\/p>\n<\/p>\n Alt\u0131n:<\/p>\n \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131 ile tan\u0131mlanan ortalamaya ili\u015fkin hipotez testi istatisti\u011fidir.<\/li>\n \u00f6rnek anlam\u0131na gelir.<\/li>\n \u00f6nerilen ortalama de\u011ferdir.<\/li>\n \u00f6rnek standart sapmas\u0131d\u0131r.<\/li>\n \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcd\u00fcr.<\/li>\n<\/ul>\n Daha \u00f6nce oldu\u011fu gibi, test istatisti\u011finin hesaplanan sonucu, bo\u015f hipotezin reddedilmesi veya reddedilmemesi i\u00e7in kritik de\u011ferle yorumlanmal\u0131d\u0131r:<\/p>\n Varyans\u0131n bilinmedi\u011fi durumlarda kritik test de\u011ferleri \u00d6\u011frenci da\u011f\u0131l\u0131m tablosundan elde edilir. <\/p>\n Oran i\u00e7in hipotez test istatisti\u011finin form\u00fcl\u00fc<\/strong> \u015f\u00f6yledir:<\/p>\n<\/p>\n Alt\u0131n:<\/p>\n orana ili\u015fkin hipotez testi istatisti\u011fidir.<\/li>\n \u00f6rnek oran\u0131d\u0131r.<\/li>\n \u00f6nerilen orant\u0131 de\u011feridir.<\/li>\n \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcd\u00fcr.<\/li>\n oran\u0131n standart sapmas\u0131d\u0131r.<\/li>\n<\/ul>\n Oran i\u00e7in hipotez testi istatisti\u011fini hesaplaman\u0131n yeterli olmad\u0131\u011f\u0131n\u0131, ancak sonucun yorumlanmas\u0131 gerekti\u011fini unutmay\u0131n:<\/p>\n Kritik de\u011ferlerin standart normal da\u011f\u0131l\u0131m tablosundan kolayl\u0131kla elde edilebilece\u011fini unutmay\u0131n. <\/p>\n Varyans i\u00e7in hipotez testi istatisti\u011fini hesaplama form\u00fcl\u00fc<\/strong> \u015f\u00f6yledir:<\/p>\n<\/p>\n Alt\u0131n:<\/p>\n ki-kare da\u011f\u0131l\u0131m\u0131na sahip varyans i\u00e7in hipotez test istatisti\u011fidir.<\/li>\n \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcd\u00fcr.<\/li>\n \u00f6rnek varyans\u0131d\u0131r.<\/li>\n \u00f6nerilen pop\u00fclasyonun varyans\u0131d\u0131r.<\/li>\n<\/ul>\n \u0130statisti\u011fin sonucunun yorumlanabilmesi i\u00e7in elde edilen de\u011ferin testin kritik de\u011feri ile kar\u015f\u0131la\u015ft\u0131r\u0131lmas\u0131 gerekir.<\/p>\n <\/span> veya kritik de\u011ferin alt\u0131ndaysa<\/p>\n .<\/li>\n <\/span> .<\/li>\n <\/span> .<\/li>\n<\/ul>\n Varyansa ili\u015fkin kritik hipotez testi de\u011ferleri ki-kare da\u011f\u0131l\u0131m tablosundan elde edilir. Ki-kare da\u011f\u0131l\u0131m\u0131 i\u00e7in serbestlik derecesinin \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc eksi 1 oldu\u011funa dikkat edin.<\/p>\n","protected":false},"excerpt":{"rendered":" Bu makale istatistikte hipotez testinin ne oldu\u011funu a\u00e7\u0131klamaktad\u0131r. B\u00f6ylece bir hipotez testinin nas\u0131l yap\u0131laca\u011f\u0131n\u0131, farkl\u0131 hipotez testi t\u00fcrlerini ve bir hipotez testi ger\u00e7ekle\u015ftirirken yap\u0131labilecek olas\u0131 hatalar\u0131 \u00f6\u011freneceksiniz. Hipotez testi nedir? Hipotez testi, istatistiksel bir hipotezi reddetmek veya reddetmek i\u00e7in kullan\u0131lan bir prosed\u00fcrd\u00fcr. Bir hipotez testinde, bir pop\u00fclasyon parametresinin de\u011ferinin, s\u00f6z konusu pop\u00fclasyonun bir \u00f6rne\u011finde g\u00f6zlemlenen […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[14],"tags":[],"class_list":["post-271","post","type-post","status-publish","format-standard","hentry","category-istatistik"],"yoast_head":"\n<\/span> S\u0131f\u0131r hipotezi ve alternatif hipotez<\/span><\/h2>\n
\n
