{"id":5230,"date":"2022-08-18T23:38:40","date_gmt":"2022-08-18T23:38:40","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&#038;p=5230"},"modified":"2022-08-18T23:40:30","modified_gmt":"2022-08-18T23:40:30","slug":"10a-in-class-activity","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/10a-in-class-activity\/","title":{"raw":"10A In-Class Activity","rendered":"10A In-Class Activity"},"content":{"raw":"Adequate sleep is crucial for students to be healthy and successful. Sleep deprivation\u00a0 can affect memory, academic performance, physical health, and mental health.[footnote]Bullock, L. (2021, March 19). C<em>ollege student sleep statistics<\/em>. Mattress Advisor. https:\/\/www.mattressadvisor.com\/college-sleep-statistics\/ [\/footnote] College\u00a0 students often lack sleep, and some occasionally resort to pulling all-nighters.\r\n\r\n<img class=\"alignnone wp-image-5231\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/08\/18225341\/10A-InClass-1.png\" alt=\"\" width=\"328\" height=\"182\" \/>\r\n\r\nCredit: iStock\/SolStock\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 1<\/h3>\r\nThe website Mattress Advisor claims that 20% of college students pull all-nighters each semester.[footnote]Bullock, L. (2021, March 19). <em>College student sleep statistics<\/em>. Mattress Advisor. https:\/\/www.mattressadvisor.com\/college-sleep-statistics\/ [\/footnote] Do you think this claim is accurate?\u00a0\u00a0What information would be helpful to answer this\u00a0\u00a0question?\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 2<\/h3>\r\nIn a previous activity, we looked at the percentage of college students who had pulled all-nighters. In the study, 34 out of 253 students said they had an all-nighter in\u00a0 the last semester.[footnote]Onyper, S., Thacher, P., Gilbert, J., &amp; Gradess, S. (2012). Class start times, sleep, and academic performance in college: A path analysis. <em>Chronobiology International<\/em>, <em>29<\/em>(3): 318\u2013335.[\/footnote]\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>Calculate the point estimate ([latex] \\hat{p} [\/latex]) for the proportion of college students who\u00a0 had pulled all-nighters.<\/li>\r\n \t<li>Looking at the point estimate alone, do you think the claim by Mattress Advisor is accurate?<\/li>\r\n \t<li>Why should we create a confidence interval if we already have an estimate\u00a0 for the population proportion?<\/li>\r\n<\/ol>\r\n<\/div>\r\nIn order to create a confidence interval for proportions, we need to verify that the sampling distribution of the sample proportions is approximately normal. Recall the\u00a0 following conditions that must be satisfied:\r\n<ul>\r\n \t<li>Random samples: The observations represent a random sample of the\u00a0 population.<\/li>\r\n \t<li>The sample is less than 10% of the population.<\/li>\r\n \t<li>Sample size: The sample is large enough that [latex]n\\hat{p}\\geq 10 [\/latex] and [latex] n(1 \u2212 \\hat{p}) \\geq 10[\/latex].<\/li>\r\n<\/ul>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 3<\/h3>\r\nWe will assume that random sampling is used and that the sample is less than 10%\u00a0 of the population. Verify the sample size condition so that we may assume that the\u00a0 sampling distribution of the sample proportions is approximately normal.\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 4<\/h3>\r\nRather than using a simple point estimate, let\u2019s calculate confidence intervals for a\u00a0 population proportion using the DCMP Inference for a Population Proportion tool at https:\/\/dcmathpathways.shinyapps.io\/Inference_prop\/ for the study, where 34 out of\u00a0 253 students said they had all-nighters in the last semester.[footnote]Onyper, S., Thacher, P., Gilbert, J., &amp; Gradess, S. (2012). Class start times, sleep, and academic performance in college: A path analysis. <em>Chronobiology International<\/em>, 29(3): 318\u2013335.[\/footnote]\r\n<ol>\r\n \t<li>Change the \u201cEnter Data\u201d box to \u201cNumber of Successes.