{"id":5299,"date":"2022-08-19T15:57:54","date_gmt":"2022-08-19T15:57:54","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=5299"},"modified":"2022-08-19T16:05:33","modified_gmt":"2022-08-19T16:05:33","slug":"10d-preview","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/10d-preview\/","title":{"raw":"10D Preview","rendered":"10D Preview"},"content":{"raw":"Preparing for the next class\r\n\r\nIn the next in-class activity, you will need to be able to identify the sample and\u00a0 population, calculate sample proportions and their differences, and identify independent\u00a0 vs. dependent samples. You will also need to know how to use technology to calculate\u00a0 the confidence interval for the difference in two proportions from independent samples\u00a0 and understand how to interpret the confidence interval in the context of the data.\r\n\r\nDo job callbacks differ based on the perceived gender of the applicant? To examine this\u00a0 question, we will analyze data from an experiment[footnote]Bertrand, M. & Mullainathan, S. (2004). Are Emily and Greg more employable than Lakisha and Jamal? A field experiment on labor market discrimination. American Economic Review 94<\/em>(4), 991\u20131013. DOI: 10.1257\/0002828042002561. http:\/\/www.nber.org\/papers\/w9873 [\/footnote] to assess the impact of gender and\u00a0 race on a job applicant receiving a callback, the opportunity to progress to the next part\u00a0 of the applicant process based on their application. The researchers submitted\u00a0 applications to job openings posted in Boston and Chicago in 2001 and 2002. The\u00a0 researchers randomly assigned names that are commonly associated with particular\u00a0 races and genders. The data are from the resume[footnote]Which resume attributes drive job callbacks? (Race and gender under study.)<\/em> (n.d.). OpenIntro. Retrieved from https:\/\/www.openintro.org\/data\/index.php?data=resume[\/footnote] dataset in the OpenIntro R\u00a0 package.\r\n
\r\n

Question 1<\/h3>\r\nIn this preview assignment, we will focus on whether there was a difference between\u00a0 the proportion of callbacks for applications the researchers identified as being\u00a0 perceived as female and the proportion of callbacks for applications the researchers\u00a0 identified as being perceived as male.\r\n\r\nOf the 3,746 applications with names perceived as female, 309 received callbacks.\u00a0 Of the 1,124 applications with names perceived as male, 83 received callbacks.\r\n
    \r\n \t
  1. What is the population of interest?\r\n
      \r\n \t
    1. Adults who submit job applications<\/li>\r\n \t
    2. Female adults who submit job applications<\/li>\r\n \t
    3. 3,746 applicants in the data who were perceived to be female<\/li>\r\n \t
    4. 4,870 applicants in the data<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
    5. What is the sample?\r\n
        \r\n \t
      1. Adults who submit job applications<\/li>\r\n \t
      2. Female adults who submit job applications<\/li>\r\n \t
      3. 3,746 applicants in the data who were perceived to be female<\/li>\r\n \t
      4. 4,870 applicants in the data<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
      5. Calculate [latex] \\hat{p}[\/latex], the proportion of applicants in the data who received callbacks.<\/li>\r\n \t
      6. Calculate [latex] \\hat{p_{F}}[\/latex], the proportion of applicants perceived as female who received\u00a0 callbacks.<\/li>\r\n \t
      7. Calculate [latex] \\hat{p_{M}}[\/latex], the proportion of applicants perceived as male who received\u00a0 callbacks.<\/li>\r\n<\/ol>\r\n<\/div>\r\n
        \r\n

