{"id":269,"date":"2023-01-18T19:32:45","date_gmt":"2023-01-19T00:32:45","guid":{"rendered":"https:\/\/opentextbc.ca\/busstatsancillary\/?post_type=chapter&p=269"},"modified":"2023-01-20T13:57:04","modified_gmt":"2023-01-20T18:57:04","slug":"finite-population-correction-factor","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/busstatsancillary\/chapter\/finite-population-correction-factor\/","title":{"raw":"7.4 Finite Population Correction Factor","rendered":"7.4 Finite Population Correction Factor"},"content":{"raw":"The following activities and questions relate to material covered in Chapter 7.4 Finite Population Correction Factor<\/a> in\u00a0Introductory Business Statistics (OpenStax)<\/em><\/a>.\r\n
Data sets for the following questions are available in Excel: 7.4 Data Sets [XLSX]<\/a>.<\/div>\r\n

Questions<\/h1>\r\n
    \r\n \t
  1. A local territorial brewery would like to know if the morning shift and the afternoon shift are equally efficient at brewing beer. The average brewing time is normally distributed with a mean of 2.38 hours days and a standard deviation of 0.36 hours. A study is completed to sample 10 shifts from the morning, and 13 shifts from the afternoon. The data was collected as below:\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    Shift<\/th>\r\nNumber of Hours to Process 100 Bottles of Beer<\/th>\r\n<\/tr>\r\n
    Morning<\/td>\r\n2<\/td>\r\n<\/tr>\r\n
    Morning<\/td>\r\n2.2<\/td>\r\n<\/tr>\r\n
    Morning<\/td>\r\n2.3<\/td>\r\n<\/tr>\r\n
    Morning<\/td>\r\n2<\/td>\r\n<\/tr>\r\n
    Morning<\/td>\r\n3<\/td>\r\n<\/tr>\r\n
    Morning<\/td>\r\n2.6<\/td>\r\n<\/tr>\r\n
    Morning<\/td>\r\n2.2<\/td>\r\n<\/tr>\r\n
    Morning<\/td>\r\n2.6<\/td>\r\n<\/tr>\r\n
    Morning<\/td>\r\n2<\/td>\r\n<\/tr>\r\n
    Morning<\/td>\r\n2.6<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    Shift<\/th>\r\nNumber of Hours to Process 100 Bottles of Beer<\/th>\r\n<\/tr>\r\n
    Afternoon<\/td>\r\n2.4<\/td>\r\n<\/tr>\r\n
    Afternoon<\/td>\r\n2.4<\/td>\r\n<\/tr>\r\n
    Afternoon<\/td>\r\n2.1<\/td>\r\n<\/tr>\r\n
    Afternoon<\/td>\r\n2.8<\/td>\r\n<\/tr>\r\n
    Afternoon<\/td>\r\n3.4<\/td>\r\n<\/tr>\r\n
    Afternoon<\/td>\r\n2.2<\/td>\r\n<\/tr>\r\n
    Afternoon<\/td>\r\n2.4<\/td>\r\n<\/tr>\r\n
    Afternoon<\/td>\r\n2<\/td>\r\n<\/tr>\r\n
    Afternoon<\/td>\r\n2<\/td>\r\n<\/tr>\r\n
    Afternoon<\/td>\r\n2.8<\/td>\r\n<\/tr>\r\n
    Afternoon<\/td>\r\n2.2<\/td>\r\n<\/tr>\r\n
    Afternoon<\/td>\r\n2<\/td>\r\n<\/tr>\r\n
    Afternoon<\/td>\r\n2.6<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nComplete the chart below and write a sentence to assess whether the morning or afternoon shift is more efficient at brewing beer.\r\n\r\n\r\n\r\n\r\n\r\n
    Shift<\/th>\r\nSample Size<\/th>\r\nAverage Number of Hours to Process 100 Bottles of Beer<\/th>\r\nSample Standard Deviation<\/th>\r\nz-score<\/th>\r\n<\/tr>\r\n
    Morning Shift<\/th>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
    Afternoon Shift<\/th>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n<\/ol>\r\n

    Solutions<\/h1>\r\n
      \r\n \t
    1. \r\n\r\n\r\n\r\n\r\n\r\n
      Shift<\/th>\r\nSample Size<\/th>\r\nAverage Number of Hours to Process 100 Bottles of Beer<\/th>\r\nSample Standard Deviation<\/th>\r\nz-score<\/th>\r\n<\/tr>\r\n
      Morning Shift<\/th>\r\n10<\/td>\r\n2.35<\/td>\r\n0.34<\/td>\r\n0.28<\/td>\r\n<\/tr>\r\n
      Afternoon Shift<\/th>\r\n13<\/td>\r\n2.41<\/td>\r\n0.41<\/td>\r\n\u22120.24<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nBecause the afternoon shift has a negative z-score (meaning they take less than the average time), the afternoon shift is more efficient at brewing beer compared to the morning shift.<\/li>\r\n<\/ol>","rendered":"

