{"id":242715,"date":"2025-07-04T08:56:16","date_gmt":"2025-07-04T08:56:16","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=242715"},"modified":"2025-07-04T08:56:18","modified_gmt":"2025-07-04T08:56:18","slug":"nick-my-home-courses-mindtap-cengage-learning-ng-cengage-com-static-nb-ui-evo-index-html","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/04\/nick-my-home-courses-mindtap-cengage-learning-ng-cengage-com-static-nb-ui-evo-index-html\/","title":{"rendered":"Nick My Home Courses MindTap – Cengage Learning ng.cengage.com\/static\/nb\/ui\/evo\/index.html"},"content":{"rendered":"\n

HW 64 ? C Nick My Home Courses MindTap – Cengage Learning ng.cengage.com\/static\/nb\/ui\/evo\/index.html?deploymentid=5991401881038963484592120786&ISBN=9780357131466&id=1798221981&snapshotid=3481785& CENGAGE MINDTAP Chapter 13 Assignment Assignment: Chapter 13 Assignment ? Q Search this course 0 X Assignment Save Submit Assignment for Grading ? Catalog and Study Tools Questions Exercise 13.05 Algo (Analysis of Variance and the Completely Randomized Design) Question 2 of 8 A-Z Rental Options College Success Tips Hint(s) Check My Work (3 remaining) Career Success Tips In a completely randomized design, 12 experimental units were used for the first treatment, 15 for the second treatment, and 20 for the third treatment. Complete the following analysis of variance (to 2 decimals, if necessary). If the answer is zero enter “0”. Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Help Give Feedback Treatments 1000 Error 1800 Total At a 0.05 level of significance, is there a significant difference between the treatments? The
-value is Select your answer What is your conclusion? Select your answer Exercise 13.05 Algo (Analysis of Variance and the Completely Randomized Design) ? Hint(s) Check My Work (3 remaining) Question 2 of 8 Save Submit Assignment for Grading 88\u00b0F Sunny 3:34 PM 7\/13\/2023<\/p>\n\n\n\n

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

Here are the completed values for the Analysis of Variance (ANOVA) table and the conclusion based on the hypothesis test.<\/p>\n\n\n\n

Completed ANOVA Table:<\/strong><\/p>\n\n\n\n

Source of Variation<\/td>Sum of Squares<\/td>Degrees of Freedom<\/td>Mean Square<\/td>F<\/td>p-value<\/td><\/tr>
Treatments<\/td>1000<\/td>2<\/strong><\/td>500.00<\/strong><\/td>27.50<\/strong><\/td>0.00<\/strong><\/td><\/tr>
Error<\/td>800<\/strong><\/td>44<\/strong><\/td>18.18<\/strong><\/td><\/td><\/td><\/tr>
Total<\/td>1800<\/td>46<\/strong><\/td><\/td><\/td><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Hypothesis Test:<\/strong><\/p>\n\n\n\n

    \n
  • The p-value is:<\/strong>\u00a0< 0.01<\/li>\n\n\n\n
  • What is your conclusion?:<\/strong>\u00a0Reject the null hypothesis. There is a significant difference between the treatments.<\/li>\n<\/ul>\n\n\n\n

    Explanation<\/strong><\/h3>\n\n\n\n

    This problem requires completing an Analysis of Variance (ANOVA) table to determine if there is a statistically significant difference between the means of three treatments.<\/p>\n\n\n\n

    First, we determine the degrees of freedom (df). The number of treatments (k) is 3, and the total number of experimental units (n) is 12 + 15 + 20 = 47.<\/p>\n\n\n\n

      \n
    • df for Treatments:<\/strong>\u00a0This is calculated as k – 1 = 3 – 1 =\u00a02<\/strong>.<\/li>\n\n\n\n
    • df for Total:<\/strong>\u00a0This is calculated as n – 1 = 47 – 1 =\u00a046<\/strong>.<\/li>\n\n\n\n
    • df for Error:<\/strong>\u00a0This is the difference between the total df and the treatment df: 46 – 2 =\u00a044<\/strong>.<\/li>\n<\/ul>\n\n\n\n

      Next, we calculate the remaining Sum of Squares (SS) and the Mean Squares (MS).<\/p>\n\n\n\n

        \n
      • Sum of Squares for Error (SSE):<\/strong>\u00a0This is the difference between the Total SS and the Treatment SS: 1800 – 1000 =\u00a0800<\/strong>.<\/li>\n\n\n\n
      • Mean Square for Treatments (MST):<\/strong>\u00a0This is the Treatment SS divided by its df: 1000 \/ 2 =\u00a0500.00<\/strong>.<\/li>\n\n\n\n
      • Mean Square for Error (MSE):<\/strong>\u00a0This is the Error SS divided by its df: 800 \/ 44 \u2248\u00a018.18<\/strong>.<\/li>\n<\/ul>\n\n\n\n

        With the Mean Squares calculated, we can find the F-statistic.<\/p>\n\n\n\n

          \n
        • F-statistic:<\/strong>\u00a0This is the ratio of the Mean Square for Treatments to the Mean Square for Error: F = MST \/ MSE = 500 \/ 18.18 \u2248\u00a027.50<\/strong>.<\/li>\n<\/ul>\n\n\n\n

          Finally, we use the F-statistic (27.50) and the degrees of freedom (df1=2, df2=44) to find the p-value and make a conclusion at a 0.05 significance level. The p-value is the probability of obtaining an F-statistic at least as extreme as ours if the null hypothesis (that all treatment means are equal) were true. The calculated p-value is extremely small (approximately 0.0000000115), which rounds to 0.00<\/strong>.<\/p>\n\n\n\n

          Since our p-value (\u22480.00) is less than the significance level (\u03b1 = 0.05), we reject the null hypothesis. This indicates that there is strong statistical evidence to conclude that not all treatment means are equal; a significant difference exists between the treatments<\/p>\n\n\n\n

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

          HW 64 ? C Nick My Home Courses MindTap – Cengage Learning ng.cengage.com\/static\/nb\/ui\/evo\/index.html?deploymentid=5991401881038963484592120786&ISBN=9780357131466&id=1798221981&snapshotid=3481785& CENGAGE MINDTAP Chapter 13 Assignment Assignment: Chapter 13 Assignment ? Q Search this course 0 X Assignment Save Submit Assignment for Grading ? Catalog and Study Tools Questions Exercise 13.05 Algo (Analysis of Variance and the Completely Randomized Design) Question 2 of […]<\/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-242715","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/242715","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=242715"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/242715\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=242715"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=242715"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=242715"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}