<\/span> Hipotez Testi T\u00fcrleri<\/span><\/h2>\n
\n
![\"\\begin{cases}H_0:](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-4f0c1b65b50009900a6facbefea23ca1_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n<\/div>\n![\"\\begin{cases}H_0:](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-1393df603c93485a0f75ebd0116c46a2_l3.png\")
\\mu_0\\end{cases}” title=”Rendered by QuickLaTeX.com” height=”65″ width=”102″ style=”vertical-align: 0px;”><\/p>\n<\/p>\n<\/div>\n![\"\\begin{cases}H_0:](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-570fdfa44817f5392b33075476008f80_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n<\/div>\n<\/div>\n<\/span> Bir hipotez testinin red b\u00f6lgesi ve kabul b\u00f6lgesi<\/span><\/h2>\n
\n
![\"Hipotez](\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/test-dhypothese-de-contraste.png\")
<\/figure>\n<\/span> Hipotez testi nas\u0131l yap\u0131l\u0131r<\/span><\/h2>\n
\n
\u27a4<\/span> Bak\u0131n\u0131z:<\/strong> Oran i\u00e7in hipotez testi<\/a>
\u27a4<\/span> Bak\u0131n\u0131z:<\/strong> Varyans i\u00e7in hipotez testi<\/a> <\/div>\n<\/span> Hipotez Testi Hatalar\u0131<\/span><\/h2>\n
\n
![\"tip](\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/erreur-type-i-et-erreur-type-ii.png\")
<\/figure>\n\n
<\/span> Hipotez Test \u0130statistikleri<\/span><\/h2>\n
<\/span> Ortalama i\u00e7in hipotez testi<\/span><\/h3>\n
![\"\\displaystyle](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-fdf1817a07bfb8c1eda9a8d8ccd8c828_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n\n
![\"Z\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0be116875001706f29a24434bd0d91c9_l3.png\" "\\"Rendered")
<\/p>\n![\"\\overline{x}\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a39858a792fb4fe9a3173e004701f2a7_l3.png\" "\\"Rendered")
<\/p>\n![\"\\mu\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-05d9eae892416bd34247a25207f8b718_l3.png\" "\\"Rendered")
<\/p>\n![\"\\sigma\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-eaaf379fee5e67946f3fedf5631047b1_l3.png\" "\\"Rendered")
<\/p>\n![\"n\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ec4217f4fa5fcd92a9edceba0e708cf7_l3.png\" "\\"Rendered")
<\/p>\n\n
![\"\\begin{array}{l}H_1:](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0e2ccadfc369eb7543b8f86dfccc528e_l3.png\")
Z_{\\alpha\/2} \\text{ se rechaza } H_0\\\\[3ex]H_1: \\mu> \\mu_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } Z>Z_{\\alpha} \\text{ se rechaza } H_0\\\\[3ex]H_1: \\mu< \\mu_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } Z<-Z_{\\alpha} \\text{ se rechaza } H_0\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"440\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n![\"\\displaystyle](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f8277d83b2d28325f25f5d118486200f_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n\n
![\"t\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-fd9cb27edab3f0a8a249bc80cc9c6ee2_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n<\/p>\n![\"s\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-1edc883862ceed1a21913f60358e31d8_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n\n
![\"\\begin{array}{l}H_1:](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-31fb206b75a47181c7c673f54ba28ee8_l3.png\")