      The following activities and questions relate to material covered in Chapter 7.4 Finite Population Correction Factor<\/a> in\u00a0Introductory Business Statistics (OpenStax)<\/em><\/a>.<\/p>\n

      Data sets for the following questions are available in Excel: 7.4 Data Sets [XLSX]<\/a>.<\/div>\n

      Questions<\/h1>\n
        \n
      1. A local territorial brewery would like to know if the morning shift and the afternoon shift are equally efficient at brewing beer. The average brewing time is normally distributed with a mean of 2.38 hours days and a standard deviation of 0.36 hours. A study is completed to sample 10 shifts from the morning, and 13 shifts from the afternoon. The data was collected as below:
        \n\n\n\n\n\n\n\n\n\n\n\n\n\n
        Shift<\/th>\nNumber of Hours to Process 100 Bottles of Beer<\/th>\n<\/tr>\n
        Morning<\/td>\n2<\/td>\n<\/tr>\n
        Morning<\/td>\n2.2<\/td>\n<\/tr>\n
        Morning<\/td>\n2.3<\/td>\n<\/tr>\n
        Morning<\/td>\n2<\/td>\n<\/tr>\n
        Morning<\/td>\n3<\/td>\n<\/tr>\n
        Morning<\/td>\n2.6<\/td>\n<\/tr>\n
        Morning<\/td>\n2.2<\/td>\n<\/tr>\n
        Morning<\/td>\n2.6<\/td>\n<\/tr>\n
        Morning<\/td>\n2<\/td>\n<\/tr>\n
        Morning<\/td>\n2.6<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
        Shift<\/th>\nNumber of Hours to Process 100 Bottles of Beer<\/th>\n<\/tr>\n
        Afternoon<\/td>\n2.4<\/td>\n<\/tr>\n
        Afternoon<\/td>\n2.4<\/td>\n<\/tr>\n
        Afternoon<\/td>\n2.1<\/td>\n<\/tr>\n
        Afternoon<\/td>\n2.8<\/td>\n<\/tr>\n
        Afternoon<\/td>\n3.4<\/td>\n<\/tr>\n
        Afternoon<\/td>\n2.2<\/td>\n<\/tr>\n
        Afternoon<\/td>\n2.4<\/td>\n<\/tr>\n
        Afternoon<\/td>\n2<\/td>\n<\/tr>\n
        Afternoon<\/td>\n2<\/td>\n<\/tr>\n
        Afternoon<\/td>\n2.8<\/td>\n<\/tr>\n
        Afternoon<\/td>\n2.2<\/td>\n<\/tr>\n
        Afternoon<\/td>\n2<\/td>\n<\/tr>\n
        Afternoon<\/td>\n2.6<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

        Complete the chart below and write a sentence to assess whether the morning or afternoon shift is more efficient at brewing beer.<\/p>\n\n\n\n\n\n
        Shift<\/th>\nSample Size<\/th>\nAverage Number of Hours to Process 100 Bottles of Beer<\/th>\nSample Standard Deviation<\/th>\nz-score<\/th>\n<\/tr>\n
        Morning Shift<\/th>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
        Afternoon Shift<\/th>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<\/ol>\n

        Solutions<\/h1>\n
          \n
        1. \n\n\n\n\n\n
          Shift<\/th>\nSample Size<\/th>\nAverage Number of Hours to Process 100 Bottles of Beer<\/th>\nSample Standard Deviation<\/th>\nz-score<\/th>\n<\/tr>\n
          Morning Shift<\/th>\n10<\/td>\n2.35<\/td>\n0.34<\/td>\n0.28<\/td>\n<\/tr>\n
          Afternoon Shift<\/th>\n13<\/td>\n2.41<\/td>\n0.41<\/td>\n\u22120.24<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

          Because the afternoon shift has a negative z-score (meaning they take less than the average time), the afternoon shift is more efficient at brewing beer compared to the morning shift.<\/li>\n<\/ol>\n","protected":false},"author":123,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-269","chapter","type-chapter","status-publish","hentry"],"part":90,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapters\/269","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/wp\/v2\/users\/123"}],"version-history":[{"count":5,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapters\/269\/revisions"}],"predecessor-version":[{"id":334,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapters\/269\/revisions\/334"}],"part":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/parts\/90"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapters\/269\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/wp\/v2\/media?parent=269"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapter-type?post=269"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/wp\/v2\/contributor?post=269"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/wp\/v2\/license?post=269"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}