{"id":2127,"date":"2023-07-27T01:14:34","date_gmt":"2023-07-27T01:14:34","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/?post_type=chapter&#038;p=2127"},"modified":"2025-05-16T03:43:41","modified_gmt":"2025-05-16T03:43:41","slug":"two-sample-test-for-proportions-learn-it-3-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/two-sample-test-for-proportions-learn-it-3-2\/","title":{"raw":"Two-Sample Test for Proportions: Learn It 3","rendered":"Two-Sample Test for Proportions: Learn It 3"},"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>Hypotheses<\/h2>\r\n<p>Like any other hypothesis test, the first step for <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;}\">a two-sample [latex]z[\/latex]-test for proportions <\/span>is to clearly state the null hypothesis ([latex]H_{0}[\/latex]) and the alternative hypothesis ([latex]H_{A}[\/latex]).<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]962[\/ohm2_question]<\/section>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>hypotheses for a two-sample [latex]z[\/latex]-test for proportions<\/h3>\r\n<ul>\r\n\t<li>Null hypothesis: There is no difference between the proportions of the two groups.<\/li>\r\n<\/ul>\r\n<p style=\"text-align: center;\">[latex]H_0: p_1=p_2[\/latex] or [latex]H_0: p_1-p_2=0[\/latex]<\/p>\r\n<p>&nbsp;<\/p>\r\n<ul>\r\n\t<li>Alternative hypothesis: There are three choices between a two-tailed or one-tailed test, depending on the specific research question and the direction of the expected difference in proportions between the two groups.<\/li>\r\n<\/ul>\r\n<p style=\"text-align: center;\">[latex]H_A: p_1\\lt p_2[\/latex] or [latex]H_A: p_1-p_2\\lt 0[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]H_A: p_1&gt;p_2[\/latex] or [latex]H_A: p_1-p_2&gt;0[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]H_A: p_1\\ne p_2[\/latex] or [latex]H_A: p_1-p_2\\ne0[\/latex]<\/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>Hypotheses<\/h2>\n<p>Like any other hypothesis test, the first step for <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;}\">a two-sample [latex]z[\/latex]-test for proportions <\/span>is to clearly state the null hypothesis ([latex]H_{0}[\/latex]) and the alternative hypothesis ([latex]H_{A}[\/latex]).<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm962\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=962&theme=lumen&iframe_resize_id=ohm962&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox keyTakeaway\">\n<h3>hypotheses for a two-sample [latex]z[\/latex]-test for proportions<\/h3>\n<ul>\n<li>Null hypothesis: There is no difference between the proportions of the two groups.<\/li>\n<\/ul>\n<p style=\"text-align: center;\">[latex]H_0: p_1=p_2[\/latex] or [latex]H_0: p_1-p_2=0[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<ul>\n<li>Alternative hypothesis: There are three choices between a two-tailed or one-tailed test, depending on the specific research question and the direction of the expected difference in proportions between the two groups.<\/li>\n<\/ul>\n<p style=\"text-align: center;\">[latex]H_A: p_1\\lt p_2[\/latex] or [latex]H_A: p_1-p_2\\lt 0[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]H_A: p_1>p_2[\/latex] or [latex]H_A: p_1-p_2>0[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]H_A: p_1\\ne p_2[\/latex] or [latex]H_A: p_1-p_2\\ne0[\/latex]<\/p>\n<\/section>\n","protected":false},"author":12,"menu_order":34,"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\/2127"}],"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":8,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/2127\/revisions"}],"predecessor-version":[{"id":6771,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/2127\/revisions\/6771"}],"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\/2127\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=2127"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=2127"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=2127"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=2127"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}