{"id":5251,"date":"2022-08-19T00:41:53","date_gmt":"2022-08-19T00:41:53","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=5251"},"modified":"2022-08-19T00:43:07","modified_gmt":"2022-08-19T00:43:07","slug":"10b-coreq","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/10b-coreq\/","title":{"raw":"10B Coreq","rendered":"10B Coreq"},"content":{"raw":"In the next preview assignment and in the next class, you will need to identify the essential components of a confidence interval and interpret a confidence interval for a population proportion in context. This corequisite support activity will review important concepts, notation, and terminology associated with populations and samples, as well as the connections between them.\r\nRecalling Connections Between Populations and Samples\r\n
\r\n

Question 1<\/h3>\r\nIn In-Class Activity 9.A, we learned about the differences between a population and a sample. In your own words, describe the differences between a population and a sample.\r\n\r\n<\/div>\r\n
\r\n

Question 2<\/h3>\r\nIn multiple prior lessons, we learned there are characteristics and calculations that\u00a0 relate to and\/or describe a population and those that relate to and\/or describe a\u00a0 sample. Fill in the blank:\r\n
    \r\n \t
  1. A ___________ is a characteristic of a population of interest.<\/li>\r\n \t
  2. A ___________ is a characteristic of a sample or subgroup of interest.<\/li>\r\n<\/ol>\r\n<\/div>\r\n
    \r\n

    Question 3<\/h3>\r\nFor each of the following scenarios, determine whether the characteristic is a\u00a0 parameter or a statistic.\r\n
      \r\n \t
    1. A school administer needs to identify the proportion of all students who are\u00a0 registered for at least nine credits in the Spring semester. She uses the\u00a0 school\u2019s registration system to identify all students who are registered for the\u00a0 semester and then calculates the proportion of those who are registered for\u00a0 at least nine credits.\r\nThe proportion of all students who are registered for at least nine credits is\u00a0 an example of a ____________ [parameter or statistic] because it describes\u00a0 a _____________ [population or sample].<\/li>\r\n \t
    2. A researcher would like to estimate the true proportion of procedures at a\u00a0 hospital that involved a complication. The researcher randomly selects 200\u00a0 procedures from the past year, identifies whether the procedures involved complications, and then calculates the proportion.\r\nThe proportion of procedures that involved a complication\u2014out of the 200\u00a0 randomly selected\u2014is an example of a ____________ [parameter or statistic] because it describes a _____________ [population or sample].<\/li>\r\n \t
    3. A survey of 6,870 college students found that approximately 65%, or 4,466\u00a0 of the students surveyed, ordered take-out or delivery at least once in the\u00a0 last seven days.\r\nThe calculated percentage, 65%, is a ____________ [parameter or statistic]\u00a0 because it describes a _____________ [population or sample].<\/li>\r\n<\/ol>\r\n<\/div>\r\nIn Lesson 9 and In-Class Activity 10.A, we learned about the connections between a\u00a0 population and the sampling distribution of a sample proportion from that population.\u00a0 That is, when taking many random samples of size [latex] n [\/latex] from a population distribution with\u00a0 proportion [latex]p[\/latex], the mean of the distribution of sample proportions is [latex]p[\/latex] and the standard deviation of the distribution of sample proportions is [latex] \\sqrt{\\frac{p(1-p)}{n}} [\/latex].\r\n\r\nHowever, we rarely (if ever) know the true value of the population proportion. So\u00a0 instead, we can estimate the mean and standard deviation of the sampling distribution\u00a0 by the following:\r\n
      \r\n\r\nEstimate for the mean of sample proportions = [latex]\\hat{p}[\/latex] = sample proportion\r\n\r\nEstimate for the standard deviation of sample proportions (e.g., standard error) = [latex] \\sqrt{\\frac{\\hat{p}(1-\\hat{p})}{n}}[\/latex]\r\n\r\n<\/div>\r\n \r\n
      \r\n

