{"id":1423,"date":"2023-06-22T02:23:03","date_gmt":"2023-06-22T02:23:03","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/chi-square-test-of-independence-learn-it-4\/"},"modified":"2023-10-20T20:46:41","modified_gmt":"2023-10-20T20:46:41","slug":"chi-square-test-of-independence-learn-it-4","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/chi-square-test-of-independence-learn-it-4\/","title":{"raw":"Chi-Square Test of Independence \u2013 Learn It 4","rendered":"Chi-Square Test of Independence \u2013 Learn It 4"},"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 independence&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 independence<\/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 independence 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 independence in context of the problem<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<table>\r\n<tbody>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 87.7604px;\">\u00a0<\/td>\r\n<td style=\"height: 18px; width: 85.434px;\">\u00a0<\/td>\r\n<td style=\"height: 18px; width: 87.6042px;\"><strong>Income level<\/strong><\/td>\r\n<td style=\"height: 18px; width: 91.2153px;\">\u00a0<\/td>\r\n<td style=\"width: 83.507px;\">\u00a0<\/td>\r\n<td style=\"width: 54.4792px;\">\u00a0<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 87.7604px;\">\u00a0<\/td>\r\n<td style=\"height: 18px; width: 85.434px;\">\u00a0<\/td>\r\n<td style=\"height: 18px; width: 87.6042px;\">[latex]&lt;$30,000[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 91.2153px;\">[latex]$30,000\u2013$74,999[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 83.507px;\">[latex]$75,000[\/latex] and up<\/td>\r\n<td style=\"height: 18px; width: 54.4792px;\">Total<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 87.7604px;\"><strong>Education level<\/strong><\/td>\r\n<td style=\"height: 18px; width: 85.434px;\">Post-Grad Degree<\/td>\r\n<td style=\"height: 18px; width: 87.6042px;\">[latex]2[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 91.2153px;\">[latex]8[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 83.507px;\">[latex]46[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 54.4792px;\">[latex]56[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 87.7604px;\">\u00a0<\/td>\r\n<td style=\"height: 18px; width: 85.434px;\">College Degree<\/td>\r\n<td style=\"height: 18px; width: 87.6042px;\">[latex]39[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 91.2153px;\">[latex]113[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 83.507px;\">[latex]202[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 54.4792px;\">[latex]354[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 87.7604px;\">\u00a0<\/td>\r\n<td style=\"height: 18px; width: 85.434px;\">Some College<\/td>\r\n<td style=\"height: 18px; width: 87.6042px;\">[latex]131[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 91.2153px;\">[latex]138[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 83.507px;\">[latex]120[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 54.4792px;\">[latex]389[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 87.7604px;\">\u00a0<\/td>\r\n<td style=\"height: 18px; width: 85.434px;\">HS Grad<\/td>\r\n<td style=\"height: 18px; width: 87.6042px;\">[latex]175[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 91.2153px;\">[latex]129[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 83.507px;\">[latex]65[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 54.4792px;\">[latex]369[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 87.7604px;\">\u00a0<\/td>\r\n<td style=\"height: 18px; width: 85.434px;\">No HS Degree<\/td>\r\n<td style=\"height: 18px; width: 87.6042px;\">[latex]78[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 91.2153px;\">[latex]32[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 83.507px;\">[latex]8[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 54.4792px;\">[latex]118[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 87.7604px;\">\u00a0<\/td>\r\n<td style=\"height: 18px; width: 85.434px;\">Total<\/td>\r\n<td style=\"height: 18px; width: 87.6042px;\">[latex]425[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 91.2153px;\">[latex]420[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 83.507px;\">[latex]441[\/latex]<\/td>\r\n<td style=\"height: 18px; width: 54.4792px;\">[latex]1,286[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p>Let's use the statistical tool to conduct the Chi-Squared test of Independence.