{"id":196859,"date":"2025-03-06T07:57:04","date_gmt":"2025-03-06T07:57:04","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=196859"},"modified":"2025-03-06T07:57:06","modified_gmt":"2025-03-06T07:57:06","slug":"a-researcher-conducted-a-study-with-42-coronary-artery-bypass-surgeries-and-found-the-sample-complete-the-surgery-to-be-2-hours","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/06\/a-researcher-conducted-a-study-with-42-coronary-artery-bypass-surgeries-and-found-the-sample-complete-the-surgery-to-be-2-hours\/","title":{"rendered":"A researcher conducted a study with 42 coronary artery bypass surgeries and found the sample complete the surgery to be 2 hours"},"content":{"rendered":"\n

A researcher conducted a study with 42 coronary artery bypass surgeries and found the sample complete the surgery to be 2 hours. Suppose the accepted population standard deviation is 1.3 less than the regional average of 2 hours. At a significance level of a=0.05, what is the p-value for this test? Round to 4 decimal places. Provide your answer below:<\/p>\n\n\n\n

p-value =<\/p>\n\n\n\n

The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n

The p-value for this test is approximately 0.0000.<\/p>\n\n\n\n

Explanation:<\/strong><\/p>\n\n\n\n

To determine the p-value for this test, we can perform a one-sample z-test. The steps are as follows:<\/p>\n\n\n\n

    \n
  1. Formulate the Hypotheses:<\/strong><\/li>\n<\/ol>\n\n\n\n
      \n
    • Null Hypothesis (H\u2080): The mean surgery time is equal to the regional average (\u03bc = 2 hours).<\/li>\n\n\n\n
    • Alternative Hypothesis (H\u2081): The mean surgery time is different from the regional average (\u03bc \u2260 2 hours).<\/li>\n<\/ul>\n\n\n\n
        \n
      1. Calculate the Test Statistic:<\/strong> The z-test statistic is calculated using the formula: [ z = \\frac{\\bar{x} – \\mu}{\\frac{\\sigma}{\\sqrt{n}}} ] Where:<\/li>\n<\/ol>\n\n\n\n
          \n
        • (\\bar{x}) is the sample mean<\/li>\n\n\n\n
        • (\\mu) is the population mean<\/li>\n\n\n\n
        • (\\sigma) is the population standard deviation<\/li>\n\n\n\n
        • (n) is the sample size Given:<\/li>\n\n\n\n
        • Sample mean ((\\bar{x})) = 2 hours<\/li>\n\n\n\n
        • Population mean ((\\mu)) = 2 hours<\/li>\n\n\n\n
        • Population standard deviation ((\\sigma)) = 1.3 hours<\/li>\n\n\n\n
        • Sample size ((n)) = 42 Plugging in these values: [ z = \\frac{2 – 2}{\\frac{1.3}{\\sqrt{42}}} = 0 ]<\/li>\n<\/ul>\n\n\n\n
            \n
          1. Determine the P-Value:<\/strong> A z-score of 0 corresponds to a p-value of 1. However, since this is a two-tailed test, we need to consider the areas in both tails of the standard normal distribution. The p-value is calculated as: [ \\text{p-value} = 2 \\times (1 – \\Phi(|z|)) ] Where (\\Phi) is the cumulative distribution function of the standard normal distribution.\ue206 Since |z| = 0, (\\Phi(0) = 0.5), thus:\ue206 [ \\text{p-value} = 2 \\times (1 – 0.5) = 2 \\times 0.5 = 1 ]<\/li>\n\n\n\n
          2. Compare with Significance Level:<\/strong> The significance level ((\\alpha)) is 0.05. Since the p-value (1) is greater than (\\alpha), we fail to reject the null hypothesis.<\/li>\n<\/ol>\n\n\n\n

            Conclusion:<\/strong><\/p>\n\n\n\n

            Based on the sample data, there is no statistically significant difference between the mean surgery time and the regional average of 2 hours at the 0.05 significance level.<\/p>\n","protected":false},"excerpt":{"rendered":"

            A researcher conducted a study with 42 coronary artery bypass surgeries and found the sample complete the surgery to be 2 hours. Suppose the accepted population standard deviation is 1.3 less than the regional average of 2 hours. At a significance level of a=0.05, what is the p-value for this test? Round to 4 decimal […]<\/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-196859","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/196859","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=196859"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/196859\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=196859"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=196859"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=196859"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}