      Question 4<\/h3>\r\nSuppose we took a random sample of 288 college students at a particular college\u00a0 and found that 176 were scheduled for at least nine credits in the upcoming\u00a0 semester.\r\n
        \r\n \t
      1. Calculate the sample proportion or point-estimate, [latex]\\hat{p} [\/latex].<\/li>\r\n \t
      2. Interpret your value for [latex]\\hat{p} [\/latex]. What does this value suggest in the context of this\u00a0 situation?<\/li>\r\n \t
      3. Calculate the standard error of the sample proportion using the formula\u00a0[latex]SE= \\sqrt{\\frac{\\hat{p}(1-\\hat{p})}{n}}[\/latex] and the point-estimate you calculated previously.<\/li>\r\n \t
      4. Interpret your value for the standard error. What does this value suggest in the context of this situation?<\/li>\r\n<\/ol>\r\n<\/div>\r\nPractice\r\n
        \r\n

        Question 5<\/h3>\r\nIn the 2019 National College Health Assessment, a random sample of college\u00a0 students were asked, in the last 7 days, \u201cHow many servings of fruit did you eat on\u00a0 average per day?\u201d Out of the 38,466 responses, 6,125 students stated they\u00a0 consumed an average of 0 servings of fruit per day.[footnote] American College Health Association-National College Health Assessment. (2020). Undergraduate student reference group data report, Fall 2019.<\/em> https:\/\/www.acha.org\/NCHA\/ACHA NCHA_Data\/Publications_and_Reports\/NCHA\/Data\/Reports_ACHA-NCHAIII.aspx[\/footnote]\r\n\r\nLet [latex] p [\/latex] represent the proportion of all college students who reported that they\u00a0 consume an average of 0 servings of fruit per day.\r\n
          \r\n \t
        1. Part A: Calculate the sample proportion or point-estimate, [latex]\\hat{p}[\/latex]<\/li>\r\n \t
        2. Part B: Calculate the standard error of the sample proportions using the formula\u00a0[latex] SE = \\sqrt{\\frac{\\hat{p}(1-\\hat{p})}{n}} [\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n
          \r\n

          Question 6<\/h3>\r\nInterpret your calculations from Question 5. What are these values estimating with\u00a0 respect to the given context\/situation?\r\n\r\n<\/div>\r\n
          \r\n

          Question 7<\/h3>\r\nLooking at the value of the standard error that you calculated in Question 5, why do\u00a0 you suppose the value is so small? Explain.\r\n\r\n<\/div>\r\n \r\n\r\n ","rendered":"

          In the next preview assignment and in the next class, you will need to identify the essential components of a confidence interval and interpret a confidence interval for a population proportion in context. This corequisite support activity will review important concepts, notation, and terminology associated with populations and samples, as well as the connections between them.
          \nRecalling Connections Between Populations and Samples<\/p>\n

          \n

          Question 1<\/h3>\n

          In In-Class Activity 9.A, we learned about the differences between a population and a sample. In your own words, describe the differences between a population and a sample.<\/p>\n<\/div>\n

          \n

          Question 2<\/h3>\n

          In multiple prior lessons, we learned there are characteristics and calculations that\u00a0 relate to and\/or describe a population and those that relate to and\/or describe a\u00a0 sample. Fill in the blank:<\/p>\n

            \n
          1. A ___________ is a characteristic of a population of interest.<\/li>\n
          2. A ___________ is a characteristic of a sample or subgroup of interest.<\/li>\n<\/ol>\n<\/div>\n
            \n

            Question 3<\/h3>\n

            For each of the following scenarios, determine whether the characteristic is a\u00a0 parameter or a statistic.<\/p>\n

              \n
            1. A school administer needs to identify the proportion of all students who are\u00a0 registered for at least nine credits in the Spring semester. She uses the\u00a0 school\u2019s registration system to identify all students who are registered for the\u00a0 semester and then calculates the proportion of those who are registered for\u00a0 at least nine credits.
              \nThe proportion of all students who are registered for at least nine credits is\u00a0 an example of a ____________ [parameter or statistic] because it describes\u00a0 a _____________ [population or sample].<\/li>\n
            2. A researcher would like to estimate the true proportion of procedures at a\u00a0 hospital that involved a complication. The researcher randomly selects 200\u00a0 procedures from the past year, identifies whether the procedures involved complications, and then calculates the proportion.
              \nThe proportion of procedures that involved a complication\u2014out of the 200\u00a0 randomly selected\u2014is an example of a ____________ [parameter or statistic] because it describes a _____________ [population or sample].<\/li>\n
            3. A survey of 6,870 college students found that approximately 65%, or 4,466\u00a0 of the students surveyed, ordered take-out or delivery at least once in the\u00a0 last seven days.
              \nThe calculated percentage, 65%, is a ____________ [parameter or statistic]\u00a0 because it describes a _____________ [population or sample].<\/li>\n<\/ol>\n<\/div>\n