        Question 2<\/h3>\r\nWe are interested in understanding [latex] p_{F} - p_{M}[\/latex], the true difference between the\u00a0 proportion of applicants perceived as female who received callbacks and the\u00a0 proportion of applicants perceived as male who received callbacks.\r\n
          \r\n \t
        1. Calculate the associated sample statistic [latex] \\hat{p_{F}} - \\hat{p_{M}}[\/latex], the best guess for the difference in proportions given our data.<\/li>\r\n \t
        2. Based on your answer to Part a, do you think the proportions of callbacks\u00a0 differ based on perceived gender? Explain.<\/li>\r\n<\/ol>\r\n<\/div>\r\nThough we have an estimate, or a \u201cbest guess,\u201d for the difference in proportions of applicants who received callbacks between the two groups, we expect there is some variability associated with that estimate. In other words, if we calculated the difference in the proportions of applicants who received callbacks from two other random samples of 3,746 applicants who were perceived as female and 1,124 applicants who were perceived as male, we would expect to get a different (yet probably close) value of [latex] \\hat{p_{F}} - \\hat{p_{M}}[\/latex] compared to what we did in the previous exercise.\r\n\r\nSimilar to a single proportion, we can calculate a confidence interval to obtain a plausible range of values the true difference in proportions takes, assuming certain conditions hold. For the remainder of this assignment, you will focus on the independence condition and on using technology to calculate the confidence interval. In the in-class activity, you will learn more about the underlying mathematics and other conditions.\r\n
          \r\n

          Question 3<\/h3>\r\nThere are two different methods for calculating confidence intervals for the\u00a0 difference in proportions. The method you use depends on whether the two groups\u00a0 are independent or dependent (paired). If the two groups are independent, the\u00a0 sample for one group is drawn independently of the other group. Knowing the\u00a0 observations of one group does not provide useful information about the other\u00a0 sample. Additionally, the groups can be different sizes.\r\n\r\nIf the two groups are dependent (also known as paired), the samples for the two\u00a0 groups are not drawn independently of one another. Knowing the observations of one group does provide useful information about the other sample. Additionally, both\u00a0 groups must be the same size.\r\n\r\nBelow are a few analysis objectives. Identify which of the following involves samples\u00a0 from independent groups. Select all that apply.\r\n
            \r\n \t
          1. Assess student learning by looking at the difference in the mean score of a\u00a0 statistics test taken at the beginning and end of the semester<\/li>\r\n \t
          2. Assess the difference in proportions of students who major in statistics between\u00a0 public and private colleges<\/li>\r\n \t
          3. Assess the difference in mean daily hours users spend on their phones between\u00a0 iPhone and Samsung users<\/li>\r\n \t
          4. Assess the difference in participants\u2019 fitness levels before and after a six-week\u00a0 training program<\/li>\r\n \t
          5. Assess the difference in proportions of participants who pass a fitness test\u00a0 between those who do a six-week training program and those who don\u2019t<\/li>\r\n<\/ol>\r\n<\/div>\r\n
            \r\n

            Question 4<\/h3>\r\nLet\u2019s go back to the job applicants analysis. What are the two groups in this study?\u00a0 Are they independent or dependent? Select the best response.\r\n
              \r\n \t
            1. The two groups are those who received callbacks and those who didn\u2019t. They are\u00a0 independent, since the sample for one group was drawn independently of the\u00a0 sample for the other group.<\/li>\r\n \t
            2. The two groups are those who received callbacks and those who didn\u2019t. They are\u00a0 not independent, since the sample for one group gives useful information about\u00a0 the sample for the other group.<\/li>\r\n \t
            3. The two groups are those who were perceived as female and those who were\u00a0 perceived as male. They are independent, since the sample for one group was\u00a0 drawn independently of the sample for the other group.<\/li>\r\n \t
            4. The two groups are those who were perceived as female and those who were\u00a0 perceived as male. They are not independent, since the sample for one group\u00a0 gives useful information about the sample for the other group.<\/li>\r\n<\/ol>\r\n<\/div>\r\n
              \r\n

