{"id":258510,"date":"2025-07-18T07:27:54","date_gmt":"2025-07-18T07:27:54","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=258510"},"modified":"2025-07-18T07:27:56","modified_gmt":"2025-07-18T07:27:56","slug":"the-chi-square-value-for-a-one-tailed-upper-tail-hypothesis-test-at-95-confidence-and-a-sample-size-of-25-is-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/18\/the-chi-square-value-for-a-one-tailed-upper-tail-hypothesis-test-at-95-confidence-and-a-sample-size-of-25-is-2\/","title":{"rendered":"The chi-square value for a one-tailed (upper tail) hypothesis test at 95% confidence and a sample size of 25 is"},"content":{"rendered":"\n<p>The chi-square value for a one-tailed (upper tail) hypothesis test at 95% confidence and a sample size of 25 is <\/p>\n\n\n\n<p>Select one: <\/p>\n\n\n\n<p>a. 39.3641 <\/p>\n\n\n\n<p>b. 37.6525 <\/p>\n\n\n\n<p>c. 36.4151 <\/p>\n\n\n\n<p>d. 33.1963<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The correct answer is <strong>b. 37.6525<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>The chi-square test is commonly used to test hypotheses about variances or to assess goodness of fit. The chi-square distribution is widely used in statistical hypothesis testing, especially in the context of variances and categorical data.<\/p>\n\n\n\n<p>For a <strong>one-tailed (upper tail)<\/strong> hypothesis test, you are interested in determining the critical value where the upper tail area corresponds to the desired confidence level. In this case, the hypothesis test is conducted at a 95% confidence level, meaning the alpha level (\u03b1\\alpha) is 0.05, and you are looking for the critical value that corresponds to the upper 5% of the chi-square distribution.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">How to find the chi-square critical value:<\/h3>\n\n\n\n<p>The chi-square distribution depends on the <strong>degrees of freedom (df)<\/strong>, which is determined by the sample size. For this case, the sample size is 25, so the degrees of freedom are calculated as: df=n\u22121=25\u22121=24df = n &#8211; 1 = 25 &#8211; 1 = 24<\/p>\n\n\n\n<p>Next, the chi-square critical value for a one-tailed test is located by looking up the value corresponding to the <strong>upper 5%<\/strong> (i.e., 0.05) in a chi-square distribution table, using 24 degrees of freedom. From standard chi-square distribution tables or using statistical software, the chi-square critical value for <strong>df = 24<\/strong> at <strong>\u03b1=0.05\\alpha = 0.05<\/strong> is approximately <strong>37.6525<\/strong>.<\/p>\n\n\n\n<p>This value indicates the threshold beyond which you would reject the null hypothesis if your calculated chi-square statistic exceeds this value. Thus, if the chi-square value from your data is greater than 37.6525, you would conclude that the observed data is inconsistent with the null hypothesis at the 95% confidence level.<\/p>\n\n\n\n<p>To summarize:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Sample size<\/strong>: 25<\/li>\n\n\n\n<li><strong>Degrees of freedom (df)<\/strong>: 24<\/li>\n\n\n\n<li><strong>Confidence level<\/strong>: 95%<\/li>\n\n\n\n<li><strong>Critical chi-square value<\/strong>: 37.6525<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>The chi-square value for a one-tailed (upper tail) hypothesis test at 95% confidence and a sample size of 25 is Select one: a. 39.3641 b. 37.6525 c. 36.4151 d. 33.1963 The correct answer and explanation is: The correct answer is b. 37.6525. Explanation: The chi-square test is commonly used to test hypotheses about variances or [&hellip;]<\/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-258510","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/258510","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=258510"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/258510\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=258510"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=258510"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=258510"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}