{"id":259346,"date":"2025-07-18T23:47:31","date_gmt":"2025-07-18T23:47:31","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=259346"},"modified":"2025-07-18T23:47:33","modified_gmt":"2025-07-18T23:47:33","slug":"the-f-statistic-from-an-experiment-with-k-equals-three-and-n-equals-50s-3-67-at-a-equals-0-05-will-you-reject-the-no-hypothesis","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/18\/the-f-statistic-from-an-experiment-with-k-equals-three-and-n-equals-50s-3-67-at-a-equals-0-05-will-you-reject-the-no-hypothesis\/","title":{"rendered":"The F statistic from an experiment with K equals three and N equals 50s 3.67 at a equals 0.05 Will you reject the no hypothesis"},"content":{"rendered":"\n
The F statistic from an experiment with K equals three and N equals 50s 3.67 at a equals 0.05 Will you reject the no hypothesis<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
To determine whether we reject the null hypothesis based on the given information, we need to compare the calculated F-statistic to the critical F-value from an F-distribution table.<\/p>\n\n\n\n
Degrees of freedom for the numerator (between groups) = K\u22121=3\u22121=2K – 1 = 3 – 1 = 2K\u22121=3\u22121=2<\/li>\n\n\n\n
Degrees of freedom for the denominator (within groups) = N\u2212K=50\u22123=47N – K = 50 – 3 = 47N\u2212K=50\u22123=47<\/li>\n<\/ul>\n<\/li>\n\n\n\n
Find the Critical F-Value:<\/strong> Using an F-distribution table or a statistical calculator for \u03b1=0.05\\alpha = 0.05\u03b1=0.05, we look up the critical value for F0.05,2,47F_{0.05, 2, 47}F0.05,2,47\u200b, where 2 is the degrees of freedom for the numerator and 47 is the degrees of freedom for the denominator. The critical F-value for \u03b1=0.05\\alpha = 0.05\u03b1=0.05, df1=2df_1 = 2df1\u200b=2, and df2=47df_2 = 47df2\u200b=47 is approximately 3.22<\/strong>.<\/li>\n\n\n\n
Decision Rule:<\/strong>\n
\n
If the calculated F-statistic is greater than the critical F-value, we reject the null hypothesis.<\/li>\n\n\n\n
If the calculated F-statistic is less than or equal to the critical F-value, we fail to reject the null hypothesis.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
Comparison:<\/strong>\n
\n
The calculated F-statistic is 3.67.<\/li>\n\n\n\n
The critical F-value at \u03b1=0.05\\alpha = 0.05\u03b1=0.05 is 3.22.<\/li>\n\n\n\n
Since 3.67 > 3.22, we reject the null hypothesis.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n
Conclusion:<\/h3>\n\n\n\n
We reject the null hypothesis because the calculated F-statistic (3.67) exceeds the critical value (3.22) at a significance level of 0.05. This indicates that there are statistically significant differences between the groups in the experiment.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"
The F statistic from an experiment with K equals three and N equals 50s 3.67 at a equals 0.05 Will you reject the no hypothesis The Correct Answer and Explanation is: To determine whether we reject the null hypothesis based on the given information, we need to compare the calculated F-statistic to the critical F-value […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-259346","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/259346","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=259346"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/259346\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=259346"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=259346"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=259346"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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