{"id":2123,"date":"2023-07-27T00:47:31","date_gmt":"2023-07-27T00:47:31","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/?post_type=chapter&#038;p=2123"},"modified":"2025-05-16T03:43:01","modified_gmt":"2025-05-16T03:43:01","slug":"two-sample-test-for-proportions-learn-it-2-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/two-sample-test-for-proportions-learn-it-2-2\/","title":{"raw":"Two-Sample Test for Proportions: Learn It 2","rendered":"Two-Sample Test for Proportions: Learn It 2"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Recognize when a one-sample z-test or a two-sample z-test is needed to answer a research question&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Recognize when a one-sample [latex]z[\/latex]-test or a two-sample [latex]z[\/latex]-test is needed to answer a research question.<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Complete a two-sample z-test for proportions from hypotheses to conclusions&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Complete a two-sample [latex]z[\/latex]-test for proportions from hypotheses to conclusions.<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Will I get a callback?<\/h2>\r\n<p>Scenario:<\/p>\r\n<p>In 2004, two University of Chicago economists (Marianne Bertrand and Sendhil Mullainathan) decided to conduct an experiment[footnote]Bertrand, M. &amp; Mullainathan, S. (2003, July). Are Emily and Greg more employable than Lakisha and Jamal? A field experiment on labor market discrimination. National Bureau of Economic Research. https:\/\/www.nber.org\/papers\/w9873[\/footnote] to test for labor market discrimination.<\/p>\r\n<p>The investigators created [latex]4,890[\/latex] mock identical resum\u00e9s, which were sent to job placement ads in Chicago and Boston. To gauge market racial discrimination, each resum\u00e9 was randomly assigned either a commonly-white or commonly-black name. The experimenters then measured the proportion of resum\u00e9s from each group (white and black) that received callbacks.[footnote]Lesson adapted from Skew The Script. https:\/\/skewthescript.org\/7-8[\/footnote]<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]960[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1768[\/ohm2_question]<\/section>\r\n<section>The steps and the logic of the hypothesis test for comparing two population proportions are the same as we are conducting a hypothesis test for a population proportion.\r\n\r\n<p>We will need to: Write the null and alternative hypotheses, collect the data and check its conditions, assess the evidence (calculate its test statistics, find the p-value, compare p-value with the significance level), and state its conclusion.<\/p>\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Recognize when a one-sample z-test or a two-sample z-test is needed to answer a research question&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Recognize when a one-sample [latex]z[\/latex]-test or a two-sample [latex]z[\/latex]-test is needed to answer a research question.<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Complete a two-sample z-test for proportions from hypotheses to conclusions&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Complete a two-sample [latex]z[\/latex]-test for proportions from hypotheses to conclusions.<\/span><\/li>\n<\/ul>\n<\/section>\n<h2>Will I get a callback?<\/h2>\n<p>Scenario:<\/p>\n<p>In 2004, two University of Chicago economists (Marianne Bertrand and Sendhil Mullainathan) decided to conduct an experiment<a class=\"footnote\" title=\"Bertrand, M. &amp; Mullainathan, S. (2003, July). Are Emily and Greg more employable than Lakisha and Jamal? A field experiment on labor market discrimination. National Bureau of Economic Research. https:\/\/www.nber.org\/papers\/w9873\" id=\"return-footnote-2123-1\" href=\"#footnote-2123-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a> to test for labor market discrimination.<\/p>\n<p>The investigators created [latex]4,890[\/latex] mock identical resum\u00e9s, which were sent to job placement ads in Chicago and Boston. To gauge market racial discrimination, each resum\u00e9 was randomly assigned either a commonly-white or commonly-black name. The experimenters then measured the proportion of resum\u00e9s from each group (white and black) that received callbacks.<a class=\"footnote\" title=\"Lesson adapted from Skew The Script. https:\/\/skewthescript.org\/7-8\" id=\"return-footnote-2123-2\" href=\"#footnote-2123-2\" aria-label=\"Footnote 2\"><sup class=\"footnote\">[2]<\/sup><\/a><\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm960\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=960&theme=lumen&iframe_resize_id=ohm960&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1768\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1768&theme=lumen&iframe_resize_id=ohm1768&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section>The steps and the logic of the hypothesis test for comparing two population proportions are the same as we are conducting a hypothesis test for a population proportion.<\/p>\n<p>We will need to: Write the null and alternative hypotheses, collect the data and check its conditions, assess the evidence (calculate its test statistics, find the p-value, compare p-value with the significance level), and state its conclusion.<\/p>\n<\/section>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-2123-1\">Bertrand, M. &amp; Mullainathan, S. (2003, July). Are Emily and Greg more employable than Lakisha and Jamal? A field experiment on labor market discrimination. National Bureau of Economic Research. https:\/\/www.nber.org\/papers\/w9873 <a href=\"#return-footnote-2123-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><li id=\"footnote-2123-2\">Lesson adapted from Skew The Script. https:\/\/skewthescript.org\/7-8 <a href=\"#return-footnote-2123-2\" class=\"return-footnote\" aria-label=\"Return to footnote 2\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":12,"menu_order":33,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":1205,"module-header":"learn_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/2123"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/users\/12"}],"version-history":[{"count":5,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/2123\/revisions"}],"predecessor-version":[{"id":6770,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/2123\/revisions\/6770"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/1205"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/2123\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=2123"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=2123"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=2123"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=2123"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}