{"id":1418,"date":"2023-06-22T02:22:59","date_gmt":"2023-06-22T02:22:59","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/chi-square-test-of-homogeneity-apply-it-1\/"},"modified":"2025-05-16T23:43:31","modified_gmt":"2025-05-16T23:43:31","slug":"chi-square-test-of-homogeneity-apply-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/chi-square-test-of-homogeneity-apply-it-1\/","title":{"raw":"Chi-Square Test of Homogeneity \u2013 Apply It 1","rendered":"Chi-Square Test of Homogeneity \u2013 Apply 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;Complete a chi-square test of homogeneity&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}\">Complete a chi-square test of homogeneity<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Write the conclusion of a chi-square test of homogeneity in context of the 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}\">Write the conclusion of a chi-square test of homogeneity in context of the problem<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Steroid Use in Collegiate Sports<\/h2>\r\n<p>In 2006, the NCAA published a report called \u201cSubstance Use: NCAA Study of Substance Use of College Student-Athletes.\u201d[footnote]https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/datasets\/ncaa_2006_substance_use_report.pdf[\/footnote]<\/p>\r\n<p>Let's use the data from the 2006 NCAA published report to investigate the following question: <em>Does steroid use by student athletes differ for the three NCAA divisions?<\/em><\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1 ]2866[\/ohm2_question]<\/section>\r\n<p>A note on NCAA divisions: The National Collegiate Athletic Association (NCAA) is divided into three divisions and oversees a wide range of collegiate sports. Division I schools have to sponsor more sports teams. These schools tend to be large universities with large athletic budgets supplemented by revenue from the games. They must offer athletic scholarships. Division II schools tend to be the smaller public universities and many private institutions. They have much smaller budgets that come solely from the college. The NCAA limits the amount that Division II colleges can spend on athletic scholarships. Division III consists of colleges and universities that treat athletics as an extracurricular activity for students, instead of a source of revenue. These institutions do not offer athletic scholarships.<\/p>\r\n<p>Below are the summarized data from three samples, one from each division, in a two-way table.<\/p>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<th>\u00a0<\/th>\r\n<th colspan=\"2\">Admit Steroid Use<\/th>\r\n<th>\u00a0<\/th>\r\n<\/tr>\r\n<tr>\r\n<th>\u00a0<\/th>\r\n<th>Yes<\/th>\r\n<th>No<\/th>\r\n<th>Totals<\/th>\r\n<\/tr>\r\n<tr>\r\n<th>Division I<\/th>\r\n<td>103<\/td>\r\n<td>8,440<\/td>\r\n<td>8,543<\/td>\r\n<\/tr>\r\n<tr>\r\n<th>Division II<\/th>\r\n<td>52<\/td>\r\n<td>4,289<\/td>\r\n<td>4,341<\/td>\r\n<\/tr>\r\n<tr>\r\n<th>Division III<\/th>\r\n<td>65<\/td>\r\n<td>6,428<\/td>\r\n<td>6,493<\/td>\r\n<\/tr>\r\n<tr>\r\n<th>Totals<\/th>\r\n<td>220<\/td>\r\n<td>19,157<\/td>\r\n<td>19,377<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<section>Let's use the statistical tool to conduct the Chi-Squared test of Homogeneity.\u00a0<\/section>\r\n<section>Remember to select \"Contingency Table\" under Enter Data and input our values accordingly.<\/section>\r\n<section><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>]<\/section>\r\n<section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1 ]2868[\/ohm2_question]<\/section>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1 ]2867[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Complete a chi-square test of homogeneity&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}\">Complete a chi-square test of homogeneity<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Write the conclusion of a chi-square test of homogeneity in context of the 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}\">Write the conclusion of a chi-square test of homogeneity in context of the problem<\/span><\/li>\n<\/ul>\n<\/section>\n<h2>Steroid Use in Collegiate Sports<\/h2>\n<p>In 2006, the NCAA published a report called \u201cSubstance Use: NCAA Study of Substance Use of College Student-Athletes.\u201d<a class=\"footnote\" title=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/datasets\/ncaa_2006_substance_use_report.pdf\" id=\"return-footnote-1418-1\" href=\"#footnote-1418-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a><\/p>\n<p>Let&#8217;s use the data from the 2006 NCAA published report to investigate the following question: <em>Does steroid use by student athletes differ for the three NCAA divisions?<\/em><\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2866\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2866&theme=lumen&iframe_resize_id=ohm2866&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>A note on NCAA divisions: The National Collegiate Athletic Association (NCAA) is divided into three divisions and oversees a wide range of collegiate sports. Division I schools have to sponsor more sports teams. These schools tend to be large universities with large athletic budgets supplemented by revenue from the games. They must offer athletic scholarships. Division II schools tend to be the smaller public universities and many private institutions. They have much smaller budgets that come solely from the college. The NCAA limits the amount that Division II colleges can spend on athletic scholarships. Division III consists of colleges and universities that treat athletics as an extracurricular activity for students, instead of a source of revenue. These institutions do not offer athletic scholarships.<\/p>\n<p>Below are the summarized data from three samples, one from each division, in a two-way table.<\/p>\n<table>\n<tbody>\n<tr>\n<th>\u00a0<\/th>\n<th colspan=\"2\">Admit Steroid Use<\/th>\n<th>\u00a0<\/th>\n<\/tr>\n<tr>\n<th>\u00a0<\/th>\n<th>Yes<\/th>\n<th>No<\/th>\n<th>Totals<\/th>\n<\/tr>\n<tr>\n<th>Division I<\/th>\n<td>103<\/td>\n<td>8,440<\/td>\n<td>8,543<\/td>\n<\/tr>\n<tr>\n<th>Division II<\/th>\n<td>52<\/td>\n<td>4,289<\/td>\n<td>4,341<\/td>\n<\/tr>\n<tr>\n<th>Division III<\/th>\n<td>65<\/td>\n<td>6,428<\/td>\n<td>6,493<\/td>\n<\/tr>\n<tr>\n<th>Totals<\/th>\n<td>220<\/td>\n<td>19,157<\/td>\n<td>19,377<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<section>Let&#8217;s use the statistical tool to conduct the Chi-Squared test of Homogeneity.\u00a0<\/section>\n<section>Remember to select &#8220;Contingency Table&#8221; under Enter Data and input our values accordingly.<\/section>\n<section><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>]<\/section>\n<section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2868\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2868&theme=lumen&iframe_resize_id=ohm2868&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2867\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2867&theme=lumen&iframe_resize_id=ohm2867&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-1418-1\">https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/datasets\/ncaa_2006_substance_use_report.pdf <a href=\"#return-footnote-1418-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":8,"menu_order":25,"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\/1418"}],"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":6,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1418\/revisions"}],"predecessor-version":[{"id":6877,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1418\/revisions\/6877"}],"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\/1418\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1418"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1418"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1418"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1418"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}