{"id":3210,"date":"2022-07-01T08:08:36","date_gmt":"2022-07-01T12:08:36","guid":{"rendered":"https:\/\/openbooks.macewan.ca\/rcommander\/?post_type=chapter&p=3210"},"modified":"2025-05-07T18:11:15","modified_gmt":"2025-05-07T22:11:15","slug":"12-7-assignment-12","status":"publish","type":"chapter","link":"https:\/\/openbooks.macewan.ca\/introstats\/chapter\/12-7-assignment-12\/","title":{"raw":"12.7 Assignment 12","rendered":"12.7 Assignment 12"},"content":{"raw":"

Purposes<\/h2>\r\nThe following questions have two parts. The first part assesses your knowledge of identifying cases where one-way ANOVA should be used, explaining the main idea of one-way ANOVA, and conducting a one-way ANOVA F test based on the computer outputs. The second part assesses your skills in using R Commander to conduct a one-way ANOVA F test.\r\n

Resources<\/h2>\r\nM12_Rent_ANOVA_Q5_FourColumnS.xlsx<\/a>\r\n\r\nM12_Salary_ANOVA_Q7.xlsx<\/a>\r\n\r\nM12_Rent_ANOVA_Q6.xlsx<\/a>\r\n

Instructions<\/h2>\r\n

Part A<\/strong><\/h3>\r\nComplete the following:<\/strong>\r\n
    \r\n \t
  1. What does ANOVA stand for? (2 marks)<\/li>\r\n \t
  2. When shall we use a one-way ANOVA F test? (2 marks)<\/li>\r\n \t
  3. Suppose that a one-way ANOVA is being performed to compare the means of three populations and that the sample sizes are 10, 12, and 15. Determine the degrees of freedom for the F<\/em> statistic. (2 marks)<\/li>\r\n \t
  4. We stated earlier that a one-way ANOVA test is always right-tailed because the null hypothesis is rejected only when the test statistic, F, is too large. Why is the null hypothesis rejected only when F is too large? (3 marks)<\/li>\r\n \t
  5. Fill in the missing entries in the following ANOVA table. (4 marks)\r\n<\/colgroup>\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    Source<\/th>\r\ndf<\/em><\/th>\r\nSS<\/em><\/th>\r\nMS<\/em> = [latex]\\frac{SS}{df}[\/latex]<\/th>\r\nF-statistic<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
    Treatment<\/th>\r\n2<\/td>\r\n?<\/td>\r\n21.652<\/td>\r\n[latex]F_{o} = ?[\/latex]<\/td>\r\n<\/tr>\r\n
    Error<\/th>\r\n?<\/td>\r\n84.400<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
    Total<\/th>\r\n14<\/td>\r\n?<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n \t
  6. The data on monthly rents, in dollars, for independent random samples of newly completed apartments in the four U.S. regions are presented in the following table. (See the spreadsheet M12_Rent_ANOVA_Q5_FourColumnS.xlsx<\/strong>)\r\n<\/colgroup>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    Northeast<\/strong><\/th>\r\nMidwest<\/strong><\/th>\r\nSouth<\/strong><\/th>\r\nWest<\/strong><\/th>\r\n<\/tr>\r\n<\/thead>\r\n
    1005<\/td>\r\n870<\/td>\r\n891<\/td>\r\n1025<\/td>\r\n<\/tr>\r\n
    898<\/td>\r\n748<\/td>\r\n630<\/td>\r\n1012<\/td>\r\n<\/tr>\r\n
    948<\/td>\r\n699<\/td>\r\n861<\/td>\r\n1090<\/td>\r\n<\/tr>\r\n
    1181<\/td>\r\n814<\/td>\r\n1036<\/td>\r\n926<\/td>\r\n<\/tr>\r\n
    1244<\/td>\r\n721<\/td>\r\n<\/td>\r\n1269<\/td>\r\n<\/tr>\r\n
    <\/td>\r\n606<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
    Given the ANOVA table, test at a 5% significance level whether a difference exists in the mean rent of newly completed apartments in the four U.S. regions. (8 marks)<\/blockquote>\r\n<\/colgroup>\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    Source<\/th>\r\ndf<\/em><\/th>\r\nSS<\/em><\/th>\r\nMS<\/em> = [latex]\\frac{SS}{df}[\/latex]<\/th>\r\nF-statistic<\/th>\r\nP-value<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
