{"id":5470,"date":"2022-08-30T23:24:58","date_gmt":"2022-08-30T23:24:58","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&#038;p=5470"},"modified":"2022-08-30T23:24:58","modified_gmt":"2022-08-30T23:24:58","slug":"14d-coreq","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/14d-coreq\/","title":{"raw":"14D Coreq","rendered":"14D Coreq"},"content":{"raw":"In the next preview assignment and in the next class, you will be making multiple pair wise comparisons and working with confidence interval estimates of differences in\u00a0 population means.\r\n\r\nPair-wise Comparisons for ANOVA\r\n\r\nRecall the study done by the National Survey of Student Engagement, which found that,\u00a0 on average, college students spend 17 hours per week preparing and studying for their\u00a0 classes.[footnote]Aaron. (2014, July 24). Which college majors study the most? MyMajors. https:\/\/www.mymajors.com\/blog\/college-majors-study\/[\/footnote][footnote]Survey Instruments. (2013). National Survey of Student Engagement.\u00a0https:\/\/nsse.indiana.edu\/nsse\/survey-instruments\/index.html[\/footnote]\r\n\r\nIn In-Class Activity 14.B, we conducted a one-way ANOVA to determine if there are any\u00a0 statistically-significant differences between the means of the following majors:\r\n<ul>\r\n \t<li>Arts and Humanities<\/li>\r\n \t<li>STEM<\/li>\r\n \t<li>Education<\/li>\r\n \t<li>Business<\/li>\r\n<\/ul>\r\nUsing a 5% level of significance, we rejected the null hypothesis that the means are\u00a0 equal and accepted the alternative hypothesis that at least two means are different.\r\n\r\nThe question now\u2014which means are different? To answer this question, we need to\u00a0 make multiple pair-wise comparisons.\r\n\r\nWe could begin by comparing business and education. This is an example of a pair wise comparison. However, there are more!\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 1<\/h3>\r\n1) How many total pair-wise comparisons can be made? List the pairs below.<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 2<\/h3>\r\n2) What strategy did you use to determine the total number of pair-wise comparisons in\u00a0 Question 1?<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 3<\/h3>\r\n3) Suppose this scenario had included engineering. How many total pair-wise\u00a0 comparisons could be made?<\/div>\r\nWorking with Intervals that Estimate a Difference\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 4<\/h3>\r\n4) In previous in-class activities, we used \ufffd to represent a population mean and \ufffd\u0305to\u00a0 represent a sample mean. When we are comparing two populations, we add\u00a0 subscripts to indicate which population (and sample) is being referenced.\r\n\r\nPart A: In the context of the hours studied by major, \ufffd%&amp;'()*+,- would represent the\u00a0 mean study time of education majors. How would you represent the mean\u00a0 study time of business majors?\r\n\r\nPart B: What does \ufffd%&amp;'()*+,- \u2212 \ufffd\/'0+-%00 represent?\r\n\r\nPart C: What would it mean if \ufffd%&amp;'()*+,- \u2212 \ufffd\/'0+-%00 was equal to 0?\r\n\r\nPart D: What would it mean if \ufffd%&amp;'()*+,- \u2212 \ufffd\/'0+-%00 was greater than 0?\r\n\r\nPart E: What would it mean if \ufffd%&amp;'()*+,- \u2212 \ufffd\/'0+-%00 was less than 0?\r\n\r\nPart F: Assume your sample data produced the following estimated confidence\u00a0 interval for \ufffd%&amp;'()*+,- \u2212 \ufffd\/'0+-%00:\r\n\r\n(\u22122.3, \u22120.99)\r\n\r\nIf you were comparing the means of education and business majors, what\u00a0 conclusion would you reach?\r\n\r\nPart G: Assume your sample data produced the following estimated confidence\u00a0 interval for \ufffd%&amp;'()*+,- \u2212 \ufffd\/'0+-%00:\r\n\r\n(\u22120.3, 0.5)\r\n\r\nIf you were comparing the means of education and business majors, what\u00a0 conclusion would you reach?\r\n\r\n<\/div>","rendered":"<p>In the next preview assignment and in the next class, you will be making multiple pair wise comparisons and working with confidence interval estimates of differences in\u00a0 population means.<\/p>\n<p>Pair-wise Comparisons for ANOVA<\/p>\n<p>Recall the study done by the National Survey of Student Engagement, which found that,\u00a0 on average, college students spend 17 hours per week preparing and studying for their\u00a0 classes.<a class=\"footnote\" title=\"Aaron. (2014, July 24). Which college majors study the most? MyMajors. https:\/\/www.mymajors.com\/blog\/college-majors-study\/\" id=\"return-footnote-5470-1\" href=\"#footnote-5470-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a><a class=\"footnote\" title=\"Survey Instruments. (2013). National Survey of Student Engagement.