{"id":190812,"date":"2025-02-13T09:02:05","date_gmt":"2025-02-13T09:02:05","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=190812"},"modified":"2025-02-13T09:02:08","modified_gmt":"2025-02-13T09:02:08","slug":"if-a-p-value-for-your-hypothesis-testing-about-the-population-mean-is-0-073","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/13\/if-a-p-value-for-your-hypothesis-testing-about-the-population-mean-is-0-073\/","title":{"rendered":"If a p-value for your hypothesis testing about the population mean is 0.073"},"content":{"rendered":"\n<p>If a p-value for your hypothesis testing about the population mean is 0.073 , and the level of significance used was 5%, then the conclusion would be to: Select one: a. Reject the null hypothesis H subscript o b. Don\u00c3\u00a2\u00e2\u201a\u00ac\u00e2\u201e\u00a2t Reject the null hypothesis H subscript o c. Not enough information to make conclusion d. Accept the alternative hypothesis H subscript a If a p-value for your hypothesis testing about the population mean is 0.073 , and the level of significance used was 5%, then the conclusion would be to: Select one: a. Reject the null hypothesis H subscript o b. Don\u00c3\u00a2\u00e2\u201a\u00ac\u00e2\u201e\u00a2t Reject the null hypothesis H subscript o c. Not enough information to make conclusion d. Accept the alternative hypothesis H subscript a<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>The correct answer is:<br><strong>b. Don\u2019t Reject the null hypothesis H\u2080<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>In hypothesis testing, the <strong>p-value<\/strong> represents the probability of obtaining results at least as extreme as the observed data, assuming the null hypothesis (<strong>H\u2080<\/strong>) is true. The level of significance (<strong>\u03b1<\/strong>) is the threshold set to determine whether the null hypothesis should be rejected.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Step 1: Compare the p-value to \u03b1<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Given <strong>p-value = 0.073<\/strong><\/li>\n\n\n\n<li>Given <strong>\u03b1 = 0.05 (5%)<\/strong><\/li>\n\n\n\n<li>The rule states: If <strong>p-value \u2264 \u03b1<\/strong>, reject <strong>H\u2080<\/strong>. Otherwise, do not reject <strong>H\u2080<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>Since <strong>0.073 &gt; 0.05<\/strong>, the p-value is greater than the significance level. This means that there is not enough statistical evidence to reject the null hypothesis at a 5% significance level.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Step 2: Interpreting the Decision<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u201cDo not reject H\u2080\u201d<\/strong> means that the evidence is insufficient to conclude that the alternative hypothesis (<strong>H\u2090<\/strong>) is true.<\/li>\n\n\n\n<li>This does NOT mean that H\u2080 is accepted as true\u2014only that we do not have strong enough evidence against it.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Step 3: Common Misconceptions<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Rejecting H\u2080<\/strong> means that we have strong statistical evidence supporting H\u2090. Since <strong>p = 0.073 is slightly higher than 0.05<\/strong>, the evidence is <strong>not strong enough<\/strong> to reject H\u2080.<\/li>\n\n\n\n<li><strong>Failing to reject H\u2080 does not prove H\u2080 is true<\/strong>\u2014it just means we lack enough evidence to conclude otherwise.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Conclusion:<\/h4>\n\n\n\n<p>Since the p-value (0.073) is greater than the significance level (0.05), we <strong>do not reject the null hypothesis<\/strong>. This means there is not enough evidence to support the alternative hypothesis.<\/p>\n\n\n\n<p>Thus, the correct choice is: <strong>b. Don\u2019t reject the null hypothesis H\u2080<\/strong>.<\/p>\n\n\n\n<p>Here is an illustration of hypothesis testing decision-making, showing the process of comparing the p-value to the significance level (\u03b1) and concluding whether to reject or not reject the null hypothesis. Let me know if you need any modifications!<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/02\/image-470.png\" alt=\"\" class=\"wp-image-190813\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>If a p-value for your hypothesis testing about the population mean is 0.073 , and the level of significance used was 5%, then the conclusion would be to: Select one: a. Reject the null hypothesis H subscript o b. Don\u00c3\u00a2\u00e2\u201a\u00ac\u00e2\u201e\u00a2t Reject the null hypothesis H subscript o c. Not enough information to make conclusion d. [&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-190812","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/190812","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=190812"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/190812\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=190812"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=190812"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=190812"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}