{"id":5397,"date":"2022-08-20T21:54:14","date_gmt":"2022-08-20T21:54:14","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=5397"},"modified":"2022-08-20T21:56:43","modified_gmt":"2022-08-20T21:56:43","slug":"11g-coreq","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/11g-coreq\/","title":{"raw":"11G Coreq","rendered":"11G Coreq"},"content":{"raw":"In the next preview assignment and in the next class, you will need to understand how\u00a0 an interval containing a difference of two quantities relates to the quantities themselves.\r\n\r\nIntervals\r\n\r\nIn particular, we will be examining intervals estimating the difference of two proportions.\u00a0 We will consider a Gallup survey that asked respondents whether they considered\u00a0 themselves to be vegetarian.\r\n
\r\n

Question 1<\/h3>\r\nLet [latex] p_{1} [\/latex] be the true proportion (written as a decimal) of U.S. women who considered themselves to be vegetarian. On the following number line, sketch and label an interval that contains all the possible values for [latex] p_{1} [\/latex].\r\n\r\n\"\"\r\n\r\n<\/div>\r\n
\r\n

Question 2<\/h3>\r\nLet [latex] p_{2} [\/latex] be the true proportion (written as a decimal) of U.S. men who considered themselves to be vegetarian. On the following number line, sketch and label an interval that contains all the possible values for [latex] p_{2} [\/latex].\r\n\r\n\"\"\r\n\r\n<\/div>\r\n
\r\n

Question 3<\/h3>\r\nOn the following number line, sketch and label an interval that contains all the possible values for [latex] p_{1} - p_{2}[\/latex].\r\n\r\n\"\"\r\n\r\n<\/div>\r\n
\r\n

Question 4<\/h3>\r\nThe Gallup survey that was mentioned at the beginning of this corequisite support activity found that 6% of U.S. adult women surveyed considered themselves to be vegetarian and 4% of U.S. adult men surveyed considered themselves to be vegetarian.[footnote]d.). What percentage of Americans are vegetarian?<\/em> Gallup. https:\/\/news.gallup.com\/poll\/267074\/percentage-americans-vegetarian.aspx[\/footnote]\r\n
    \r\n \t
  1. Part A: Using the notation from the previous in-class activity, how would you represent these statistics?<\/li>\r\n \t
  2. Part B: On the following number line, plot and label these statistics using the notation you suggested in the previous question.\r\n\"\"<\/li>\r\n \t
  3. Part C: On the following number line, plot and label the difference p1-p2.\r\n\"\"<\/li>\r\n \t
  4. Where does [latex] \\hat{p_{1}} - \\hat{p_{2}}[\/latex]. lie on the number line in relation to 0? Explain.<\/li>\r\n<\/ol>\r\n<\/div>\r\n
    \r\n

    Question 5<\/h3>\r\nThe survey had 485 respondents who were women and 548 respondents who were men.\r\n
      \r\n \t
    1. Part A: How many women who responded said they were vegetarian? Round to the nearest whole number.<\/li>\r\n \t
    2. Part B: How many men who responded said they were vegetarian? Round to the nearest whole number.<\/li>\r\n<\/ol>\r\n<\/div>\r\n
      \r\n

      Question 6<\/h3>\r\nGo to the DCMP Compare Two Population Proportions tool at https:\/\/dcmathpathways.shinyapps.io\/2sample_prop\/<\/a>. Under \u201cEnter Data,\u201d select \u201cNumber of Successes.\u201d Using Group 1 for the women and Group 2 for the men, input the information from the previous question. Generate a 95% confidence interval for the quantity [latex] p_{1} - p_{2}[\/latex]. Sketch and label the interval, and include the quantity [latex] \\hat{p_{1}} - \\hat{p_{2}}[\/latex].\r\n\r\n<\/div>\r\n
      \r\n

      Question 7<\/h3>\r\n7)\u00a0\u00a0\u00a0 For each of the following situations, decide whether the null quantity [latex] p_{1} - p_{2} = 0[\/latex] falls within the confidence interval.\r\n
        \r\n \t
      1. Part A: Suppose the proportions were those given in Question 4: [latex] p_{1} = \\hat{p_{1}}, p_{2} = \\hat{p_{2}} [\/latex], with the resulting confidence interval from Question 6.<\/li>\r\n \t
      2. Part B: Suppose we had different sample proportions. Suppose now that\u00a0[latex] \\hat{p_{1}} = 0.07 [\/latex] and [latex] \\hat{p_{2}} = 0.02 [\/latex], with a resulting confidence interval of (0.024, 0.076).<\/li>\r\n \t
      3. Part C: Suppose we had different sample proportions. Suppose now that [latex] \\hat{p_{1}} = 0.05 [\/latex] and [latex] \\hat{p_{2}} = 0.057 [\/latex], with a resulting confidence interval of (\u20130.034, 0.020).<\/li>\r\n<\/ol>\r\n<\/div>\r\n
        \r\n

        Question 8<\/h3>\r\nDoes the proportion of women who said they were vegetarian have to be greater than the proportion of men who said they were vegetarian in order for [latex] p_{1} - p_{2}[\/latex] to fall within the confidence interval?\r\n\r\n<\/div>\r\n ","rendered":"