    Region<\/th>\r\n3<\/td>\r\n400513<\/td>\r\n133504<\/td>\r\n[latex]F_{o} = 7.541[\/latex]<\/td>\r\n0.0023<\/td>\r\n<\/tr>\r\n
    Error<\/th>\r\n16<\/td>\r\n283265<\/td>\r\n17704<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
    Total<\/th>\r\n19<\/td>\r\n683778<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n \t
  7. The following table gives the salaries (in thousand dollars) for computer science (CS) majors obtaining a bachelor's degree, a master's degree, or a Ph.D. (See the spreadsheet M12_Salary_ANOVA_Q7.xlsx<\/strong>)\r\n<\/colgroup>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    Salary<\/strong><\/th>\r\nDegree<\/strong><\/th>\r\nSalary<\/strong><\/th>\r\nDegree<\/strong><\/th>\r\nSalary<\/strong><\/th>\r\nDegree<\/strong><\/th>\r\n<\/tr>\r\n<\/thead>\r\n
    50.8<\/td>\r\nBachelor\u2019s<\/td>\r\n65.8<\/td>\r\nMaster\u2019s<\/td>\r\n73.3<\/td>\r\nPh.D<\/td>\r\n<\/tr>\r\n
    59.4<\/td>\r\nBachelor\u2019s<\/td>\r\n57.5<\/td>\r\nMaster\u2019s<\/td>\r\n65.7<\/td>\r\nPh.D<\/td>\r\n<\/tr>\r\n
    55.9<\/td>\r\nBachelor\u2019s<\/td>\r\n66.9<\/td>\r\nMaster\u2019s<\/td>\r\n71.7<\/td>\r\nPh.D<\/td>\r\n<\/tr>\r\n
    45.1<\/td>\r\nBachelor\u2019s<\/td>\r\n62.8<\/td>\r\nMaster\u2019s<\/td>\r\n72.5<\/td>\r\nPh.D<\/td>\r\n<\/tr>\r\n
    54.1<\/td>\r\nBachelor\u2019s<\/td>\r\n68.5<\/td>\r\nMaster\u2019s<\/td>\r\n73.0<\/td>\r\nPh.D<\/td>\r\n<\/tr>\r\n
    50.7<\/td>\r\nBachelor\u2019s<\/td>\r\n69.3<\/td>\r\nMaster\u2019s<\/td>\r\n67.2<\/td>\r\nPh.D<\/td>\r\n<\/tr>\r\n
    46.8<\/td>\r\nBachelor\u2019s<\/td>\r\n61.5<\/td>\r\nMaster\u2019s<\/td>\r\n67.5<\/td>\r\nPh.D<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
      \r\n \t
    1. Fill in missing entries of the following ANOVA table. (4 marks)\r\n<\/colgroup>\r\n\r\n\r\n\r\n\r\n\r\n\r\n
      Source<\/th>\r\ndf<\/em><\/th>\r\nSS<\/em><\/th>\r\nMS<\/em> = [latex]\\frac{SS}{df}[\/latex]<\/th>\r\nF-statistic<\/th>\r\nP-value<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
      Degree<\/th>\r\n?<\/td>\r\n?<\/td>\r\n616.9<\/td>\r\n[latex]F_{o} = 34.62[\/latex]<\/td>\r\n< 0.0001<\/td>\r\n<\/tr>\r\n
      Error<\/th>\r\n?<\/td>\r\n?<\/td>\r\n17.8<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
      Total<\/th>\r\n20<\/td>\r\n1554.5<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n \t
    2. Test at the 1% significance level whether a difference exists in mean salary for computer science (CS) majors obtaining a bachelor's degree, a master's degree or a Ph.D. (8 marks)<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n

      Part B<\/strong><\/h3>\r\nFinish the following questions using R and R commander<\/strong>.\r\n
        \r\n \t
      1. Refer to Question 6 in Part A. The data are provided in the file M12_Rent_ANOVA_Q6.xlsx<\/strong>. Import the data into R commander. Regenerate the ANOVA table in Question 6 in Part A. Make sure you copy and paste the computer output.\u00a0(3 marks)<\/li>\r\n \t
      2. Refer to Question 7 in Part A. The data are provided in the file M12_Salary_ANOVA_Q7.xlsx<\/strong>. Import the data into R commander. Obtain the ANOVA table and compare it with Question 7 in Part A. Make sure you copy and paste the computer output. (4 marks)<\/li>\r\n<\/ol>","rendered":"

