{"id":1259,"date":"2023-06-22T02:09:43","date_gmt":"2023-06-22T02:09:43","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/connecting-tests-intervals-learn-it-1\/"},"modified":"2025-05-16T03:48:11","modified_gmt":"2025-05-16T03:48:11","slug":"connecting-tests-intervals-learn-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/connecting-tests-intervals-learn-it-1\/","title":{"raw":"Connecting Tests and Intervals: Learn It 1","rendered":"Connecting Tests and Intervals: Learn It 1"},"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;Explain how a confidence interval is related to a two-sided hypothesis test&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;}\">Explain how a confidence interval is related to a two-sided hypothesis test.<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Confidence Interval - Hypothesis Testing<\/h2>\r\n<p>Confidence intervals contain a range of plausible estimates of the population parameter. Confidence intervals can also be used in hypothesis testing to assess whether a hypothesized population parameter falls within a certain range of values.<\/p>\r\n<p>Let's explore this idea of using a confidence interval for a hypothesis test!<\/p>\r\n<h3>Lego Structure Experiment[footnote]https:\/\/www.sciencenews.org\/article\/psychology-numbers-people-add-default-subtract-better[\/footnote]<\/h3>\r\n<p>Picture a bridge made of Legos. One side has three support pieces, the others have two support pieces. How would you stabilize the bridge?<\/p>\r\n<p>Most people would add a piece so that there are three supports on each side. But why not remove a piece so that each side has two supports instead? It turns out that getting people to subtract (whether a Lego block, ingredients in a recipe, or words in an essay) requires reminders and rewards.<\/p>\r\n<p><img class=\"aligncenter wp-image-445 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2022\/11\/23211634\/040621_sg_subtraction_inline1.jpeg\" alt=\"A lego structure.\" width=\"300\" height=\"240\" \/><\/p>\r\n<p>In one experiment, the team offered [latex]197[\/latex] people wandering around a crowded university quad a dollar to solve a puzzle. Participants viewed a Lego structure in which a figurine (represented by the piece of paper) was standing atop a platform with a large pillar behind her (see picture above). Atop that pillar, a single block in one corner supported a flat roof. Researchers asked the participants to stabilize the roof to avoid squashing the figurine. About half the participants were told: \"Each piece you add costs [latex]10[\/latex] cents.\" Even with that financial penalty, only [latex]40[\/latex] out of [latex]98[\/latex] participants thought to remove the destabilizing block and just rest the roof on top of the wide pillar. The researchers gave the remaining participants a more explicit message: \"Each piece you add costs [latex]10[\/latex] cents, but removing pieces is free.\" That cue prompted [latex]60[\/latex] out of [latex]99[\/latex] participants to remove the block.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1068[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1785[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Explain how a confidence interval is related to a two-sided hypothesis test&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;}\">Explain how a confidence interval is related to a two-sided hypothesis test.<\/span><\/li>\n<\/ul>\n<\/section>\n<h2>Confidence Interval &#8211; Hypothesis Testing<\/h2>\n<p>Confidence intervals contain a range of plausible estimates of the population parameter. Confidence intervals can also be used in hypothesis testing to assess whether a hypothesized population parameter falls within a certain range of values.<\/p>\n<p>Let&#8217;s explore this idea of using a confidence interval for a hypothesis test!<\/p>\n<h3>Lego Structure Experiment<a class=\"footnote\" title=\"https:\/\/www.sciencenews.org\/article\/psychology-numbers-people-add-default-subtract-better\" id=\"return-footnote-1259-1\" href=\"#footnote-1259-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a><\/h3>\n<p>Picture a bridge made of Legos. One side has three support pieces, the others have two support pieces. How would you stabilize the bridge?<\/p>\n<p>Most people would add a piece so that there are three supports on each side. But why not remove a piece so that each side has two supports instead? It turns out that getting people to subtract (whether a Lego block, ingredients in a recipe, or words in an essay) requires reminders and rewards.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-445 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2022\/11\/23211634\/040621_sg_subtraction_inline1.jpeg\" alt=\"A lego structure.\" width=\"300\" height=\"240\" \/><\/p>\n<p>In one experiment, the team offered [latex]197[\/latex] people wandering around a crowded university quad a dollar to solve a puzzle. Participants viewed a Lego structure in which a figurine (represented by the piece of paper) was standing atop a platform with a large pillar behind her (see picture above). Atop that pillar, a single block in one corner supported a flat roof. Researchers asked the participants to stabilize the roof to avoid squashing the figurine. About half the participants were told: &#8220;Each piece you add costs [latex]10[\/latex] cents.&#8221; Even with that financial penalty, only [latex]40[\/latex] out of [latex]98[\/latex] participants thought to remove the destabilizing block and just rest the roof on top of the wide pillar. The researchers gave the remaining participants a more explicit message: &#8220;Each piece you add costs [latex]10[\/latex] cents, but removing pieces is free.&#8221; That cue prompted [latex]60[\/latex] out of [latex]99[\/latex] participants to remove the block.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1068\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1068&theme=lumen&iframe_resize_id=ohm1068&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1785\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1785&theme=lumen&iframe_resize_id=ohm1785&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-1259-1\">https:\/\/www.sciencenews.org\/article\/psychology-numbers-people-add-default-subtract-better <a href=\"#return-footnote-1259-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":8,"menu_order":40,"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":"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\/1259"}],"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":7,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1259\/revisions"}],"predecessor-version":[{"id":6776,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1259\/revisions\/6776"}],"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\/1259\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1259"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1259"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1259"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1259"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}