<\/p>\r\n<section>Remember to select \"Contingency Table\" under Enter Data and input out 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 ]2885[\/ohm2_question]<\/section>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1 ]2887[\/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 independence&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 independence<\/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 independence 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 independence in context of the problem<\/span><\/li>\n<\/ul>\n<\/section>\n<table>\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 87.7604px;\">\u00a0<\/td>\n<td style=\"height: 18px; width: 85.434px;\">\u00a0<\/td>\n<td style=\"height: 18px; width: 87.6042px;\"><strong>Income level<\/strong><\/td>\n<td style=\"height: 18px; width: 91.2153px;\">\u00a0<\/td>\n<td style=\"width: 83.507px;\">\u00a0<\/td>\n<td style=\"width: 54.4792px;\">\u00a0<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 87.7604px;\">\u00a0<\/td>\n<td style=\"height: 18px; width: 85.434px;\">\u00a0<\/td>\n<td style=\"height: 18px; width: 87.6042px;\">[latex]<$30,000[\/latex]<\/td>\n<td style=\"height: 18px; width: 91.2153px;\">[latex]$30,000\u2013$74,999[\/latex]<\/td>\n<td style=\"height: 18px; width: 83.507px;\">[latex]$75,000[\/latex] and up<\/td>\n<td style=\"height: 18px; width: 54.4792px;\">Total<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 87.7604px;\"><strong>Education level<\/strong><\/td>\n<td style=\"height: 18px; width: 85.434px;\">Post-Grad Degree<\/td>\n<td style=\"height: 18px; width: 87.6042px;\">[latex]2[\/latex]<\/td>\n<td style=\"height: 18px; width: 91.2153px;\">[latex]8[\/latex]<\/td>\n<td style=\"height: 18px; width: 83.507px;\">[latex]46[\/latex]<\/td>\n<td style=\"height: 18px; width: 54.4792px;\">[latex]56[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 87.7604px;\">\u00a0<\/td>\n<td style=\"height: 18px; width: 85.434px;\">College Degree<\/td>\n<td style=\"height: 18px; width: 87.6042px;\">[latex]39[\/latex]<\/td>\n<td style=\"height: 18px; width: 91.2153px;\">[latex]113[\/latex]<\/td>\n<td style=\"height: 18px; width: 83.507px;\">[latex]202[\/latex]<\/td>\n<td style=\"height: 18px; width: 54.4792px;\">[latex]354[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 87.7604px;\">\u00a0<\/td>\n<td style=\"height: 18px; width: 85.434px;\">Some College<\/td>\n<td style=\"height: 18px; width: 87.6042px;\">[latex]131[\/latex]<\/td>\n<td style=\"height: 18px; width: 91.2153px;\">[latex]138[\/latex]<\/td>\n<td style=\"height: 18px; width: 83.507px;\">[latex]120[\/latex]<\/td>\n<td style=\"height: 18px; width: 54.4792px;\">[latex]389[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 87.7604px;\">\u00a0<\/td>\n<td style=\"height: 18px; width: 85.434px;\">HS Grad<\/td>\n<td style=\"height: 18px; width: 87.6042px;\">[latex]175[\/latex]<\/td>\n<td style=\"height: 18px; width: 91.2153px;\">[latex]129[\/latex]<\/td>\n<td style=\"height: 18px; width: 83.507px;\">[latex]65[\/latex]<\/td>\n<td style=\"height: 18px; width: 54.4792px;\">[latex]369[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 87.7604px;\">\u00a0<\/td>\n<td style=\"height: 18px; width: 85.434px;\">No HS Degree<\/td>\n<td style=\"height: 18px; width: 87.6042px;\">[latex]78[\/latex]<\/td>\n<td style=\"height: 18px; width: 91.2153px;\">[latex]32[\/latex]<\/td>\n<td style=\"height: 18px; width: 83.507px;\">[latex]8[\/latex]<\/td>\n<td style=\"height: 18px; width: 54.4792px;\">[latex]118[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 87.7604px;\">\u00a0<\/td>\n<td style=\"height: 18px; width: 85.434px;\">Total<\/td>\n<td style=\"height: 18px; width: 87.6042px;\">[latex]425[\/latex]<\/td>\n<td style=\"height: 18px; width: 91.2153px;\">[latex]420[\/latex]<\/td>\n<td style=\"height: 18px; width: 83.507px;\">[latex]441[\/latex]<\/td>\n<td style=\"height: 18px; width: 54.4792px;\">[latex]1,286[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Let&#8217;s use the statistical tool to conduct the Chi-Squared test of Independence.<\/p>\n<section>Remember to select &#8220;Contingency Table&#8221; under Enter Data and input out 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? 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