\u201d<\/li>\r\n \t<li>Input the sample size ([latex]n[\/latex]) and the number of successes ([latex]x[\/latex]), which in this case is\u00a0 the number of students who pulled all-nighters.<\/li>\r\n \t<li>Specify appropriate labels for success\/failure by checking the appropriate boxes and typing in labels. For example, we can label success as \u201cAll-nighters\u201d and\u00a0 failure as \u201cNo all-nighters.\u201d<\/li>\r\n \t<li>Slide the confidence level to the desired level. The default is 95%<\/li>\r\n \t<li>View the z critical value by selecting the box \u201cShow z-score for Margin of Error.\u201d<\/li>\r\n \t<li>The confidence interval will appear to the right along with the point estimate,\u00a0 standard error, margin of error, and z critical value (labeled as \u201cz-score\u201d).<\/li>\r\n<\/ol>\r\n&nbsp;\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>What is the standard error for the proportion of college students who had all nighters?<\/li>\r\n \t<li>Assume the level of confidence is 95%. What is the z critical value, [latex]z^{*}[\/latex], that\u00a0 corresponds to the confidence level?<\/li>\r\n \t<li>Calculate the margin of error for the sample proportion of college students\u00a0 who had all-nighters from the equation for the margin of error ([latex]E[\/latex]):[latex]E = z^{*} \\bullet (standard~error)[\/latex]Notice how the values in the web tool match the calculated value from the\u00a0 equation.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 5<\/h3>\r\nNow let\u2019s estimate the proportion of college students who had all-nighters by\u00a0 creating a 95% confidence interval.\r\n<ol>\r\n \t<li>Begin by writing the confidence interval in both [latex] \\pm [\/latex] format and interval notation\u00a0 form (lower bound, upper bound).<\/li>\r\n \t<li>Represent the confidence interval on the following number line. Include the\u00a0 point estimate, upper bound, and lower bound.\r\n<img class=\"alignnone wp-image-5232\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/08\/18230239\/10A-InClass-2-300x35.png\" alt=\"\" width=\"583\" height=\"68\" \/><\/li>\r\n<\/ol>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 6<\/h3>\r\nUse the DCMP tool to calculate the 99% confidence interval for the proportion of\u00a0 college students who had all-nighters.\r\n<ol>\r\n \t<li>Write the 99% confidence interval using interval notation form (lower bound,\u00a0 upper bound).<\/li>\r\n \t<li>How is this confidence interval different from the 95% confidence interval?<\/li>\r\n \t<li>Looking at the point estimate, standard error, z critical value, and margin of\u00a0 error, what do you think contributed to the change from the 95% confidence\u00a0 interval to the 99% confidence interval?<\/li>\r\n \t<li>What do you think would happen to the length of the interval if we changed it\u00a0 to 90% confidence?<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 7<\/h3>\r\nBased on your answers to Questions 4 and 5, do you think there is evidence to\u00a0 support the claim from Mattress Advisor? Explain.\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\n&nbsp;","rendered":"<p>Adequate sleep is crucial for students to be healthy and successful. Sleep deprivation\u00a0 can affect memory, academic performance, physical health, and mental health.<a class=\"footnote\" title=\"Bullock, L. (2021, March 19). College student sleep statistics. Mattress Advisor. https:\/\/www.mattressadvisor.com\/college-sleep-statistics\/\" id=\"return-footnote-5230-1\" href=\"#footnote-5230-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a> College\u00a0 students often lack sleep, and some occasionally resort to pulling all-nighters.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-5231\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/08\/18225341\/10A-InClass-1.png\" alt=\"\" width=\"328\" height=\"182\" \/><\/p>\n<p>Credit: iStock\/SolStock<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Question 1<\/h3>\n<p>The website Mattress Advisor claims that 20% of college students pull all-nighters each semester.