{"id":1242,"date":"2023-06-22T02:09:31","date_gmt":"2023-06-22T02:09:31","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/errors-in-hypothesis-testing-learn-it-1\/"},"modified":"2025-05-16T03:39:14","modified_gmt":"2025-05-16T03:39:14","slug":"errors-in-hypothesis-testing-learn-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/errors-in-hypothesis-testing-learn-it-1\/","title":{"raw":"Errors in Hypothesis Testing: Learn It 1","rendered":"Errors in Hypothesis Testing: Learn 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;Recognize Type I and Type II errors and their consequences&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Recognize Type I and Type II errors and their consequences.<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Errors<\/h2>\r\n<p>Errors sometimes arise in hypothesis testing. This is because we are reaching a conclusion about the entire population based on a sample. We cannot eliminate hypothesis testing errors entirely.<\/p>\r\n<p>Sometimes, due to chance, the result of the hypothesis test does not align with reality.<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>errors in hypothesis testing<\/h3>\r\n<p>If we reject a correct null hypothesis, we are committing a <strong>type I error<\/strong>. If we do not reject a null hypothesis that is actually incorrect, we are committing a <strong>type II error<\/strong>.<\/p>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>&nbsp;<\/td>\r\n<td>Reject the null hypothesis<\/td>\r\n<td>Do not reject the null hypothesis<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Null hypothesis is correct<\/td>\r\n<td><strong>Type I error<\/strong><\/td>\r\n<td>No error<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Null hypothesis is incorrect<\/td>\r\n<td>No error<\/td>\r\n<td><strong>Type II error<\/strong><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<ul>\r\n\t<li><em>[latex]\u03b1[\/latex]<\/em>\u00a0= probability of a Type I error =\u00a0<strong>P(Type I error)<\/strong>\u00a0= probability of rejecting the null hypothesis when the null hypothesis is true.<br \/>\r\n<em>[latex]\u03b1[\/latex] <\/em>is also known as the <strong>significance level\u00a0<\/strong>of the hypothesis test.<\/li>\r\n\t<li><em>[latex]\u03b2[\/latex]<\/em>\u00a0= probability of a Type II error =\u00a0<strong>P(Type II error)<\/strong> = probability of not rejecting the null hypothesis when the null hypothesis is false.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<section class=\"textbox example\" aria-label=\"Example\">\r\n<p>The video below will walk you through how to solve the following problem. Choose your favorite instructor and follow along.<\/p>\r\n<p>[ohm2_question hide_question_numbers=1]1579[\/ohm2_question]<\/p>\r\n<\/section>\r\n<section class=\"textbox example\">[videopicker divId=\"tnh-video-picker\" title=\"Type I and Type II Errors\" label=\"Select Instructor\"]<br \/>\r\n[videooption displayName=\"Dr. Pamela E. Harris\" value=\"https:\/\/www.youtube.com\/watch?v=bRlfvsSsErQ\"][videooption displayName=\"Dr. Aris Winger\" value=\"https:\/\/www.youtube.com\/watch?v=ex2uBJtK8kE\"] [videooption displayName=\"Dr. Lane Fisher\" value=\"https:\/\/www.youtube.com\/watch?v=OVqNNnU4HSg\"]<br \/>\r\n[\/videopicker]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]11076[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Recognize Type I and Type II errors and their consequences&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Recognize Type I and Type II errors and their consequences.<\/span><\/li>\n<\/ul>\n<\/section>\n<h2>Errors<\/h2>\n<p>Errors sometimes arise in hypothesis testing. This is because we are reaching a conclusion about the entire population based on a sample. We cannot eliminate hypothesis testing errors entirely.<\/p>\n<p>Sometimes, due to chance, the result of the hypothesis test does not align with reality.<\/p>\n<section class=\"textbox keyTakeaway\">\n<h3>errors in hypothesis testing<\/h3>\n<p>If we reject a correct null hypothesis, we are committing a <strong>type I error<\/strong>. If we do not reject a null hypothesis that is actually incorrect, we are committing a <strong>type II error<\/strong>.<\/p>\n<table>\n<tbody>\n<tr>\n<td>&nbsp;<\/td>\n<td>Reject the null hypothesis<\/td>\n<td>Do not reject the null hypothesis<\/td>\n<\/tr>\n<tr>\n<td>Null hypothesis is correct<\/td>\n<td><strong>Type I error<\/strong><\/td>\n<td>No error<\/td>\n<\/tr>\n<tr>\n<td>Null hypothesis is incorrect<\/td>\n<td>No error<\/td>\n<td><strong>Type II error<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ul>\n<li><em>[latex]\u03b1[\/latex]<\/em>\u00a0= probability of a Type I error =\u00a0<strong>P(Type I error)<\/strong>\u00a0= probability of rejecting the null hypothesis when the null hypothesis is true.<br \/>\n<em>[latex]\u03b1[\/latex] <\/em>is also known as the <strong>significance level\u00a0<\/strong>of the hypothesis test.<\/li>\n<li><em>[latex]\u03b2[\/latex]<\/em>\u00a0= probability of a Type II error =\u00a0<strong>P(Type II error)<\/strong> = probability of not rejecting the null hypothesis when the null hypothesis is false.<\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox example\" aria-label=\"Example\">\n<p>The video below will walk you through how to solve the following problem. Choose your favorite instructor and follow along.<\/p>\n<p><iframe loading=\"lazy\" id=\"ohm1579\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1579&theme=lumen&iframe_resize_id=ohm1579&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<section class=\"textbox example\">\n<div id=\"tnh-video-picker\" class=\"videoPicker\">\n<h3>Type I and Type II Errors<\/h3>\n<form><label>Select Instructor:<\/label><select name=\"video\"><option value=\"https:\/\/www.youtube.com\/embed\/bRlfvsSsErQ\">Dr. Pamela E. Harris<\/option><option value=\"https:\/\/www.youtube.com\/embed\/ex2uBJtK8kE\">Dr. Aris Winger<\/option><option value=\"https:\/\/www.youtube.com\/embed\/OVqNNnU4HSg\">Dr. Lane Fisher<\/option><\/select><\/form>\n<div class=\"videoContainer\"><iframe src=\"https:\/\/www.youtube.com\/embed\/bRlfvsSsErQ\" allowfullscreen><\/iframe><\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm11076\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=11076&theme=lumen&iframe_resize_id=ohm11076&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":24,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":1205,"module-header":"learn_it","content_attributions":[],"internal_book_links":[],"video_content":[{"divId":"tnh-video-picker","title":"Type I and Type II Errors","label":"Select Instructor","video_collection":[{"displayName":"Dr. Pamela E. 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