{"id":1241,"date":"2023-06-22T02:09:30","date_gmt":"2023-06-22T02:09:30","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/one-sample-hypothesis-test-for-proportions-dig-deeper\/"},"modified":"2023-10-20T17:44:00","modified_gmt":"2023-10-20T17:44:00","slug":"one-sample-hypothesis-test-for-proportions-dig-deeper","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/one-sample-hypothesis-test-for-proportions-dig-deeper\/","title":{"raw":"One-Sample Hypothesis Test for Proportions: Fresh Take","rendered":"One-Sample Hypothesis Test for Proportions: Fresh Take"},"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 one-sample z-test for proportions from hypotheses to conclusions&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;}\">Complete a one-sample [latex]z[\/latex]-test for proportions from hypotheses to conclusions<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Use a P-value to explain the conclusions of a completed z-test for proportions&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;}\">Use a P-value to explain the conclusions of a completed [latex]z[\/latex]-test for proportions<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<section>\r\n<section class=\"textbox recall\"><strong>Steps for Hypothesis Testing<\/strong>\r\n<ol>\r\n\t<li>Write out the null and alternative hypotheses.<\/li>\r\n\t<li>Check the conditions for the hypothesis test.<\/li>\r\n\t<li>Calculate a test statistic.<\/li>\r\n\t<li>Calculate a P-value.<\/li>\r\n\t<li>Compare the P-value to the significance level, [latex]\\alpha[\/latex], to make a decision.<\/li>\r\n\t<li>Write a conclusion in context (e.g., we do\/do not have convincing evidence\u2026).<\/li>\r\n<\/ol>\r\n<\/section>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]948[\/ohm2_question]<\/section>\r\n<p>You have learned that all hypothesis tests result in one of two actions: either you reject the null hypothesis in favor of the alternative OR you do not reject the null hypothesis.<\/p>\r\n<p>Thus, at the end of this drug study, you will choose one of the following:<\/p>\r\n<ul>\r\n\t<li><strong>Reject the null hypothesis<\/strong> - There is evidence that the proportion of people taking the drug who have a second heart attack is less than [latex]0.15[\/latex]. There is evidence the drug works!<\/li>\r\n\t<li><strong>Do NOT reject the null hypothesis<\/strong> - There is not sufficient evidence to declare that the proportion of people taking the drug who have a second heart attack is less than [latex]0.15[\/latex]. There is not sufficient evidence to say the drug works.<\/li>\r\n<\/ul>\r\n<section class=\"textbox proTip\">Consider a court system analogy[footnote]Skew the Script. (2021). AP\u00ae Statistics Lessons. https:\/\/skewthescript.org\/ap-stats-curriculum[\/footnote]: a person on trial is assumed to be innocent, the default\/null belief ([latex]H_0[\/latex]), until proven guilty through evidence ([latex]H_A[\/latex]).There are two possible outcomes at the end of the trial:\r\n\r\n<ul>\r\n\t<li>There is enough evidence to reject the person\u2019s innocence (Reject [latex]H_0[\/latex]).<\/li>\r\n\t<li>There is not enough evidence to reject the person\u2019s innocence (Fail to Reject [latex]H_0[\/latex]).<\/li>\r\n<\/ul>\r\n<p>It is important to note that you cannot \u201caccept [latex]H_0[\/latex].\u201d It\u2019s assumed to be true already, so our research isn\u2019t proving the null hypothesis. This is why a person is declared \u201cnot guilty\u201d rather than \u201cinnocent\u201d in court\u2014their innocence was assumed at the beginning.<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1746[\/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 one-sample z-test for proportions from hypotheses to conclusions&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;}\">Complete a one-sample [latex]z[\/latex]-test for proportions from hypotheses to conclusions<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Use a P-value to explain the conclusions of a completed z-test for proportions&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;}\">Use a P-value to explain the conclusions of a completed [latex]z[\/latex]-test for proportions<\/span><\/li>\n<\/ul>\n<\/section>\n<section>\n<section class=\"textbox recall\"><strong>Steps for Hypothesis Testing<\/strong><\/p>\n<ol>\n<li>Write out the null and alternative hypotheses.<\/li>\n<li>Check the conditions for the hypothesis test.<\/li>\n<li>Calculate a test statistic.<\/li>\n<li>Calculate a P-value.<\/li>\n<li>Compare the P-value to the significance level, [latex]\\alpha[\/latex], to make a decision.<\/li>\n<li>Write a conclusion in context (e.g., we do\/do not have convincing evidence\u2026).<\/li>\n<\/ol>\n<\/section>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm948\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=948&theme=lumen&iframe_resize_id=ohm948&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>You have learned that all hypothesis tests result in one of two actions: either you reject the null hypothesis in favor of the alternative OR you do not reject the null hypothesis.<\/p>\n<p>Thus, at the end of this drug study, you will choose one of the following:<\/p>\n<ul>\n<li><strong>Reject the null hypothesis<\/strong> &#8211; There is evidence that the proportion of people taking the drug who have a second heart attack is less than [latex]0.15[\/latex]. There is evidence the drug works!<\/li>\n<li><strong>Do NOT reject the null hypothesis<\/strong> &#8211; There is not sufficient evidence to declare that the proportion of people taking the drug who have a second heart attack is less than [latex]0.15[\/latex]. There is not sufficient evidence to say the drug works.<\/li>\n<\/ul>\n<section class=\"textbox proTip\">Consider a court system analogy<a class=\"footnote\" title=\"Skew the Script. (2021). AP\u00ae Statistics Lessons. https:\/\/skewthescript.org\/ap-stats-curriculum\" id=\"return-footnote-1241-1\" href=\"#footnote-1241-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a>: a person on trial is assumed to be innocent, the default\/null belief ([latex]H_0[\/latex]), until proven guilty through evidence ([latex]H_A[\/latex]).There are two possible outcomes at the end of the trial:<\/p>\n<ul>\n<li>There is enough evidence to reject the person\u2019s innocence (Reject [latex]H_0[\/latex]).<\/li>\n<li>There is not enough evidence to reject the person\u2019s innocence (Fail to Reject [latex]H_0[\/latex]).<\/li>\n<\/ul>\n<p>It is important to note that you cannot \u201caccept [latex]H_0[\/latex].\u201d It\u2019s assumed to be true already, so our research isn\u2019t proving the null hypothesis. This is why a person is declared \u201cnot guilty\u201d rather than \u201cinnocent\u201d in court\u2014their innocence was assumed at the beginning.<\/p>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1746\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1746&theme=lumen&iframe_resize_id=ohm1746&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-1241-1\">Skew the Script. (2021). AP\u00ae Statistics Lessons. https:\/\/skewthescript.org\/ap-stats-curriculum <a href=\"#return-footnote-1241-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":8,"menu_order":23,"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":"fresh_take","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\/1241"}],"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":3,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1241\/revisions"}],"predecessor-version":[{"id":3778,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1241\/revisions\/3778"}],"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\/1241\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1241"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1241"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1241"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1241"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}