{"id":1399,"date":"2023-06-22T02:22:43","date_gmt":"2023-06-22T02:22:43","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/introduction-to-chi-square-statistics-apply-it-2\/"},"modified":"2025-05-16T23:18:44","modified_gmt":"2025-05-16T23:18:44","slug":"introduction-to-chi-square-statistics-apply-it-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/introduction-to-chi-square-statistics-apply-it-2\/","title":{"raw":"Introduction to Chi-Square Statistics \u2013 Apply It 2","rendered":"Introduction to Chi-Square Statistics \u2013 Apply 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;Calculate and describe the value of a chi-square statistics in context of a real-world problem&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:12801,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;arial&quot;,&quot;16&quot;:9}\">Calculate and describe the value of a chi-square statistics in context of a real-world problem<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Write a null and alternative hypothesis for a chi-square test&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:12801,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;arial&quot;,&quot;16&quot;:9}\">Write a null and alternative hypothesis for a chi-square test<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>[latex]\\chi^2[\/latex] Test Statistic<\/h2>\r\n<p>Imagine that Harvard claims: \u201cWe only accept the top academic applicants, and we treat those applicants equally. Our admitted class is as good as a random sample from the distribution of top academic applicants.\u201d<\/p>\r\n<p>You would like to decide if there\u2019s convincing evidence against this claim.<\/p>\r\n<ul>\r\n\t<li>Formally, the <strong>null hypothesis<\/strong>, [latex]H_0[\/latex], is that the distribution of the admitted group is the same as the distribution of the top academic applicants.<\/li>\r\n\t<li>The <strong>alternative hypothesis<\/strong>, [latex]H_A[\/latex], is that the distribution of the admitted group is different than the distribution of the top academic applicants.<\/li>\r\n<\/ul>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1 ]2342[\/ohm2_question]<\/section>\r\n<section class=\"textbox recall\">\r\n<p class=\"student12ptnumberlist\">The following is the formula for the chi-square test statistic:<\/p>\r\n<p style=\"text-align: center;\">[latex]\\chi^2=\\sum\\dfrac{(\\text{Observed}-\\text{Expected})^2}{\\text{Expected}}[\/latex]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1 ]2344[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1 ]2345[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Calculate and describe the value of a chi-square statistics in context of a real-world problem&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:12801,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;arial&quot;,&quot;16&quot;:9}\">Calculate and describe the value of a chi-square statistics in context of a real-world problem<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Write a null and alternative hypothesis for a chi-square test&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:12801,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;arial&quot;,&quot;16&quot;:9}\">Write a null and alternative hypothesis for a chi-square test<\/span><\/li>\n<\/ul>\n<\/section>\n<h2>[latex]\\chi^2[\/latex] Test Statistic<\/h2>\n<p>Imagine that Harvard claims: \u201cWe only accept the top academic applicants, and we treat those applicants equally. Our admitted class is as good as a random sample from the distribution of top academic applicants.\u201d<\/p>\n<p>You would like to decide if there\u2019s convincing evidence against this claim.<\/p>\n<ul>\n<li>Formally, the <strong>null hypothesis<\/strong>, [latex]H_0[\/latex], is that the distribution of the admitted group is the same as the distribution of the top academic applicants.<\/li>\n<li>The <strong>alternative hypothesis<\/strong>, [latex]H_A[\/latex], is that the distribution of the admitted group is different than the distribution of the top academic applicants.<\/li>\n<\/ul>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2342\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2342&theme=lumen&iframe_resize_id=ohm2342&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox recall\">\n<p class=\"student12ptnumberlist\">The following is the formula for the chi-square test statistic:<\/p>\n<p style=\"text-align: center;\">[latex]\\chi^2=\\sum\\dfrac{(\\text{Observed}-\\text{Expected})^2}{\\text{Expected}}[\/latex]<\/p>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2344\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2344&theme=lumen&iframe_resize_id=ohm2344&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2345\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2345&theme=lumen&iframe_resize_id=ohm2345&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":10,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":1388,"module-header":"apply_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\/1399"}],"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\/8"}],"version-history":[{"count":4,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1399\/revisions"}],"predecessor-version":[{"id":6864,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1399\/revisions\/6864"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/1388"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1399\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1399"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1399"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1399"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1399"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}