        Purposes<\/h2>\n

        The following questions have two parts. The first part assesses your knowledge of identifying cases where one-way ANOVA should be used, explaining the main idea of one-way ANOVA, and conducting a one-way ANOVA F test based on the computer outputs. The second part assesses your skills in using R Commander to conduct a one-way ANOVA F test.<\/p>\n

        Resources<\/h2>\n

        M12_Rent_ANOVA_Q5_FourColumnS.xlsx<\/a><\/p>\n

        M12_Salary_ANOVA_Q7.xlsx<\/a><\/p>\n

        M12_Rent_ANOVA_Q6.xlsx<\/a><\/p>\n

        Instructions<\/h2>\n

        Part A<\/strong><\/h3>\n

        Complete the following:<\/strong><\/p>\n

          \n
        1. What does ANOVA stand for? (2 marks)<\/li>\n
        2. When shall we use a one-way ANOVA F test? (2 marks)<\/li>\n
        3. Suppose that a one-way ANOVA is being performed to compare the means of three populations and that the sample sizes are 10, 12, and 15. Determine the degrees of freedom for the F<\/em> statistic. (2 marks)<\/li>\n
        4. We stated earlier that a one-way ANOVA test is always right-tailed because the null hypothesis is rejected only when the test statistic, F, is too large. Why is the null hypothesis rejected only when F is too large? (3 marks)<\/li>\n
        5. Fill in the missing entries in the following ANOVA table. (4 marks)
          \n\n\n\n\n\n\n<\/colgroup>\n\n\n\n\n\n\n
          Source<\/th>\ndf<\/em><\/th>\nSS<\/em><\/th>\nMS<\/em> = [latex]\\frac{SS}{df}[\/latex]<\/th>\nF-statistic<\/th>\n<\/tr>\n<\/thead>\n
          Treatment<\/th>\n2<\/td>\n?<\/td>\n21.652<\/td>\n[latex]F_{o} = ?[\/latex]<\/td>\n<\/tr>\n
          Error<\/th>\n?<\/td>\n84.400<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
          Total<\/th>\n14<\/td>\n?<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n
        6. The data on monthly rents, in dollars, for independent random samples of newly completed apartments in the four U.S. regions are presented in the following table. (See the spreadsheet M12_Rent_ANOVA_Q5_FourColumnS.xlsx<\/strong>)
          \n\n\n\n\n\n<\/colgroup>\n\n\n\n\n\n\n\n\n\n
          Northeast<\/strong><\/th>\nMidwest<\/strong><\/th>\nSouth<\/strong><\/th>\nWest<\/strong><\/th>\n<\/tr>\n<\/thead>\n
          1005<\/td>\n870<\/td>\n891<\/td>\n1025<\/td>\n<\/tr>\n
          898<\/td>\n748<\/td>\n630<\/td>\n1012<\/td>\n<\/tr>\n
          948<\/td>\n699<\/td>\n861<\/td>\n1090<\/td>\n<\/tr>\n
          1181<\/td>\n814<\/td>\n1036<\/td>\n926<\/td>\n<\/tr>\n
          1244<\/td>\n721<\/td>\n<\/td>\n1269<\/td>\n<\/tr>\n
          <\/td>\n606<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