              In Lesson 9 and In-Class Activity 10.A, we learned about the connections between a\u00a0 population and the sampling distribution of a sample proportion from that population.\u00a0 That is, when taking many random samples of size [latex]n[\/latex] from a population distribution with\u00a0 proportion [latex]p[\/latex], the mean of the distribution of sample proportions is [latex]p[\/latex] and the standard deviation of the distribution of sample proportions is [latex]\\sqrt{\\frac{p(1-p)}{n}}[\/latex].<\/p>\n

              However, we rarely (if ever) know the true value of the population proportion. So\u00a0 instead, we can estimate the mean and standard deviation of the sampling distribution\u00a0 by the following:<\/p>\n

              \n

              Estimate for the mean of sample proportions = [latex]\\hat{p}[\/latex] = sample proportion<\/p>\n

              Estimate for the standard deviation of sample proportions (e.g., standard error) = [latex]\\sqrt{\\frac{\\hat{p}(1-\\hat{p})}{n}}[\/latex]<\/p>\n<\/div>\n

               <\/p>\n

              \n

              Question 4<\/h3>\n

              Suppose we took a random sample of 288 college students at a particular college\u00a0 and found that 176 were scheduled for at least nine credits in the upcoming\u00a0 semester.<\/p>\n

                \n
              1. Calculate the sample proportion or point-estimate, [latex]\\hat{p}[\/latex].<\/li>\n
              2. Interpret your value for [latex]\\hat{p}[\/latex]. What does this value suggest in the context of this\u00a0 situation?<\/li>\n
              3. Calculate the standard error of the sample proportion using the formula\u00a0[latex]SE= \\sqrt{\\frac{\\hat{p}(1-\\hat{p})}{n}}[\/latex] and the point-estimate you calculated previously.<\/li>\n
              4. Interpret your value for the standard error. What does this value suggest in the context of this situation?<\/li>\n<\/ol>\n<\/div>\n

                Practice<\/p>\n

                \n

                Question 5<\/h3>\n

                In the 2019 National College Health Assessment, a random sample of college\u00a0 students were asked, in the last 7 days, \u201cHow many servings of fruit did you eat on\u00a0 average per day?\u201d Out of the 38,466 responses, 6,125 students stated they\u00a0 consumed an average of 0 servings of fruit per day.[1]<\/sup><\/a><\/p>\n

                Let [latex]p[\/latex] represent the proportion of all college students who reported that they\u00a0 consume an average of 0 servings of fruit per day.<\/p>\n

                  \n
                1. Part A: Calculate the sample proportion or point-estimate, [latex]\\hat{p}[\/latex]<\/li>\n
                2. Part B: Calculate the standard error of the sample proportions using the formula\u00a0[latex]SE = \\sqrt{\\frac{\\hat{p}(1-\\hat{p})}{n}}[\/latex]<\/li>\n<\/ol>\n<\/div>\n
                  \n

                  Question 6<\/h3>\n

                  Interpret your calculations from Question 5. What are these values estimating with\u00a0 respect to the given context\/situation?<\/p>\n<\/div>\n

                  \n

                  Question 7<\/h3>\n

                  Looking at the value of the standard error that you calculated in Question 5, why do\u00a0 you suppose the value is so small? Explain.<\/p>\n<\/div>\n

                   <\/p>\n

                   <\/p>\n

                  1. American College Health Association-National College Health Assessment. (2020). Undergraduate student reference group data report, Fall 2019.<\/em> https:\/\/www.acha.org\/NCHA\/ACHA NCHA_Data\/Publications_and_Reports\/NCHA\/Data\/Reports_ACHA-NCHAIII.aspx ↵<\/a><\/li><\/ol><\/div>","protected":false},"author":574340,"menu_order":4,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-5251","chapter","type-chapter","status-publish","hentry"],"part":5220,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5251","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/users\/574340"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5251\/revisions"}],"predecessor-version":[{"id":5252,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5251\/revisions\/5252"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/5220"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5251\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=5251"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=5251"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=5251"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=5251"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}