{"id":1211,"date":"2023-06-22T02:09:09","date_gmt":"2023-06-22T02:09:09","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/null-and-alternative-hypotheses-learn-it-2\/"},"modified":"2025-05-16T03:32:33","modified_gmt":"2025-05-16T03:32:33","slug":"null-and-alternative-hypotheses-learn-it-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/null-and-alternative-hypotheses-learn-it-2\/","title":{"raw":"Null and Alternative Hypotheses: Learn It 3","rendered":"Null and Alternative Hypotheses: 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;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<h2>Is it fair?<\/h2>\r\n<p>Recall the scenario: Suppose that you are playing a game with your friend that involves flipping a coin. Each round consists of flipping the coin [latex]10[\/latex] times. In one round of play, your friend gets [latex]8[\/latex] heads out of the [latex]10[\/latex] total flips.<\/p>\r\n<p>Your friend claims the coin is fair, but you aren\u2019t convinced. You can\u2019t prove for certain that your friend\u2019s coin is weighted unfairly (without special equipment, of course), but you can test your hypotheses with a sample of coin flips.<\/p>\r\n<section class=\"textbox proTip\">The statistical evidence, often represented by the <strong>P-value<\/strong>, is used to determine the strength of the evidence against the null hypothesis. The P-value represents the <strong>probability<\/strong> of obtaining the observed data, or more extreme data, under the assumption that the null hypothesis is true.\r\n\r\n<ul>\r\n\t<li>The\u00a0<strong>smaller<\/strong> the probability, the more\u00a0<strong>unlikely<\/strong> it is to observe the sample data given that the null hypothesis is true.<\/li>\r\n\t<li>The <strong>larger <\/strong>the probability, the more\u00a0<strong>likely<\/strong>\u00a0it is to observe the sample data.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<p class=\"para\" style=\"margin: 6.0pt 0in 6.0pt 0in;\">If the proportion of heads in your sample is high enough, it provides strong evidence that your friend\u2019s coin is weighted in their favor. In other words, a high enough proportion of heads would be sufficient evidence for you to reject the assumption that your friend\u2019s coin is fair.<\/p>\r\n<p class=\"para\" style=\"margin: 6.0pt 0in 6.0pt 0in;\">Let\u2019s suppose that you flip the coin [latex]20[\/latex] times for your sample.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1054[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1055[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]930[\/ohm2_question]<\/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<h2>Is it fair?<\/h2>\n<p>Recall the scenario: Suppose that you are playing a game with your friend that involves flipping a coin. Each round consists of flipping the coin [latex]10[\/latex] times. In one round of play, your friend gets [latex]8[\/latex] heads out of the [latex]10[\/latex] total flips.<\/p>\n<p>Your friend claims the coin is fair, but you aren\u2019t convinced. You can\u2019t prove for certain that your friend\u2019s coin is weighted unfairly (without special equipment, of course), but you can test your hypotheses with a sample of coin flips.<\/p>\n<section class=\"textbox proTip\">The statistical evidence, often represented by the <strong>P-value<\/strong>, is used to determine the strength of the evidence against the null hypothesis. The P-value represents the <strong>probability<\/strong> of obtaining the observed data, or more extreme data, under the assumption that the null hypothesis is true.<\/p>\n<ul>\n<li>The\u00a0<strong>smaller<\/strong> the probability, the more\u00a0<strong>unlikely<\/strong> it is to observe the sample data given that the null hypothesis is true.<\/li>\n<li>The <strong>larger <\/strong>the probability, the more\u00a0<strong>likely<\/strong>\u00a0it is to observe the sample data.<\/li>\n<\/ul>\n<\/section>\n<p class=\"para\" style=\"margin: 6.0pt 0in 6.0pt 0in;\">If the proportion of heads in your sample is high enough, it provides strong evidence that your friend\u2019s coin is weighted in their favor. In other words, a high enough proportion of heads would be sufficient evidence for you to reject the assumption that your friend\u2019s coin is fair.<\/p>\n<p class=\"para\" style=\"margin: 6.0pt 0in 6.0pt 0in;\">Let\u2019s suppose that you flip the coin [latex]20[\/latex] times for your sample.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1054\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1054&theme=lumen&iframe_resize_id=ohm1054&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1055\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1055&theme=lumen&iframe_resize_id=ohm1055&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm930\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=930&theme=lumen&iframe_resize_id=ohm930&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":10,"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":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\/1211"}],"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":11,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1211\/revisions"}],"predecessor-version":[{"id":6751,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1211\/revisions\/6751"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/1205"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1211\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1211"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1211"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1211"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1211"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}