{"id":192118,"date":"2025-02-17T09:59:16","date_gmt":"2025-02-17T09:59:16","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=192118"},"modified":"2025-02-17T09:59:18","modified_gmt":"2025-02-17T09:59:18","slug":"imagine-you-are-doing-a-related-samples-t-test-and-you-are-on-step-three-of-the-hypothesis-test","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/17\/imagine-you-are-doing-a-related-samples-t-test-and-you-are-on-step-three-of-the-hypothesis-test\/","title":{"rendered":"Imagine you are doing a Related-Samples t-test, and you are on Step Three of the hypothesis test"},"content":{"rendered":"\n

Imagine you are doing a Related-Samples t-test, and you are on Step Three of the hypothesis test.\u00c3\u201a\u00c2 The sample of difference scores that you calculated is -2, -4, -3, +1.\u00c3\u201a\u00c2 What is the correct t-obtained?\u00c3\u201a\u00c2 NOTE: The answer options also show many numbers that you calculate as part of the WORK for getting the t-obtained.\u00c3\u201a\u00c2 VERY IMPORTANT HINT: The SS of these difference scores is\u00c3\u201a\u00c2 14.00. Group of answer choices
Imagine you are doing a Related-Samples t-test, and you are on Step Three of the hypothesis test.\u00c3\u201a\u00c2 The sample of difference scores that you calculated is -2, -4, -3, +1.\u00c3\u201a\u00c2 What is the correct t-obtained?\u00c3\u201a\u00c2<\/p>\n\n\n\n

NOTE: The answer options also show many numbers that you calculate as part of the WORK for getting the t-obtained.\u00c3\u201a\u00c2<\/p>\n\n\n\n

VERY IMPORTANT HINT: The SS of these difference scores is\u00c3\u201a\u00c2 14.00.<\/p>\n\n\n\n

Group of answer choices<\/p>\n\n\n\n

    \n
  1. MD\u00c3\u201a\u00c2 (mean of D\u00c3\u00a2\u00e2\u201a\u00ac\u00e2\u201e\u00a2s) = -1.17<\/li>\n<\/ol>\n\n\n\n

    SD\u00c3\u201a\u00c2 (standard deviation of D\u00c3\u00a2\u00e2\u201a\u00ac\u00e2\u201e\u00a2s) = 2.14<\/p>\n\n\n\n

    SMD\u00c3\u201a\u00c2 (standard error) = 0.87<\/p>\n\n\n\n

    t-obt = -1.34<\/p>\n\n\n\n

      \n
    1. MD\u00c3\u201a\u00c2 (mean of D\u00c3\u00a2\u00e2\u201a\u00ac\u00e2\u201e\u00a2s) = -2.20<\/li>\n<\/ol>\n\n\n\n

      SD\u00c3\u201a\u00c2 (standard deviation of D\u00c3\u00a2\u00e2\u201a\u00ac\u00e2\u201e\u00a2s) = 3.35<\/p>\n\n\n\n

      SMD\u00c3\u201a\u00c2 (standard error) = 1.50<\/p>\n\n\n\n

      t-obt = -1.47<\/p>\n\n\n\n

        \n
      1. MD\u00c3\u201a\u00c2 (mean of D\u00c3\u00a2\u00e2\u201a\u00ac\u00e2\u201e\u00a2s) = -1.67<\/li>\n<\/ol>\n\n\n\n

        SD\u00c3\u201a\u00c2 (standard deviation of D\u00c3\u00a2\u00e2\u201a\u00ac\u00e2\u201e\u00a2s) = 3.21<\/p>\n\n\n\n

        SMD\u00c3\u201a\u00c2 (standard error) = 1.86<\/p>\n\n\n\n

        t-obt = -0.90<\/p>\n\n\n\n

          \n
        1. MD\u00c3\u201a\u00c2 (mean of D\u00c3\u00a2\u00e2\u201a\u00ac\u00e2\u201e\u00a2s) = -2.00<\/li>\n<\/ol>\n\n\n\n

          SD\u00c3\u201a\u00c2 (standard deviation of D\u00c3\u00a2\u00e2\u201a\u00ac\u00e2\u201e\u00a2s) = 2.16<\/p>\n\n\n\n

          SMD\u00c3\u201a\u00c2 (standard error) = 1.08<\/p>\n\n\n\n

          t-obt = -1.85<\/p>\n\n\n\n

          The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n

          The correct answer is option 4.<\/p>\n\n\n\n

          Here\u2019s how the calculations work:<\/p>\n\n\n\n

            \n
          1. Mean of the Difference Scores (MD)<\/strong>:
            [
            MD = \\frac{-2 + (-4) + (-3) + 1}{4} = \\frac{-8}{4} = -2.00
            ]
            So, MD is -2.00.<\/li>\n\n\n\n
          2. Standard Deviation (SD)<\/strong>:
            We are given the sum of squares (SS) for the difference scores, which is 14.00. To calculate the SD, we divide the SS by the degrees of freedom (which is (N-1) where (N) is the sample size) and then take the square root:
            [
            SD = \\sqrt{\\frac{SS}{N-1}} = \\sqrt{\\frac{14.00}{4-1}} = \\sqrt{\\frac{14.00}{3}} = 2.16
            ]<\/li>\n\n\n\n
          3. Standard Error of the Mean Difference (SMD)<\/strong>:
            The standard error (SMD) is calculated by dividing the SD by the square root of the sample size:
            [
            SMD = \\frac{SD}{\\sqrt{N}} = \\frac{2.16}{\\sqrt{4}} = \\frac{2.16}{2} = 1.08
            ]<\/li>\n\n\n\n
          4. t-obtained (t-obt)<\/strong>:
            Finally, the t-statistic is calculated as:
            [
            t_{obt} = \\frac{MD}{SMD} = \\frac{-2.00}{1.08} \\approx -1.85
            ]<\/li>\n<\/ol>\n\n\n\n

            Thus, the t-obtained is approximately -1.85, which corresponds to option 4.<\/p>\n\n\n\n

            Let me generate a visualization of this calculation process for clarity.<\/p>\n\n\n\n

            Here is the step-by-step visualization of the Related-Samples t-test calculation. It shows how we arrived at the mean of the differences, standard deviation, standard error, and the t-obtained value. Let me know if you need any further explanation!<\/p>\n\n\n\n

            \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

            Imagine you are doing a Related-Samples t-test, and you are on Step Three of the hypothesis test.\u00c3\u201a\u00c2 The sample of difference scores that you calculated is -2, -4, -3, +1.\u00c3\u201a\u00c2 What is the correct t-obtained?\u00c3\u201a\u00c2 NOTE: The answer options also show many numbers that you calculate as part of the WORK for getting the t-obtained.\u00c3\u201a\u00c2 […]<\/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-192118","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/192118","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=192118"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/192118\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=192118"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=192118"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=192118"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}