{"id":1448,"date":"2023-06-22T02:28:41","date_gmt":"2023-06-22T02:28:41","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/test-for-significance-of-slope-learn-it-3\/"},"modified":"2025-05-17T02:33:06","modified_gmt":"2025-05-17T02:33:06","slug":"test-for-significance-of-slope-learn-it-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/test-for-significance-of-slope-learn-it-3\/","title":{"raw":"Test for Significance of Slope - Learn It 3","rendered":"Test for Significance of Slope &#8211; 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;Perform a test for significance of slope and interpret the results&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:6913,&quot;3&quot;:{&quot;1&quot;:0},&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:{&quot;1&quot;:2,&quot;2&quot;:0},&quot;15&quot;:&quot;Calibri&quot;}\">Perform a test for significance of slope and interpret the results<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Check the conditions that are necessary to perform a test for significance of slope&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:6913,&quot;3&quot;:{&quot;1&quot;:0},&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:{&quot;1&quot;:2,&quot;2&quot;:0},&quot;15&quot;:&quot;Calibri&quot;}\">Check the conditions that are necessary to perform a test for significance of slope<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<p>Let's analyze the \u201cTomatometer\u201d data. These data came from the movie ratings website <em>Rotten Tomatoes<\/em>[footnote]rottentomatoes.com[\/footnote]. On this website, movie critics write reviews, and regular moviegoers submit ratings ([latex]1\u20135[\/latex] stars) for movies and TV shows. We focused on [latex]125[\/latex] movies from the website and the following variables.<\/p>\r\n<ul>\r\n\t<li><em>tomatometer<\/em>: The \u201cTomatometer\u201d score calculated as the percentage of professional movie and TV critics who write positive reviews for the movie<\/li>\r\n\t<li><em>audience_score<\/em>: The percentage of the general public (regular moviegoers) who rate the movie [latex]3.5[\/latex] stars or higher (out of [latex]5[\/latex] stars)<\/li>\r\n<\/ul>\r\n<p>Select\u00a0<strong>\"Movie Ratings\"<\/strong> data set in the statistical tool below.<\/p>\r\n<p><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/linear_regression\/\" width=\"100%\" height=\"1050\" frameborder=\"no\"><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\">\ufeff<\/span><\/iframe><br \/>\r\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/linear_regression\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3053[\/ohm2_question]<\/section>\r\n<p>Previously, you used the following test statistic to conduct a one-sample hypothesis test for the mean with [latex]H_0: \\mu = \\mu_0[\/latex]:<\/p>\r\n<p>[latex]t = \\dfrac{\\bar{x}-\\mu_0}{[\\text{std. error of }\\bar{x}]}=\\dfrac{\\bar{x}-\\mu_0}{\\frac{s}{\\sqrt{n}}}[\/latex]<\/p>\r\n<p>The slope of the population line, [latex]\\beta_1[\/latex], similarly follows a [latex]t[\/latex] Distribution.<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>Test Statistics for the Hypothesis Test for Significance of Slope<\/h3>\r\n<p>The test statistic to test [latex]H_0: \\beta_1 = 0[\/latex] is:<\/p>\r\n<p style=\"text-align: center;\">[latex]t=\\dfrac{b-0}{[\\text{std. error of }b]} = \\dfrac{b}{SE_b}[\/latex]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3164[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Perform a test for significance of slope and interpret the results&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:6913,&quot;3&quot;:{&quot;1&quot;:0},&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:{&quot;1&quot;:2,&quot;2&quot;:0},&quot;15&quot;:&quot;Calibri&quot;}\">Perform a test for significance of slope and interpret the results<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Check the conditions that are necessary to perform a test for significance of slope&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:6913,&quot;3&quot;:{&quot;1&quot;:0},&quot;11&quot;:4,&quot;12&quot;:0,&quot;14&quot;:{&quot;1&quot;:2,&quot;2&quot;:0},&quot;15&quot;:&quot;Calibri&quot;}\">Check the conditions that are necessary to perform a test for significance of slope<\/span><\/li>\n<\/ul>\n<\/section>\n<p>Let&#8217;s analyze the \u201cTomatometer\u201d data. These data came from the movie ratings website <em>Rotten Tomatoes<\/em><a class=\"footnote\" title=\"rottentomatoes.com\" id=\"return-footnote-1448-1\" href=\"#footnote-1448-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a>. On this website, movie critics write reviews, and regular moviegoers submit ratings ([latex]1\u20135[\/latex] stars) for movies and TV shows. We focused on [latex]125[\/latex] movies from the website and the following variables.<\/p>\n<ul>\n<li><em>tomatometer<\/em>: The \u201cTomatometer\u201d score calculated as the percentage of professional movie and TV critics who write positive reviews for the movie<\/li>\n<li><em>audience_score<\/em>: The percentage of the general public (regular moviegoers) who rate the movie [latex]3.5[\/latex] stars or higher (out of [latex]5[\/latex] stars)<\/li>\n<\/ul>\n<p>Select\u00a0<strong>&#8220;Movie Ratings&#8221;<\/strong> data set in the statistical tool below.<\/p>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/linear_regression\/\" width=\"100%\" height=\"1050\" frameborder=\"no\"><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\">\ufeff<\/span><\/iframe><br \/>\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/linear_regression\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3053\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3053&theme=lumen&iframe_resize_id=ohm3053&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>Previously, you used the following test statistic to conduct a one-sample hypothesis test for the mean with [latex]H_0: \\mu = \\mu_0[\/latex]:<\/p>\n<p>[latex]t = \\dfrac{\\bar{x}-\\mu_0}{[\\text{std. error of }\\bar{x}]}=\\dfrac{\\bar{x}-\\mu_0}{\\frac{s}{\\sqrt{n}}}[\/latex]<\/p>\n<p>The slope of the population line, [latex]\\beta_1[\/latex], similarly follows a [latex]t[\/latex] Distribution.<\/p>\n<section class=\"textbox keyTakeaway\">\n<h3>Test Statistics for the Hypothesis Test for Significance of Slope<\/h3>\n<p>The test statistic to test [latex]H_0: \\beta_1 = 0[\/latex] is:<\/p>\n<p style=\"text-align: center;\">[latex]t=\\dfrac{b-0}{[\\text{std. error of }b]} = \\dfrac{b}{SE_b}[\/latex]<\/p>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3164\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3164&theme=lumen&iframe_resize_id=ohm3164&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-1448-1\">rottentomatoes.com <a href=\"#return-footnote-1448-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","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":1438,"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\/1448"}],"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":5,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1448\/revisions"}],"predecessor-version":[{"id":6288,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1448\/revisions\/6288"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/1438"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1448\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1448"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1448"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1448"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1448"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}