              Question 5<\/h3>\r\nWe will focus on calculating the confidence interval for the difference between two population proportions for independent groups. To calculate the confidence interval, use the Confidence Interval & Significance Test tab on the DCMP Compare Two Population Proportions tool: https:\/\/dcmathpathways.shinyapps.io\/2sample_prop\/<\/a>.\r\n\r\nTo enter the summary data at the beginning of this preview assignment, select \u201cNumber of Successes\u201d under \u201cEnter Data\u201d on the left-hand side. Since we are interested in calculating the confidence interval for [latex] \\hat{p_{F}} - \\hat{p_{M}}[\/latex], Group 1 is the group perceived as female and Group 2 is the group perceived as male.\r\n\r\nEnter the number of successes and sample sizes for each group in the tool. You can also add informative group labels. The following is a screenshot to help you get started.\r\n\r\n\"\"\r\n\r\nOnce you have entered the information for both groups, the confidence interval will\u00a0 be calculated in the tool. You can change the confidence interval using the slider on the left-hand side.\r\n\r\nWhat is the 95% confidence interval for the difference in proportions of applicants\u00a0 who received callbacks between those perceived as female and those perceived as male?\r\n\r\n<\/div>\r\n
              \r\n

              Question 6<\/h3>\r\nWhat does the 95% confidence interval mean? Select all that apply.\r\n
                \r\n \t
              1. We are 95% confident that the true difference in proportions of applicants who\u00a0 received callbacks between those perceived as female and those perceived as\u00a0 male is between \u22120.009 and 0.0263.<\/li>\r\n \t
              2. We are 95% confident that the difference in proportions of applicants who\u00a0 received callbacks between those perceived as female and those perceived as\u00a0 male in the sample is between \u22120.009 and 0.0263.<\/li>\r\n \t
              3. The confidence interval does not provide sufficient evidence of a difference in the\u00a0 proportions of callbacks between the two groups since 0 is in the interval.<\/li>\r\n \t
              4. The confidence interval does provide sufficient evidence of a difference in the\u00a0 proportions of callbacks between the two groups since 0 is in the interval.<\/li>\r\n<\/ol>\r\ne) There is a 95% probability that the true difference in proportions of applicants who\u00a0 received callbacks between those perceived as female and those perceived as\u00a0 male is between \u22120.009 and 0.0263.\r\n\r\n<\/div>\r\n ","rendered":"

                Preparing for the next class<\/p>\n

                In the next in-class activity, you will need to be able to identify the sample and\u00a0 population, calculate sample proportions and their differences, and identify independent\u00a0 vs. dependent samples. You will also need to know how to use technology to calculate\u00a0 the confidence interval for the difference in two proportions from independent samples\u00a0 and understand how to interpret the confidence interval in the context of the data.<\/p>\n

                Do job callbacks differ based on the perceived gender of the applicant? To examine this\u00a0 question, we will analyze data from an experiment[1]<\/sup><\/a> to assess the impact of gender and\u00a0 race on a job applicant receiving a callback, the opportunity to progress to the next part\u00a0 of the applicant process based on their application. The researchers submitted\u00a0 applications to job openings posted in Boston and Chicago in 2001 and 2002. The\u00a0 researchers randomly assigned names that are commonly associated with particular\u00a0 races and genders. The data are from the resume[2]<\/sup><\/a> dataset in the OpenIntro R\u00a0 package.<\/p>\n

                \n

                Question 1<\/h3>\n

                In this preview assignment, we will focus on whether there was a difference between\u00a0 the proportion of callbacks for applications the researchers identified as being\u00a0 perceived as female and the proportion of callbacks for applications the researchers\u00a0 identified as being perceived as male.<\/p>\n

                Of the 3,746 applications with names perceived as female, 309 received callbacks.\u00a0 Of the 1,124 applications with names perceived as male, 83 received callbacks.<\/p>\n

