{"id":2021,"date":"2023-07-25T20:08:05","date_gmt":"2023-07-25T20:08:05","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/?post_type=chapter&#038;p=2021"},"modified":"2025-05-16T03:32:13","modified_gmt":"2025-05-16T03:32:13","slug":"null-and-alternative-hypotheses-learn-it-2-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/null-and-alternative-hypotheses-learn-it-2-2\/","title":{"raw":"Null and Alternative Hypotheses: Learn It 2","rendered":"Null and Alternative Hypotheses: Learn It 2"},"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>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>If you wanted to claim that your friend was indeed cheating, you would need to produce evidence in order to prove that their coin was not fair. Statistics is a very useful tool in this scenario and can be used to test these kinds of hypotheses.<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>hypothesis test<\/h3>\r\n<p class=\"para\" style=\"margin: 6.0pt 0in 6.0pt 0in;\">In a statistical hypothesis test:<\/p>\r\n<ul>\r\n\t<li>The <strong>null hypothesis<\/strong>, [latex] H_{0} [\/latex], is what we assume to be true to begin with. It is often a statement of no change from the previous value or from what is expected.<\/li>\r\n<\/ul>\r\n<p style=\"text-align: center;\">[latex]H_0: p = \\text{null value}[\/latex]<\/p>\r\n<ul>\r\n\t<li>The <strong>alternative hypothesis<\/strong>, [latex] H_{A} [\/latex], is what we consider to be plausible if the null hypothesis is false.<\/li>\r\n<\/ul>\r\n<p style=\"text-align: center;\">[latex] H_{A}: p&gt;\\text{null value}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex] H_{A}: p&lt;\\text{null value}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex] H_{A}: p \\neq \\text{null value}[\/latex]<\/p>\r\n<ul>\r\n\t<li>The evidence used is <strong>probability<\/strong>. The statistical evidence that we gather is always evidence in support of the alternative hypothesis and against the null hypothesis. We ask ourselves the question, \u201cDo we have enough evidence to reject the null hypothesis?\u201d<\/li>\r\n\t<li>The <strong>outcomes<\/strong> of the hypothesis test are either:\r\n\r\n<ul>\r\n\t<li>We reject the null hypothesis (we have gathered enough evidence).<\/li>\r\n\t<li>We fail to reject the null hypothesis (we have not gathered sufficient evidence, so we cannot reject the starting assumption).<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/section>\r\n<p>Before we can conduct a hypothesis test and calculate the probability, we need to check if the conditions for the hypothesis test have been met.<\/p>\r\n<\/section>\r\n<section class=\"textbox recall\">The <strong>Central Limit Theorem<\/strong> states that, as the sample size gets larger, the distribution of the sample proportion will become closer to a normal distribution. If [latex]np\\geq 10[\/latex] and [latex]n(1-p) \\geq 10[\/latex], then the <strong>Central Limit Theorem<\/strong> states that the distribution of the sample proportions follows an approximate normal distribution with <strong>mean<\/strong> [latex]p[\/latex] and <strong>standard deviation<\/strong> [latex]\\sqrt{\\frac{p(1-p)}{n}}[\/latex]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]11073[\/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<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>If you wanted to claim that your friend was indeed cheating, you would need to produce evidence in order to prove that their coin was not fair. Statistics is a very useful tool in this scenario and can be used to test these kinds of hypotheses.<\/p>\n<section class=\"textbox keyTakeaway\">\n<h3>hypothesis test<\/h3>\n<p class=\"para\" style=\"margin: 6.0pt 0in 6.0pt 0in;\">In a statistical hypothesis test:<\/p>\n<ul>\n<li>The <strong>null hypothesis<\/strong>, [latex]H_{0}[\/latex], is what we assume to be true to begin with. It is often a statement of no change from the previous value or from what is expected.<\/li>\n<\/ul>\n<p style=\"text-align: center;\">[latex]H_0: p = \\text{null value}[\/latex]<\/p>\n<ul>\n<li>The <strong>alternative hypothesis<\/strong>, [latex]H_{A}[\/latex], is what we consider to be plausible if the null hypothesis is false.<\/li>\n<\/ul>\n<p style=\"text-align: center;\">[latex]H_{A}: p>\\text{null value}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]H_{A}: p<\\text{null value}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]H_{A}: p \\neq \\text{null value}[\/latex]<\/p>\n<ul>\n<li>The evidence used is <strong>probability<\/strong>. The statistical evidence that we gather is always evidence in support of the alternative hypothesis and against the null hypothesis. We ask ourselves the question, \u201cDo we have enough evidence to reject the null hypothesis?\u201d<\/li>\n<li>The <strong>outcomes<\/strong> of the hypothesis test are either:\n<ul>\n<li>We reject the null hypothesis (we have gathered enough evidence).<\/li>\n<li>We fail to reject the null hypothesis (we have not gathered sufficient evidence, so we cannot reject the starting assumption).<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/section>\n<p>Before we can conduct a hypothesis test and calculate the probability, we need to check if the conditions for the hypothesis test have been met.<\/p>\n<\/section>\n<section class=\"textbox recall\">The <strong>Central Limit Theorem<\/strong> states that, as the sample size gets larger, the distribution of the sample proportion will become closer to a normal distribution. If [latex]np\\geq 10[\/latex] and [latex]n(1-p) \\geq 10[\/latex], then the <strong>Central Limit Theorem<\/strong> states that the distribution of the sample proportions follows an approximate normal distribution with <strong>mean<\/strong> [latex]p[\/latex] and <strong>standard deviation<\/strong> [latex]\\sqrt{\\frac{p(1-p)}{n}}[\/latex]<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm11073\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=11073&theme=lumen&iframe_resize_id=ohm11073&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":12,"menu_order":9,"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\/2021"}],"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\/12"}],"version-history":[{"count":12,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/2021\/revisions"}],"predecessor-version":[{"id":6750,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/2021\/revisions\/6750"}],"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\/2021\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=2021"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=2021"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=2021"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=2021"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}