{"id":2118,"date":"2023-07-27T00:28:00","date_gmt":"2023-07-27T00:28:00","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/?post_type=chapter&#038;p=2118"},"modified":"2025-05-16T03:42:31","modified_gmt":"2025-05-16T03:42:31","slug":"two-sample-test-for-proportions-learn-it-1-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/two-sample-test-for-proportions-learn-it-1-2\/","title":{"raw":"Two-Sample Test for Proportions: Learn It 1","rendered":"Two-Sample Test for Proportions: Learn It 1"},"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<p class=\"para\" style=\"margin-left: 0in; text-indent: 0in;\">A one-sample test of proportions is used to test a claim about a population proportion based on data from a single sample. However, in some situations, we may have two independent samples, and we need to compare the proportions between the two groups.<\/p>\r\n<section class=\"textbox proTip\"><strong>A two-sample test of proportions<\/strong> is employed to test a claim about two population proportions, whether there is a significant difference in proportions between the two distinct groups or populations.\r\n\r\n<p>Note that when testing a claim that compares two populations, you must also check that the two populations are independent.<\/p>\r\n<\/section>\r\n<p>Let's see if we can distinguish between situations where a one-sample test would be appropriate and where a two-sample test would be appropriate.<\/p>\r\n<h3>Will I get a callback?<\/h3>\r\n<p><img class=\"aligncenter wp-image-416 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2022\/11\/23211630\/Picture1-4-1.jpg\" alt=\"An example poster of a job posting. It reads &quot;join our team WE ARE HIRING&quot;. In the bottom left corner, there is text reading &quot;SEND US YOUR CV YOURWEBSITE.COM&quot;.\" width=\"300\" height=\"202\" \/><\/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<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]11077[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]961[\/ohm2_question]<\/section>\r\n<section><\/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<p class=\"para\" style=\"margin-left: 0in; text-indent: 0in;\">A one-sample test of proportions is used to test a claim about a population proportion based on data from a single sample. However, in some situations, we may have two independent samples, and we need to compare the proportions between the two groups.<\/p>\n<section class=\"textbox proTip\"><strong>A two-sample test of proportions<\/strong> is employed to test a claim about two population proportions, whether there is a significant difference in proportions between the two distinct groups or populations.<\/p>\n<p>Note that when testing a claim that compares two populations, you must also check that the two populations are independent.<\/p>\n<\/section>\n<p>Let&#8217;s see if we can distinguish between situations where a one-sample test would be appropriate and where a two-sample test would be appropriate.<\/p>\n<h3>Will I get a callback?<\/h3>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-416 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2022\/11\/23211630\/Picture1-4-1.jpg\" alt=\"An example poster of a job posting. It reads &quot;join our team WE ARE HIRING&quot;. In the bottom left corner, there is text reading &quot;SEND US YOUR CV YOURWEBSITE.COM&quot;.\" width=\"300\" height=\"202\" \/><\/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-2118-1\" href=\"#footnote-2118-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a> to test for labor market discrimination.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm11077\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=11077&theme=lumen&iframe_resize_id=ohm11077&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm961\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=961&theme=lumen&iframe_resize_id=ohm961&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section><\/section>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-2118-1\">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-2118-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":12,"menu_order":32,"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\/2118"}],"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":9,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/2118\/revisions"}],"predecessor-version":[{"id":6769,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/2118\/revisions\/6769"}],"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\/2118\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=2118"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=2118"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=2118"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=2118"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}