{"id":1397,"date":"2023-06-22T02:22:41","date_gmt":"2023-06-22T02:22:41","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/introduction-to-chi-square-statistics-learn-it-3\/"},"modified":"2025-05-16T23:08:32","modified_gmt":"2025-05-16T23:08:32","slug":"introduction-to-chi-square-statistics-learn-it-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/introduction-to-chi-square-statistics-learn-it-3\/","title":{"raw":"Introduction to Chi-Square Statistics \u2013 Learn It 3","rendered":"Introduction to Chi-Square Statistics \u2013 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;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<p class=\"para\" style=\"margin: 6.0pt 0in 6.0pt 0in;\">So, what does our chi-square test statistic value mean? To assess what our chi-square value tells us about the distance between the expected and observed counts, we\u2019ll turn to the chi-square distribution.<\/p>\r\n<p>Let's explore the Chi-Square Distribution using the statistical tool below.<\/p>\r\n<section class=\"textbox proTip\">Note that the number of <strong>degrees of freedom<\/strong> is one fewer than the number of possible categories for our categorical variable, that is, [latex] df = (\\text{number of categories} \u2013 1)[\/latex].<\/section>\r\n<p><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/chisqdist\/\" width=\"100%\" height=\"700\" frameborder=\"no\"><\/iframe><br \/>\r\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/chisqdist\/\" 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 ]2327[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1 ]2328[\/ohm2_question]<\/section>\r\n<section>Suppose that the claim made is: \"The distribution of birthdates among all professional Italian football players is the same as the distribution of birthdates in the general Italian population\". You would like to decide if there\u2019s convincing evidence against this claim.\r\n\r\n<ul>\r\n\t<li>Formally, the\u00a0<strong>null hypothesis<\/strong>, [latex]H_0[\/latex], is that the distribution of birthdates among all professional Italian football players is the same as the distribution of birthdates in the general Italian population.<\/li>\r\n\t<li>The\u00a0<strong>alternative hypothesis<\/strong>, [latex]H_A[\/latex], is that the distribution of birthdates among all professional Italian football players is different from the distribution of birthdates in the general Italian population.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1 ]2330[\/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<p class=\"para\" style=\"margin: 6.0pt 0in 6.0pt 0in;\">So, what does our chi-square test statistic value mean? To assess what our chi-square value tells us about the distance between the expected and observed counts, we\u2019ll turn to the chi-square distribution.<\/p>\n<p>Let&#8217;s explore the Chi-Square Distribution using the statistical tool below.<\/p>\n<section class=\"textbox proTip\">Note that the number of <strong>degrees of freedom<\/strong> is one fewer than the number of possible categories for our categorical variable, that is, [latex]df = (\\text{number of categories} \u2013 1)[\/latex].<\/section>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/chisqdist\/\" width=\"100%\" height=\"700\" frameborder=\"no\"><\/iframe><br \/>\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/chisqdist\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2327\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2327&theme=lumen&iframe_resize_id=ohm2327&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2328\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2328&theme=lumen&iframe_resize_id=ohm2328&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section>Suppose that the claim made is: &#8220;The distribution of birthdates among all professional Italian football players is the same as the distribution of birthdates in the general Italian population&#8221;. You would like to decide if there\u2019s convincing evidence against this claim.<\/p>\n<ul>\n<li>Formally, the\u00a0<strong>null hypothesis<\/strong>, [latex]H_0[\/latex], is that the distribution of birthdates among all professional Italian football players is the same as the distribution of birthdates in the general Italian population.<\/li>\n<li>The\u00a0<strong>alternative hypothesis<\/strong>, [latex]H_A[\/latex], is that the distribution of birthdates among all professional Italian football players is different from the distribution of birthdates in the general Italian population.<\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2330\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2330&theme=lumen&iframe_resize_id=ohm2330&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":8,"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":"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\/1397"}],"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\/1397\/revisions"}],"predecessor-version":[{"id":6862,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1397\/revisions\/6862"}],"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\/1397\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1397"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1397"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1397"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1397"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}