                  \n
                1. What is the population of interest?\n
                    \n
                  1. Adults who submit job applications<\/li>\n
                  2. Female adults who submit job applications<\/li>\n
                  3. 3,746 applicants in the data who were perceived to be female<\/li>\n
                  4. 4,870 applicants in the data<\/li>\n<\/ol>\n<\/li>\n
                  5. What is the sample?\n
                      \n
                    1. Adults who submit job applications<\/li>\n
                    2. Female adults who submit job applications<\/li>\n
                    3. 3,746 applicants in the data who were perceived to be female<\/li>\n
                    4. 4,870 applicants in the data<\/li>\n<\/ol>\n<\/li>\n
                    5. Calculate [latex]\\hat{p}[\/latex], the proportion of applicants in the data who received callbacks.<\/li>\n
                    6. Calculate [latex]\\hat{p_{F}}[\/latex], the proportion of applicants perceived as female who received\u00a0 callbacks.<\/li>\n
                    7. Calculate [latex]\\hat{p_{M}}[\/latex], the proportion of applicants perceived as male who received\u00a0 callbacks.<\/li>\n<\/ol>\n<\/div>\n
                      \n

                      Question 2<\/h3>\n

                      We are interested in understanding [latex]p_{F} - p_{M}[\/latex], the true difference between the\u00a0 proportion of applicants perceived as female who received callbacks and the\u00a0 proportion of applicants perceived as male who received callbacks.<\/p>\n

                        \n
                      1. Calculate the associated sample statistic [latex]\\hat{p_{F}} - \\hat{p_{M}}[\/latex], the best guess for the difference in proportions given our data.<\/li>\n
                      2. Based on your answer to Part a, do you think the proportions of callbacks\u00a0 differ based on perceived gender? Explain.<\/li>\n<\/ol>\n<\/div>\n

                        Though we have an estimate, or a \u201cbest guess,\u201d for the difference in proportions of applicants who received callbacks between the two groups, we expect there is some variability associated with that estimate. In other words, if we calculated the difference in the proportions of applicants who received callbacks from two other random samples of 3,746 applicants who were perceived as female and 1,124 applicants who were perceived as male, we would expect to get a different (yet probably close) value of [latex]\\hat{p_{F}} - \\hat{p_{M}}[\/latex] compared to what we did in the previous exercise.<\/p>\n

                        Similar to a single proportion, we can calculate a confidence interval to obtain a plausible range of values the true difference in proportions takes, assuming certain conditions hold. For the remainder of this assignment, you will focus on the independence condition and on using technology to calculate the confidence interval. In the in-class activity, you will learn more about the underlying mathematics and other conditions.<\/p>\n

                        \n

                        Question 3<\/h3>\n

                        There are two different methods for calculating confidence intervals for the\u00a0 difference in proportions. The method you use depends on whether the two groups\u00a0 are independent or dependent (paired). If the two groups are independent, the\u00a0 sample for one group is drawn independently of the other group. Knowing the\u00a0 observations of one group does not provide useful information about the other\u00a0 sample. Additionally, the groups can be different sizes.<\/p>\n

                        If the two groups are dependent (also known as paired), the samples for the two\u00a0 groups are not drawn independently of one another. Knowing the observations of one group does provide useful information about the other sample. Additionally, both\u00a0 groups must be the same size.<\/p>\n

                        Below are a few analysis objectives. Identify which of the following involves samples\u00a0 from independent groups. Select all that apply.<\/p>\n

                          \n
                        1. Assess student learning by looking at the difference in the mean score of a\u00a0 statistics test taken at the beginning and end of the semester<\/li>\n
                        2. Assess the difference in proportions of students who major in statistics between\u00a0 public and private colleges<\/li>\n
                        3. Assess the difference in mean daily hours users spend on their phones between\u00a0 iPhone and Samsung users<\/li>\n
                        4. Assess the difference in participants\u2019 fitness levels before and after a six-week\u00a0 training program<\/li>\n
                        5. Assess the difference in proportions of participants who pass a fitness test\u00a0 between those who do a six-week training program and those who don\u2019t<\/li>\n<\/ol>\n<\/div>\n
                          \n

                          Question 4<\/h3>\n

                          Let\u2019s go back to the job applicants analysis. What are the two groups in this study?\u00a0 Are they independent or dependent? Select the best response.<\/p>\n