          Given the ANOVA table, test at a 5% significance level whether a difference exists in the mean rent of newly completed apartments in the four U.S. regions. (8 marks)<\/p><\/blockquote>\n\n\n\n\n\n\n\n<\/colgroup>\n\n\n\n\n\n\n
          Source<\/th>\ndf<\/em><\/th>\nSS<\/em><\/th>\nMS<\/em> = [latex]\\frac{SS}{df}[\/latex]<\/th>\nF-statistic<\/th>\nP-value<\/th>\n<\/tr>\n<\/thead>\n
          Region<\/th>\n3<\/td>\n400513<\/td>\n133504<\/td>\n[latex]F_{o} = 7.541[\/latex]<\/td>\n0.0023<\/td>\n<\/tr>\n
          Error<\/th>\n16<\/td>\n283265<\/td>\n17704<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
          Total<\/th>\n19<\/td>\n683778<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n
        7. The following table gives the salaries (in thousand dollars) for computer science (CS) majors obtaining a bachelor’s degree, a master’s degree, or a Ph.D. (See the spreadsheet M12_Salary_ANOVA_Q7.xlsx<\/strong>)
          \n\n\n\n\n\n\n\n<\/colgroup>\n\n\n\n\n\n\n\n\n\n\n
          Salary<\/strong><\/th>\nDegree<\/strong><\/th>\nSalary<\/strong><\/th>\nDegree<\/strong><\/th>\nSalary<\/strong><\/th>\nDegree<\/strong><\/th>\n<\/tr>\n<\/thead>\n
          50.8<\/td>\nBachelor\u2019s<\/td>\n65.8<\/td>\nMaster\u2019s<\/td>\n73.3<\/td>\nPh.D<\/td>\n<\/tr>\n
          59.4<\/td>\nBachelor\u2019s<\/td>\n57.5<\/td>\nMaster\u2019s<\/td>\n65.7<\/td>\nPh.D<\/td>\n<\/tr>\n
          55.9<\/td>\nBachelor\u2019s<\/td>\n66.9<\/td>\nMaster\u2019s<\/td>\n71.7<\/td>\nPh.D<\/td>\n<\/tr>\n
          45.1<\/td>\nBachelor\u2019s<\/td>\n62.8<\/td>\nMaster\u2019s<\/td>\n72.5<\/td>\nPh.D<\/td>\n<\/tr>\n
          54.1<\/td>\nBachelor\u2019s<\/td>\n68.5<\/td>\nMaster\u2019s<\/td>\n73.0<\/td>\nPh.D<\/td>\n<\/tr>\n
          50.7<\/td>\nBachelor\u2019s<\/td>\n69.3<\/td>\nMaster\u2019s<\/td>\n67.2<\/td>\nPh.D<\/td>\n<\/tr>\n
          46.8<\/td>\nBachelor\u2019s<\/td>\n61.5<\/td>\nMaster\u2019s<\/td>\n67.5<\/td>\nPh.D<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
            \n
          1. Fill in missing entries of the following ANOVA table. (4 marks)
            \n\n\n\n\n\n\n\n<\/colgroup>\n\n\n\n\n\n\n
            Source<\/th>\ndf<\/em><\/th>\nSS<\/em><\/th>\nMS<\/em> = [latex]\\frac{SS}{df}[\/latex]<\/th>\nF-statistic<\/th>\nP-value<\/th>\n<\/tr>\n<\/thead>\n
            Degree<\/th>\n?<\/td>\n?<\/td>\n616.9<\/td>\n[latex]F_{o} = 34.62[\/latex]<\/td>\n< 0.0001<\/td>\n<\/tr>\n
            Error<\/th>\n?<\/td>\n?<\/td>\n17.8<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
            Total<\/th>\n20<\/td>\n1554.5<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n
          2. Test at the 1% significance level whether a difference exists in mean salary for computer science (CS) majors obtaining a bachelor’s degree, a master’s degree or a Ph.D. (8 marks)<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

            Part B<\/strong><\/h3>\n

            Finish the following questions using R and R commander<\/strong>.<\/p>\n

              \n
            1. Refer to Question 6 in Part A. The data are provided in the file M12_Rent_ANOVA_Q6.xlsx<\/strong>. Import the data into R commander. Regenerate the ANOVA table in Question 6 in Part A. Make sure you copy and paste the computer output.\u00a0(3 marks)<\/li>\n
            2. Refer to Question 7 in Part A. The data are provided in the file M12_Salary_ANOVA_Q7.xlsx<\/strong>. Import the data into R commander. Obtain the ANOVA table and compare it with Question 7 in Part A. Make sure you copy and paste the computer output. (4 marks)<\/li>\n<\/ol>\n","protected":false},"author":19,"menu_order":7,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-3210","chapter","type-chapter","status-publish","hentry"],"part":1189,"_links":{"self":[{"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/pressbooks\/v2\/chapters\/3210","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/wp\/v2\/users\/19"}],"version-history":[{"count":18,"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/pressbooks\/v2\/chapters\/3210\/revisions"}],"predecessor-version":[{"id":5528,"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/pressbooks\/v2\/chapters\/3210\/revisions\/5528"}],"part":[{"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/pressbooks\/v2\/parts\/1189"}],"metadata":[{"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/pressbooks\/v2\/chapters\/3210\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/wp\/v2\/media?parent=3210"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/pressbooks\/v2\/chapter-type?post=3210"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/wp\/v2\/contributor?post=3210"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/wp\/v2\/license?post=3210"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}