{"id":5283,"date":"2022-08-19T14:40:18","date_gmt":"2022-08-19T14:40:18","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&#038;p=5283"},"modified":"2022-08-19T14:41:06","modified_gmt":"2022-08-19T14:41:06","slug":"10d-coreq","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/10d-coreq\/","title":{"raw":"10D Coreq","rendered":"10D Coreq"},"content":{"raw":"In the next preview assignment and in the next class, you will be required to describe\u00a0 the sampling distribution of a statistic, use technology to calculate a confidence interval,\u00a0 and interpret the interval in the context of the data.\r\n\r\nIs Yawning Contagious?\r\n\r\nThe objective of this analysis is to explore the proportion of people who yawn after seeing someone else yawn. We will use data from an experiment conducted on the television show Mythbusters. The data are from the <strong>yawn<\/strong> dataset in the OpenIntro R\u00a0 package.[footnote]Data from the yawn dataset in the OpenIntro R package. https:\/\/www.openintro.org\/data\/index.php?data=yawn[\/footnote]\r\n\r\nIn the experiment, 50 participants were randomly assigned to two groups:\r\n<ul>\r\n \t<li>Treatment (34 participants), who saw a person near them yawn<\/li>\r\n \t<li>Control (16 participants), who didn\u2019t see anyone yawn<\/li>\r\n<\/ul>\r\nAll of the participants were instructed to wait in a room, and the experimenters recorded\u00a0 whether or not the participants yawned. The participants arrived at different times, so no\u00a0 two participants were in the waiting room at the same time.\r\n\r\nWe will focus on the data for the 34 participants in the treatment group and analyze the\u00a0 categorical variable yawn with the possible values \u201cyes\u201d and \u201cno.\u201d\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 1<\/h3>\r\nMake a graphical display of the distribution of yawn using the data in spreadsheet\u00a0 DCMP_STAT_10D_yawn. Use the graph to describe the distribution of the variable.\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 2<\/h3>\r\nCalculate\u00a0 [latex] \\hat{p} [\/latex], the proportion of participants in the treatment group who yawned. Round your answer to 3 decimal places.\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 3<\/h3>\r\nWhen certain conditions are met, we know the sampling distribution of the sample\u00a0 proportion, [latex] \\hat{p}[\/latex].\r\n<ol>\r\n \t<li>For large samples, what is the name of the distribution?<\/li>\r\n \t<li>What is the mean of the sampling distribution of the sample proportion?\u00a0 Describe the mean in the context of the data.<\/li>\r\n \t<li>What is the standard error of the sampling distribution of the sample\u00a0 proportion? You can use technology to obtain this value.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 4<\/h3>\r\nNow let\u2019s calculate a confidence interval (i.e., a range of plausible values for [latex] p [\/latex], the\u00a0 true proportion of people who yawn after seeing someone else yawn).\r\n<ol>\r\n \t<li>Use technology to calculate a 95% confidence interval for [latex] p [\/latex].<\/li>\r\n \t<li>Interpret the interval in the context of the data.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 5<\/h3>\r\nSuppose you read an article that claims that the true proportion of people who yawn after seeing someone else yawn is 0.63. Based on your analysis, would you be surprised by this claim? Explain.\r\n\r\n<\/div>\r\n&nbsp;","rendered":"<p>In the next preview assignment and in the next class, you will be required to describe\u00a0 the sampling distribution of a statistic, use technology to calculate a confidence interval,\u00a0 and interpret the interval in the context of the data.<\/p>\n<p>Is Yawning Contagious?<\/p>\n<p>The objective of this analysis is to explore the proportion of people who yawn after seeing someone else yawn. We will use data from an experiment conducted on the television show Mythbusters. The data are from the <strong>yawn<\/strong> dataset in the OpenIntro R\u00a0 package.<a class=\"footnote\" title=\"Data from the yawn dataset in the OpenIntro R package. https:\/\/www.openintro.org\/data\/index.php?data=yawn\" id=\"return-footnote-5283-1\" href=\"#footnote-5283-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a><\/p>\n<p>In the experiment, 50 participants were randomly assigned to two groups:<\/p>\n<ul>\n<li>Treatment (34 participants), who saw a person near them yawn<\/li>\n<li>Control (16 participants), who didn\u2019t see anyone yawn<\/li>\n<\/ul>\n<p>All of the participants were instructed to wait in a room, and the experimenters recorded\u00a0 whether or not the participants yawned. The participants arrived at different times, so no\u00a0 two participants were in the waiting room at the same time.<\/p>\n<p>We will focus on the data for the 34 participants in the treatment group and analyze the\u00a0 categorical variable yawn with the possible values \u201cyes\u201d and \u201cno.\u201d<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Question 1<\/h3>\n<p>Make a graphical display of the distribution of yawn using the data in spreadsheet\u00a0 DCMP_STAT_10D_yawn. Use the graph to describe the distribution of the variable.<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Question 2<\/h3>\n<p>Calculate\u00a0 [latex]\\hat{p}[\/latex], the proportion of participants in the treatment group who yawned. Round your answer to 3 decimal places.<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Question 3<\/h3>\n<p>When certain conditions are met, we know the sampling distribution of the sample\u00a0 proportion, [latex]\\hat{p}[\/latex].<\/p>\n<ol>\n<li>For large samples, what is the name of the distribution?<\/li>\n<li>What is the mean of the sampling distribution of the sample proportion?\u00a0 Describe the mean in the context of the data.<\/li>\n<li>What is the standard error of the sampling distribution of the sample\u00a0 proportion? You can use technology to obtain this value.<\/li>\n<\/ol>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Question 4<\/h3>\n<p>Now let\u2019s calculate a confidence interval (i.e., a range of plausible values for [latex]p[\/latex], the\u00a0 true proportion of people who yawn after seeing someone else yawn).<\/p>\n<ol>\n<li>Use technology to calculate a 95% confidence interval for [latex]p[\/latex].<\/li>\n<li>Interpret the interval in the context of the data.<\/li>\n<\/ol>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Question 5<\/h3>\n<p>Suppose you read an article that claims that the true proportion of people who yawn after seeing someone else yawn is 0.63. Based on your analysis, would you be surprised by this claim? Explain.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-5283-1\">Data from the yawn dataset in the OpenIntro R package. https:\/\/www.openintro.org\/data\/index.php?data=yawn <a href=\"#return-footnote-5283-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":574340,"menu_order":10,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-5283","chapter","type-chapter","status-publish","hentry"],"part":5220,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5283","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/users\/574340"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5283\/revisions"}],"predecessor-version":[{"id":5284,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5283\/revisions\/5284"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/5220"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5283\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=5283"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=5283"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=5283"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=5283"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}