<a class=\"footnote\" title=\"Bullock, L. (2021, March 19). College student sleep statistics. Mattress Advisor. https:\/\/www.mattressadvisor.com\/college-sleep-statistics\/\" id=\"return-footnote-5230-2\" href=\"#footnote-5230-2\" aria-label=\"Footnote 2\"><sup class=\"footnote\">[2]<\/sup><\/a> Do you think this claim is accurate?\u00a0\u00a0What information would be helpful to answer this\u00a0\u00a0question?<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Question 2<\/h3>\n<p>In a previous activity, we looked at the percentage of college students who had pulled all-nighters. In the study, 34 out of 253 students said they had an all-nighter in\u00a0 the last semester.<a class=\"footnote\" title=\"Onyper, S., Thacher, P., Gilbert, J., &amp; Gradess, S. (2012). Class start times, sleep, and academic performance in college: A path analysis. Chronobiology International, 29(3): 318\u2013335.\" id=\"return-footnote-5230-3\" href=\"#footnote-5230-3\" aria-label=\"Footnote 3\"><sup class=\"footnote\">[3]<\/sup><\/a><\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Calculate the point estimate ([latex]\\hat{p}[\/latex]) for the proportion of college students who\u00a0 had pulled all-nighters.<\/li>\n<li>Looking at the point estimate alone, do you think the claim by Mattress Advisor is accurate?<\/li>\n<li>Why should we create a confidence interval if we already have an estimate\u00a0 for the population proportion?<\/li>\n<\/ol>\n<\/div>\n<p>In order to create a confidence interval for proportions, we need to verify that the sampling distribution of the sample proportions is approximately normal. Recall the\u00a0 following conditions that must be satisfied:<\/p>\n<ul>\n<li>Random samples: The observations represent a random sample of the\u00a0 population.<\/li>\n<li>The sample is less than 10% of the population.<\/li>\n<li>Sample size: The sample is large enough that [latex]n\\hat{p}\\geq 10[\/latex] and [latex]n(1 \u2212 \\hat{p}) \\geq 10[\/latex].<\/li>\n<\/ul>\n<div class=\"textbox key-takeaways\">\n<h3>Question 3<\/h3>\n<p>We will assume that random sampling is used and that the sample is less than 10%\u00a0 of the population. Verify the sample size condition so that we may assume that the\u00a0 sampling distribution of the sample proportions is approximately normal.<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Question 4<\/h3>\n<p>Rather than using a simple point estimate, let\u2019s calculate confidence intervals for a\u00a0 population proportion using the DCMP Inference for a Population Proportion tool at https:\/\/dcmathpathways.shinyapps.io\/Inference_prop\/ for the study, where 34 out of\u00a0 253 students said they had all-nighters in the last semester.<a class=\"footnote\" title=\"Onyper, S., Thacher, P., Gilbert, J., &amp; Gradess, S. (2012). Class start times, sleep, and academic performance in college: A path analysis. Chronobiology International, 29(3): 318\u2013335.\" id=\"return-footnote-5230-4\" href=\"#footnote-5230-4\" aria-label=\"Footnote 4\"><sup class=\"footnote\">[4]<\/sup><\/a><\/p>\n<ol>\n<li>Change the \u201cEnter Data\u201d box to \u201cNumber of Successes.\u201d<\/li>\n<li>Input the sample size ([latex]n[\/latex]) and the number of successes ([latex]x[\/latex]), which in this case is\u00a0 the number of students who pulled all-nighters.<\/li>\n<li>Specify appropriate labels for success\/failure by checking the appropriate boxes and typing in labels. For example, we can label success as \u201cAll-nighters\u201d and\u00a0 failure as \u201cNo all-nighters.\u201d<\/li>\n<li>Slide the confidence level to the desired level. The default is 95%<\/li>\n<li>View the z critical value by selecting the box \u201cShow z-score for Margin of Error.\u201d<\/li>\n<li>The confidence interval will appear to the right along with the point estimate,\u00a0 standard error, margin of error, and z critical value (labeled as \u201cz-score\u201d).<\/li>\n<\/ol>\n<p>&nbsp;<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>What is the standard error for the proportion of college students who had all nighters?<\/li>\n<li>Assume the level of confidence is 95%. What is the z critical value, [latex]z^{*}[\/latex], that\u00a0 corresponds to the confidence level?