                            \n
                          1. The two groups are those who received callbacks and those who didn\u2019t. They are\u00a0 independent, since the sample for one group was drawn independently of the\u00a0 sample for the other group.<\/li>\n
                          2. The two groups are those who received callbacks and those who didn\u2019t. They are\u00a0 not independent, since the sample for one group gives useful information about\u00a0 the sample for the other group.<\/li>\n
                          3. The two groups are those who were perceived as female and those who were\u00a0 perceived as male. They are independent, since the sample for one group was\u00a0 drawn independently of the sample for the other group.<\/li>\n
                          4. The two groups are those who were perceived as female and those who were\u00a0 perceived as male. They are not independent, since the sample for one group\u00a0 gives useful information about the sample for the other group.<\/li>\n<\/ol>\n<\/div>\n
                            \n

                            Question 5<\/h3>\n

                            We will focus on calculating the confidence interval for the difference between two population proportions for independent groups. To calculate the confidence interval, use the Confidence Interval & Significance Test tab on the DCMP Compare Two Population Proportions tool: https:\/\/dcmathpathways.shinyapps.io\/2sample_prop\/<\/a>.<\/p>\n

                            To enter the summary data at the beginning of this preview assignment, select \u201cNumber of Successes\u201d under \u201cEnter Data\u201d on the left-hand side. Since we are interested in calculating the confidence interval for [latex]\\hat{p_{F}} - \\hat{p_{M}}[\/latex], Group 1 is the group perceived as female and Group 2 is the group perceived as male.<\/p>\n

                            Enter the number of successes and sample sizes for each group in the tool. You can also add informative group labels. The following is a screenshot to help you get started.<\/p>\n

                            \"\"<\/p>\n

                            Once you have entered the information for both groups, the confidence interval will\u00a0 be calculated in the tool. You can change the confidence interval using the slider on the left-hand side.<\/p>\n

                            What is the 95% confidence interval for the difference in proportions of applicants\u00a0 who received callbacks between those perceived as female and those perceived as male?<\/p>\n<\/div>\n

                            \n

                            Question 6<\/h3>\n

                            What does the 95% confidence interval mean? Select all that apply.<\/p>\n

                              \n
                            1. We are 95% confident that the true difference in proportions of applicants who\u00a0 received callbacks between those perceived as female and those perceived as\u00a0 male is between \u22120.009 and 0.0263.<\/li>\n
                            2. We are 95% confident that the difference in proportions of applicants who\u00a0 received callbacks between those perceived as female and those perceived as\u00a0 male in the sample is between \u22120.009 and 0.0263.<\/li>\n
                            3. The confidence interval does not provide sufficient evidence of a difference in the\u00a0 proportions of callbacks between the two groups since 0 is in the interval.<\/li>\n
                            4. The confidence interval does provide sufficient evidence of a difference in the\u00a0 proportions of callbacks between the two groups since 0 is in the interval.<\/li>\n<\/ol>\n

                              e) There is a 95% probability that the true difference in proportions of applicants who\u00a0 received callbacks between those perceived as female and those perceived as\u00a0 male is between \u22120.009 and 0.0263.<\/p>\n<\/div>\n

                               <\/p>\n

                              1. Bertrand, M. & Mullainathan, S. (2004). Are Emily and Greg more employable than Lakisha and Jamal? A field experiment on labor market discrimination. American Economic Review 94<\/em>(4), 991\u20131013. DOI: 10.1257\/0002828042002561. http:\/\/www.nber.org\/papers\/w9873 ↵<\/a><\/li>
                              2. Which resume attributes drive job callbacks? (Race and gender under study.)<\/em> (n.d.). OpenIntro. Retrieved from https:\/\/www.openintro.org\/data\/index.php?data=resume ↵<\/a><\/li><\/ol><\/div>","protected":false},"author":574340,"menu_order":12,"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-5299","chapter","type-chapter","status-publish","hentry"],"part":5220,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5299","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":5,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5299\/revisions"}],"predecessor-version":[{"id":5687,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5299\/revisions\/5687"}],"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\/5299\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=5299"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=5299"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=5299"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=5299"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}