t_{\\alpha\/2|n-1} \\text{ se rechaza } H_0\\\\[3ex]H_1: \\mu> \\mu_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } t>t_{\\alpha|n-1} \\text{ se rechaza } H_0\\\\[3ex]H_1: \\mu< \\mu_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } t<-t_{\\alpha|n-1} \\text{ se rechaza } H_0\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"112\" width=\"457\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<\/span> Orant\u0131 i\u00e7in hipotez testi<\/span><\/h3>\n
![\"\\displaystyle](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-e2f5ad36dae72cd89279809ab3ea6d20_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n\n
<\/p>\n![\"\\widehat{p}\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ecd29d136a62fc6b274e1181e064e20e_l3.png\" "\\"Rendered")
<\/p>\n![\"p\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5faad0904f612a3fa5b27faafb8dc903_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\displaystyle\\sqrt{\\frac{p(1-p)}{n}}\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-661a2bbf8dccd197bcf450330420cbc1_l3.png\" "\\"Rendered")
<\/p>\n\n
![\"\\begin{array}{l}H_1:](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7d5bd583532769e3014286e8ffd94c9f_l3.png\")
Z_{\\alpha\/2} \\text{ se rechaza } H_0\\\\[3ex]H_1: p> p_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } Z>Z_{\\alpha} \\text{ se rechaza } H_0\\\\[3ex]H_1: p< p_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } Z<-Z_{\\alpha} \\text{ se rechaza } H_0\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"437\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<\/span> Varyans i\u00e7in hipotez testi<\/span><\/h3>\n
![\"\\chi^2=\\cfrac{(n-1)s^2}{\\sigma^2}\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-3917636d4c911eeaad1a005195204d08_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n\n
![\"\\chi^2\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-984dc78529fc235b078a9f3b62d0f0c4_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"s^2\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-3ab572e85f9cb7cb6f495387f2a6ab0b_l3.png\" "\\"Rendered")
<\/p>\n![\"\\sigma^2\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c6d52162ef1ec2e8130fb00687aca707_l3.png\" "\\"Rendered")
<\/p>\n\n
![\"\\chi_{1-\\alpha\/2|n-1}^2\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7bd4ac2951fb286bf19797944cba6955_l3.png\" "\\"Rendered")
<\/p>\n![\"\\chi_{\\alpha\/2|n-1}\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-931a3f10ab51df1c9003e6cb593907c4_l3.png\" "\\"Rendered")
<\/p>\n![\"\\chi_{1-\\alpha|n-1}^2\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-243ef3cc114070613fd8bee8c61f8c13_l3.png\" "\\"Rendered")
<\/p>\n![\"\\chi_{\\alpha|n-1}\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0436c61e0bdff7a21f6e6ab296607c66_l3.png\" "\\"Rendered")
<\/p>\n![\"\\begin{array}{l}H_1:](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ca46378c1a2ee04b5cc5bfa93002fe9c_l3.png\")
\\chi^2_{1-\\alpha\/2|n-1}\\text{ se rechaza } H_0\\\\[3ex]H_1: \\sigma^2\\neq \\sigma_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si }\\chi^2<\\chi^2_{\\alpha\/2|n-1}\\text{ se rechaza } H_0 \\\\[3ex]H_1: \\sigma^2> \\sigma_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } \\chi^2>\\chi^2_{1-\\alpha|n-1}\\text{ se rechaza } H_0\\\\[3ex]H_1: \\sigma^2< \\sigma_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } \\chi^2<\\chi^2_{\\alpha|n-1}\\text{ se rechaza } H_0\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"160\" width=\"489\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n