{"id":1212,"date":"2023-06-22T02:09:10","date_gmt":"2023-06-22T02:09:10","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/null-and-alternative-hypotheses-learn-it-3\/"},"modified":"2025-05-16T03:33:03","modified_gmt":"2025-05-16T03:33:03","slug":"null-and-alternative-hypotheses-learn-it-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/null-and-alternative-hypotheses-learn-it-3\/","title":{"raw":"Null and Alternative Hypotheses: Learn It 4","rendered":"Null and Alternative Hypotheses: 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;Write a null and alternative hypothesis for a hypothesis test&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;}\">Write a null and alternative hypothesis for a hypothesis test.<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Decide if a sample statistic provides enough evidence to reject the null hypothesis&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;}\">Decide if a sample statistic provides enough evidence to reject the null hypothesis.<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<section>\r\n<h2>Is it fair?<\/h2>\r\n<p class=\"para\" style=\"margin: 6.0pt 0in 6.0pt 0in;\">In your experiment of [latex]20[\/latex] coin flips, you assumed your friend\u2019s coin is fair, and that assumption was used to calculate the probability of obtaining [latex]17[\/latex] or more heads. The probability of [latex]0.0013[\/latex] given in the previous question is the probability of obtaining [latex]17[\/latex] or more heads out of [latex]20[\/latex] flips if the coin is fair, and this low probability is evidence that the coin is not fair.<\/p>\r\n<p class=\"para\" style=\"margin: 6.0pt 0in 6.0pt 0in;\">Note that no matter what probability you obtain, even if it is a high probability, it is not evidence that the coin is fair. This is because fairness was already the given assumption, and the probability was computed using the assumption that the coin is fair. If we assume something is true, we can\u2019t use that assumption to prove that it\u2019s true (that would be using circular logic). From our sample of coin flips, we either get enough evidence to say the coin is weighted or we don\u2019t.<\/p>\r\n<section class=\"textbox proTip\"><strong><strong><strong>Outcomes of the hypothesis test<\/strong><\/strong><\/strong>\r\n<p><span style=\"font-family: 'Public Sans', -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen-Sans, Ubuntu, Cantarell, 'Helvetica Neue', sans-serif;\">In hypothesis-testing language, we either get enough evidence to <\/span><strong style=\"font-family: 'Public Sans', -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen-Sans, Ubuntu, Cantarell, 'Helvetica Neue', sans-serif;\">reject<\/strong><span style=\"font-family: 'Public Sans', -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen-Sans, Ubuntu, Cantarell, 'Helvetica Neue', sans-serif;\"> the null hypothesis or we don\u2019t.<\/span><\/p>\r\n<ul>\r\n\t<li>When we don\u2019t get enough evidence to reject the null hypothesis, we <strong>fail to reject<\/strong> the null hypothesis.<\/li>\r\n\t<li>NEVER accept the null hypothesis! This is because that was already our assumption to begin with.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1056[\/ohm2_question]<\/section>\r\n<\/section>\r\n<section class=\"textbox example\">[reveal-answer q=\"188200\"]See the example question[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"188200\"][ohm2_question hide_question_numbers=1]1577[\/ohm2_question][\/hidden-answer]<br \/>\r\n[videopicker divId=\"tnh-video-picker\" title=\"Null and Alternative Hypotheses\" label=\"Select Instructor\"]<br \/>\r\n[videooption displayName=\"Dr. Pamela E. Harris\" value=\"https:\/\/www.youtube.com\/watch?v=P7gbKMZCvK8\"][videooption displayName=\"Dr. Aris Winger\" value=\"https:\/\/www.youtube.com\/watch?v=yd-D71zboJo\"] [videooption displayName=\"Dr. Lane Fisher\" value=\"https:\/\/www.youtube.com\/watch?v=HUVT78tmRvQ\"]<br \/>\r\n[\/videopicker]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Write a null and alternative hypothesis for a hypothesis test&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;}\">Write a null and alternative hypothesis for a hypothesis test.