        In the next preview assignment and in the next class, you will need to understand how\u00a0 an interval containing a difference of two quantities relates to the quantities themselves.<\/p>\n

        Intervals<\/p>\n

        In particular, we will be examining intervals estimating the difference of two proportions.\u00a0 We will consider a Gallup survey that asked respondents whether they considered\u00a0 themselves to be vegetarian.<\/p>\n

        \n

        Question 1<\/h3>\n

        Let [latex]p_{1}[\/latex] be the true proportion (written as a decimal) of U.S. women who considered themselves to be vegetarian. On the following number line, sketch and label an interval that contains all the possible values for [latex]p_{1}[\/latex].<\/p>\n

        \"\"<\/p>\n<\/div>\n

        \n

        Question 2<\/h3>\n

        Let [latex]p_{2}[\/latex] be the true proportion (written as a decimal) of U.S. men who considered themselves to be vegetarian. On the following number line, sketch and label an interval that contains all the possible values for [latex]p_{2}[\/latex].<\/p>\n

        \"\"<\/p>\n<\/div>\n

        \n

        Question 3<\/h3>\n

        On the following number line, sketch and label an interval that contains all the possible values for [latex]p_{1} - p_{2}[\/latex].<\/p>\n

        \"\"<\/p>\n<\/div>\n

        \n

        Question 4<\/h3>\n

        The Gallup survey that was mentioned at the beginning of this corequisite support activity found that 6% of U.S. adult women surveyed considered themselves to be vegetarian and 4% of U.S. adult men surveyed considered themselves to be vegetarian.[1]<\/sup><\/a><\/p>\n

          \n
        1. Part A: Using the notation from the previous in-class activity, how would you represent these statistics?<\/li>\n
        2. Part B: On the following number line, plot and label these statistics using the notation you suggested in the previous question.
          \n\"\"<\/li>\n
        3. Part C: On the following number line, plot and label the difference p1-p2.
          \n\"\"<\/li>\n
        4. Where does [latex]\\hat{p_{1}} - \\hat{p_{2}}[\/latex]. lie on the number line in relation to 0? Explain.<\/li>\n<\/ol>\n<\/div>\n
          \n

          Question 5<\/h3>\n

          The survey had 485 respondents who were women and 548 respondents who were men.<\/p>\n

            \n
          1. Part A: How many women who responded said they were vegetarian? Round to the nearest whole number.<\/li>\n
          2. Part B: How many men who responded said they were vegetarian? Round to the nearest whole number.<\/li>\n<\/ol>\n<\/div>\n
            \n

            Question 6<\/h3>\n

            Go to the DCMP Compare Two Population Proportions tool at https:\/\/dcmathpathways.shinyapps.io\/2sample_prop\/<\/a>. Under \u201cEnter Data,\u201d select \u201cNumber of Successes.\u201d Using Group 1 for the women and Group 2 for the men, input the information from the previous question. Generate a 95% confidence interval for the quantity [latex]p_{1} - p_{2}[\/latex]. Sketch and label the interval, and include the quantity [latex]\\hat{p_{1}} - \\hat{p_{2}}[\/latex].<\/p>\n<\/div>\n

            \n

            Question 7<\/h3>\n

            7)\u00a0\u00a0\u00a0 For each of the following situations, decide whether the null quantity [latex]p_{1} - p_{2} = 0[\/latex] falls within the confidence interval.<\/p>\n

              \n
            1. Part A: Suppose the proportions were those given in Question 4: [latex]p_{1} = \\hat{p_{1}}, p_{2} = \\hat{p_{2}}[\/latex], with the resulting confidence interval from Question 6.<\/li>\n
            2. Part B: Suppose we had different sample proportions. Suppose now that\u00a0[latex]\\hat{p_{1}} = 0.07[\/latex] and [latex]\\hat{p_{2}} = 0.02[\/latex], with a resulting confidence interval of (0.024, 0.076).<\/li>\n
            3. Part C: Suppose we had different sample proportions. Suppose now that [latex]\\hat{p_{1}} = 0.05[\/latex] and [latex]\\hat{p_{2}} = 0.057[\/latex], with a resulting confidence interval of (\u20130.034, 0.020).<\/li>\n<\/ol>\n<\/div>\n
              \n

              Question 8<\/h3>\n

              Does the proportion of women who said they were vegetarian have to be greater than the proportion of men who said they were vegetarian in order for [latex]p_{1} - p_{2}[\/latex] to fall within the confidence interval?<\/p>\n<\/div>\n

               <\/p>\n

              1. d.). What percentage of Americans are vegetarian?<\/em> Gallup. https:\/\/news.gallup.com\/poll\/267074\/percentage-americans-vegetarian.aspx ↵<\/a><\/li><\/ol><\/div>","protected":false},"author":574340,"menu_order":19,"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-5397","chapter","type-chapter","status-publish","hentry"],"part":5305,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5397","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":3,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5397\/revisions"}],"predecessor-version":[{"id":5406,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5397\/revisions\/5406"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/5305"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5397\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=5397"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=5397"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=5397"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=5397"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}