<\/li>\n<li>Calculate the margin of error for the sample proportion of college students\u00a0 who had all-nighters from the equation for the margin of error ([latex]E[\/latex]):[latex]E = z^{*} \\bullet (standard~error)[\/latex]Notice how the values in the web tool match the calculated value from the\u00a0 equation.<\/li>\n<\/ol>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Question 5<\/h3>\n<p>Now let\u2019s estimate the proportion of college students who had all-nighters by\u00a0 creating a 95% confidence interval.<\/p>\n<ol>\n<li>Begin by writing the confidence interval in both [latex]\\pm[\/latex] format and interval notation\u00a0 form (lower bound, upper bound).<\/li>\n<li>Represent the confidence interval on the following number line. Include the\u00a0 point estimate, upper bound, and lower bound.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-5232\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/08\/18230239\/10A-InClass-2-300x35.png\" alt=\"\" width=\"583\" height=\"68\" \/><\/li>\n<\/ol>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Question 6<\/h3>\n<p>Use the DCMP tool to calculate the 99% confidence interval for the proportion of\u00a0 college students who had all-nighters.<\/p>\n<ol>\n<li>Write the 99% confidence interval using interval notation form (lower bound,\u00a0 upper bound).<\/li>\n<li>How is this confidence interval different from the 95% confidence interval?<\/li>\n<li>Looking at the point estimate, standard error, z critical value, and margin of\u00a0 error, what do you think contributed to the change from the 95% confidence\u00a0 interval to the 99% confidence interval?<\/li>\n<li>What do you think would happen to the length of the interval if we changed it\u00a0 to 90% confidence?<\/li>\n<\/ol>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Question 7<\/h3>\n<p>Based on your answers to Questions 4 and 5, do you think there is evidence to\u00a0 support the claim from Mattress Advisor? Explain.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-5230-1\">Bullock, L. (2021, March 19). C<em>ollege student sleep statistics<\/em>. Mattress Advisor. https:\/\/www.mattressadvisor.com\/college-sleep-statistics\/  <a href=\"#return-footnote-5230-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><li id=\"footnote-5230-2\">Bullock, L. (2021, March 19). <em>College student sleep statistics<\/em>. Mattress Advisor. https:\/\/www.mattressadvisor.com\/college-sleep-statistics\/  <a href=\"#return-footnote-5230-2\" class=\"return-footnote\" aria-label=\"Return to footnote 2\">&crarr;<\/a><\/li><li id=\"footnote-5230-3\">Onyper, S., Thacher, P., Gilbert, J., &amp; Gradess, S. (2012). Class start times, sleep, and academic performance in college: A path analysis. <em>Chronobiology International<\/em>, <em>29<\/em>(3): 318\u2013335. <a href=\"#return-footnote-5230-3\" class=\"return-footnote\" aria-label=\"Return to footnote 3\">&crarr;<\/a><\/li><li id=\"footnote-5230-4\">Onyper, S., Thacher, P., Gilbert, J., &amp; Gradess, S. (2012). Class start times, sleep, and academic performance in college: A path analysis. <em>Chronobiology International<\/em>, 29(3): 318\u2013335. <a href=\"#return-footnote-5230-4\" class=\"return-footnote\" aria-label=\"Return to footnote 4\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":574340,"menu_order":2,"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-5230","chapter","type-chapter","status-publish","hentry"],"part":5220,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5230","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":4,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5230\/revisions"}],"predecessor-version":[{"id":5236,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5230\/revisions\/5236"}],"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\/5230\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=5230"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=5230"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=5230"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=5230"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}