<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Decide if a sample statistic provides enough evidence to reject the null hypothesis&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;}\">Decide if a sample statistic provides enough evidence to reject the null hypothesis.<\/span><\/li>\n<\/ul>\n<\/section>\n<section>\n<h2>Is it fair?<\/h2>\n<p class=\"para\" style=\"margin: 6.0pt 0in 6.0pt 0in;\">In your experiment of [latex]20[\/latex] coin flips, you assumed your friend\u2019s coin is fair, and that assumption was used to calculate the probability of obtaining [latex]17[\/latex] or more heads. The probability of [latex]0.0013[\/latex] given in the previous question is the probability of obtaining [latex]17[\/latex] or more heads out of [latex]20[\/latex] flips if the coin is fair, and this low probability is evidence that the coin is not fair.<\/p>\n<p class=\"para\" style=\"margin: 6.0pt 0in 6.0pt 0in;\">Note that no matter what probability you obtain, even if it is a high probability, it is not evidence that the coin is fair. This is because fairness was already the given assumption, and the probability was computed using the assumption that the coin is fair. If we assume something is true, we can\u2019t use that assumption to prove that it\u2019s true (that would be using circular logic). From our sample of coin flips, we either get enough evidence to say the coin is weighted or we don\u2019t.<\/p>\n<section class=\"textbox proTip\"><strong><strong><strong>Outcomes of the hypothesis test<\/strong><\/strong><\/strong><\/p>\n<p><span style=\"font-family: 'Public Sans', -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen-Sans, Ubuntu, Cantarell, 'Helvetica Neue', sans-serif;\">In hypothesis-testing language, we either get enough evidence to <\/span><strong style=\"font-family: 'Public Sans', -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen-Sans, Ubuntu, Cantarell, 'Helvetica Neue', sans-serif;\">reject<\/strong><span style=\"font-family: 'Public Sans', -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen-Sans, Ubuntu, Cantarell, 'Helvetica Neue', sans-serif;\"> the null hypothesis or we don\u2019t.<\/span><\/p>\n<ul>\n<li>When we don\u2019t get enough evidence to reject the null hypothesis, we <strong>fail to reject<\/strong> the null hypothesis.<\/li>\n<li>NEVER accept the null hypothesis! This is because that was already our assumption to begin with.<\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1056\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1056&theme=lumen&iframe_resize_id=ohm1056&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<\/section>\n<section class=\"textbox example\">\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q188200\">See the example question<\/button><\/p>\n<div id=\"q188200\" class=\"hidden-answer\" style=\"display: none\"><iframe loading=\"lazy\" id=\"ohm1577\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1577&theme=lumen&iframe_resize_id=ohm1577&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/div>\n<\/div>\n<div class=\"wp-nocaption \"><\/div>\n<div id=\"tnh-video-picker\" class=\"videoPicker\">\n<h3>Null and Alternative Hypotheses<\/h3>\n<form><label>Select Instructor:<\/label><select name=\"video\"><option value=\"https:\/\/www.youtube.com\/embed\/P7gbKMZCvK8\">Dr. Pamela E. Harris<\/option><option value=\"https:\/\/www.youtube.com\/embed\/yd-D71zboJo\">Dr. Aris Winger<\/option><option value=\"https:\/\/www.youtube.com\/embed\/HUVT78tmRvQ\">Dr. Lane Fisher<\/option><\/select><\/form>\n<div class=\"videoContainer\"><iframe src=\"https:\/\/www.youtube.com\/embed\/P7gbKMZCvK8\" allowfullscreen><\/iframe><\/div>\n<\/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":1205,"module-header":"learn_it","content_attributions":[],"internal_book_links":[],"video_content":[{"divId":"tnh-video-picker","title":"Null and Alternative Hypotheses","label":"Select Instructor","video_collection":[{"displayName":"Dr. Pamela E. 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