{"id":1401,"date":"2023-06-22T02:22:45","date_gmt":"2023-06-22T02:22:45","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/introduction-to-chi-square-statistics-apply-it-3\/"},"modified":"2025-05-16T23:37:01","modified_gmt":"2025-05-16T23:37:01","slug":"introduction-to-chi-square-statistics-apply-it-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/introduction-to-chi-square-statistics-apply-it-3\/","title":{"raw":"Introduction to Chi-Square Statistics \u2013 Apply It 3","rendered":"Introduction to Chi-Square Statistics \u2013 Apply 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;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] Distribution<\/h2>\r\n<p>To assess what our chi-square value tells us about the distance between the expected and observed values, we turn to the chi-square distribution, assuming the conditions of using the chi-square distribution are met (we will talk about these conditions soon!).<\/p>\r\n<section class=\"textbox interact\"><strong>Step 1: <\/strong>Select the <strong>Goodness of Fit<\/strong> tab.<br \/>\r\n<strong>Step 2: <\/strong>Under \u201cEnter Data,\u201d choose the \u201cContingency Table\u201d option.<br \/>\r\n<strong>Step 3: <\/strong>Enter the relevant data and proportions below and press \u201cSubmit.\u201d\r\n\r\n<table style=\"border-collapse: collapse; width: 100%; height: 48px;\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 20%; height: 16px;\">\u00a0<\/td>\r\n<td style=\"width: 20%; height: 16px;\"><strong>Asian American<\/strong><\/td>\r\n<td style=\"width: 20%; height: 16px;\"><strong>Hispanic<\/strong><\/td>\r\n<td style=\"width: 20%; height: 16px;\"><strong>African American<\/strong><\/td>\r\n<td style=\"width: 20%; height: 16px;\"><strong>White<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 20%; height: 16px;\"><strong>Counts<\/strong><\/td>\r\n<td style=\"width: 20%; height: 16px;\">432<\/td>\r\n<td style=\"width: 20%; height: 16px;\">247<\/td>\r\n<td style=\"width: 20%; height: 16px;\">226<\/td>\r\n<td style=\"width: 20%; height: 16px;\">1118<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 20%; height: 16px;\"><strong>Proportions<\/strong><\/td>\r\n<td style=\"width: 20%; height: 16px;\">0.574<\/td>\r\n<td style=\"width: 20%; height: 16px;\">0.031<\/td>\r\n<td style=\"width: 20%; height: 16px;\">0.008<\/td>\r\n<td style=\"width: 20%; height: 16px;\">0.387<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/section>\r\n<p><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/chisquaredtest\/\" width=\"100%\" height=\"1100\" frameborder=\"no\"><\/iframe><br \/>\r\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/chisquaredtest\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1 ]2346[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1 ]2347[\/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] Distribution<\/h2>\n<p>To assess what our chi-square value tells us about the distance between the expected and observed values, we turn to the chi-square distribution, assuming the conditions of using the chi-square distribution are met (we will talk about these conditions soon!).<\/p>\n<section class=\"textbox interact\"><strong>Step 1: <\/strong>Select the <strong>Goodness of Fit<\/strong> tab.<br \/>\n<strong>Step 2: <\/strong>Under \u201cEnter Data,\u201d choose the \u201cContingency Table\u201d option.<br \/>\n<strong>Step 3: <\/strong>Enter the relevant data and proportions below and press \u201cSubmit.\u201d<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 48px;\">\n<tbody>\n<tr style=\"height: 16px;\">\n<td style=\"width: 20%; height: 16px;\">\u00a0<\/td>\n<td style=\"width: 20%; height: 16px;\"><strong>Asian American<\/strong><\/td>\n<td style=\"width: 20%; height: 16px;\"><strong>Hispanic<\/strong><\/td>\n<td style=\"width: 20%; height: 16px;\"><strong>African American<\/strong><\/td>\n<td style=\"width: 20%; height: 16px;\"><strong>White<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 20%; height: 16px;\"><strong>Counts<\/strong><\/td>\n<td style=\"width: 20%; height: 16px;\">432<\/td>\n<td style=\"width: 20%; height: 16px;\">247<\/td>\n<td style=\"width: 20%; height: 16px;\">226<\/td>\n<td style=\"width: 20%; height: 16px;\">1118<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 20%; height: 16px;\"><strong>Proportions<\/strong><\/td>\n<td style=\"width: 20%; height: 16px;\">0.574<\/td>\n<td style=\"width: 20%; height: 16px;\">0.031<\/td>\n<td style=\"width: 20%; height: 16px;\">0.008<\/td>\n<td style=\"width: 20%; height: 16px;\">0.387<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/section>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/chisquaredtest\/\" width=\"100%\" height=\"1100\" frameborder=\"no\"><\/iframe><br \/>\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/chisquaredtest\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2346\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2346&theme=lumen&iframe_resize_id=ohm2346&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2347\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2347&theme=lumen&iframe_resize_id=ohm2347&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":11,"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\/1401"}],"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":9,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1401\/revisions"}],"predecessor-version":[{"id":6865,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1401\/revisions\/6865"}],"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\/1401\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1401"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1401"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1401"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1401"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}