\u00a0https:\/\/nsse.indiana.edu\/nsse\/survey-instruments\/index.html\" id=\"return-footnote-5470-2\" href=\"#footnote-5470-2\" aria-label=\"Footnote 2\"><sup class=\"footnote\">[2]<\/sup><\/a><\/p>\n<p>In In-Class Activity 14.B, we conducted a one-way ANOVA to determine if there are any\u00a0 statistically-significant differences between the means of the following majors:<\/p>\n<ul>\n<li>Arts and Humanities<\/li>\n<li>STEM<\/li>\n<li>Education<\/li>\n<li>Business<\/li>\n<\/ul>\n<p>Using a 5% level of significance, we rejected the null hypothesis that the means are\u00a0 equal and accepted the alternative hypothesis that at least two means are different.<\/p>\n<p>The question now\u2014which means are different? To answer this question, we need to\u00a0 make multiple pair-wise comparisons.<\/p>\n<p>We could begin by comparing business and education. This is an example of a pair wise comparison. However, there are more!<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Question 1<\/h3>\n<p>1) How many total pair-wise comparisons can be made? List the pairs below.<\/p><\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Question 2<\/h3>\n<p>2) What strategy did you use to determine the total number of pair-wise comparisons in\u00a0 Question 1?<\/p><\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Question 3<\/h3>\n<p>3) Suppose this scenario had included engineering. How many total pair-wise\u00a0 comparisons could be made?<\/p><\/div>\n<p>Working with Intervals that Estimate a Difference<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Question 4<\/h3>\n<p>4) In previous in-class activities, we used \ufffd to represent a population mean and \ufffd\u0305to\u00a0 represent a sample mean. When we are comparing two populations, we add\u00a0 subscripts to indicate which population (and sample) is being referenced.<\/p>\n<p>Part A: In the context of the hours studied by major, \ufffd%&amp;'()*+,- would represent the\u00a0 mean study time of education majors. How would you represent the mean\u00a0 study time of business majors?<\/p>\n<p>Part B: What does \ufffd%&amp;'()*+,- \u2212 \ufffd\/&#8217;0+-%00 represent?<\/p>\n<p>Part C: What would it mean if \ufffd%&amp;'()*+,- \u2212 \ufffd\/&#8217;0+-%00 was equal to 0?<\/p>\n<p>Part D: What would it mean if \ufffd%&amp;'()*+,- \u2212 \ufffd\/&#8217;0+-%00 was greater than 0?<\/p>\n<p>Part E: What would it mean if \ufffd%&amp;'()*+,- \u2212 \ufffd\/&#8217;0+-%00 was less than 0?<\/p>\n<p>Part F: Assume your sample data produced the following estimated confidence\u00a0 interval for \ufffd%&amp;'()*+,- \u2212 \ufffd\/&#8217;0+-%00:<\/p>\n<p>(\u22122.3, \u22120.99)<\/p>\n<p>If you were comparing the means of education and business majors, what\u00a0 conclusion would you reach?<\/p>\n<p>Part G: Assume your sample data produced the following estimated confidence\u00a0 interval for \ufffd%&amp;'()*+,- \u2212 \ufffd\/&#8217;0+-%00:<\/p>\n<p>(\u22120.3, 0.5)<\/p>\n<p>If you were comparing the means of education and business majors, what\u00a0 conclusion would you reach?<\/p>\n<\/div>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-5470-1\">Aaron. (2014, July 24). Which college majors study the most? MyMajors. https:\/\/www.mymajors.com\/blog\/college-majors-study\/ <a href=\"#return-footnote-5470-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><li id=\"footnote-5470-2\">Survey Instruments. (2013). National Survey of Student Engagement.\u00a0https:\/\/nsse.indiana.edu\/nsse\/survey-instruments\/index.html <a href=\"#return-footnote-5470-2\" class=\"return-footnote\" aria-label=\"Return to footnote 2\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":23592,"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-5470","chapter","type-chapter","status-publish","hentry"],"part":5448,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5470","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\/23592"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5470\/revisions"}],"predecessor-version":[{"id":5471,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5470\/revisions\/5471"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/5448"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5470\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=5470"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=5470"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=5470"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=5470"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}