{"id":1519,"date":"2023-06-22T02:40:17","date_gmt":"2023-06-22T02:40:17","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/bootstrap-confidence-interval-learn-it-2\/"},"modified":"2025-05-17T02:53:15","modified_gmt":"2025-05-17T02:53:15","slug":"bootstrap-confidence-interval-learn-it-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/bootstrap-confidence-interval-learn-it-2\/","title":{"raw":"Bootstrap Confidence Interval - Learn it 2","rendered":"Bootstrap Confidence Interval &#8211; Learn it 2"},"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;Find a bootstrap confidence interval for a population parameter and difference in population parameters&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;}\">Find a bootstrap confidence interval for a population parameter and difference in population parameters<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Describe what a bootstrap confidence interval means and use it make inference regarding the population&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;}\">Describe what a bootstrap confidence interval means and use it make inference regarding the population<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2><strong>Jumping Frog Jubilee<\/strong><\/h2>\r\n<p>Every year, bullfrogs compete in a jumping contest at the Calaveras County Jumping Frog Jubilee (a contest inspired by a short story by Mark Twain). One year, researchers recorded the jump distances of frogs entered in the contest.[footnote]Astley, H. C., Abbott, E. M., Azizi, E., Marsh, R. L., &amp; Roberts, T. J. (2013). Chasing maximal performance: A cautionary tale from the celebrated jumping frogs of Calaveras County. The Journal of Experimental Biology, 216(21), 3947\u20133953.[\/footnote]<\/p>\r\n<p>The following are the jump distances (in meters) for a sample of [latex]15[\/latex] bullfrogs.<\/p>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>0.1<\/td>\r\n<td>0.4<\/td>\r\n<td>0.6<\/td>\r\n<td>0.8<\/td>\r\n<td>1.3<\/td>\r\n<td>1.5<\/td>\r\n<td>1.6<\/td>\r\n<td>1.7<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1.8<\/td>\r\n<td>1.8<\/td>\r\n<td>1.9<\/td>\r\n<td>1.9<\/td>\r\n<td>1.9<\/td>\r\n<td>2.0<\/td>\r\n<td>2.2<\/td>\r\n<td>&nbsp;<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p>A dotplot of the sample jump distances is shown here.<\/p>\r\n<p><img class=\"aligncenter wp-image-2393 size-full\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/06\/22024017\/Picture1-3-1.png\" alt=\"A dotplot of the data listed above.\" width=\"695\" height=\"130\" \/><\/p>\r\n<p>If we were interested in estimating the population mean jump distance (the mean jump distance for all frogs entered in the competition), it would not be appropriate to use a one-sample t confidence interval because the sample size is not greater than [latex]30[\/latex] and, because the data distribution is skewed, it is not reasonable to think that the population jump distance distribution is approximately normal.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3504[\/ohm2_question]<\/section>\r\n<section>Bootstrap confidence intervals can be constructed for population parameters other than the population mean. Bootstrap confidence intervals provide an alternative to traditional intervals based on [latex]z[\/latex] or [latex]t[\/latex] distributions that can be used in situations where conditions necessary for the traditional methods are not met.\u00a0<\/section>\r\n<section class=\"textbox interact\"><strong><strong>To calculate a bootstrap confidence interval, let's use the statistical tool: <a href=\"https:\/\/istats.shinyapps.io\/Boot1samp\/\">https:\/\/istats.shinyapps.io\/Boot1samp\/<\/a>.<br \/>\r\n<\/strong><\/strong><strong><br \/>\r\nStep 1: <\/strong><span style=\"background-color: initial; font-size: 0.9em; word-spacing: normal;\">For the \u201cEnter Data\u201d option, choose \u201cYour Own.\"<br \/>\r\n<\/span><strong>Step 2: <\/strong>For \u201cName of Variable,\u201d type \u201cJump Distance.\u201d<strong><br \/>\r\nStep 3:<\/strong> Type the values from the sample or copy and paste them into the \u201cEnter Observations\u201d box. Separate the data values by spaces or commas. The values for the sample are: 0.1, 0.4, 0.6, 1.2, 0.8, 1.5, 1.6, 1.7, 1.8, 1.8, 1.9, 1.9, 1.9, 2.0, and 2.2.<br \/>\r\n<strong>Step 4:<\/strong> For the \u201cStatistic of Interest\u201d option, select \u201cMedian.\u201d<br \/>\r\n<strong>Step 5: <\/strong>Click on \u201c1,000\u201d for \u201cSelect how many bootstrap samples you want to generate,\u201d and then click on \u201cDraw Bootstrap Sample(s).\u201d<br \/>\r\n<strong>Step 6:\u00a0<\/strong>To get the confidence interval, at the very top of the display, click on the <strong>Get Confidence Interval<\/strong> tab. Check to make sure that the confidence level is set to [latex]95\\%[\/latex]. The corresponding bootstrap confidence interval is on the right-hand side of the display.<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3506[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Find a bootstrap confidence interval for a population parameter and difference in population parameters&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;}\">Find a bootstrap confidence interval for a population parameter and difference in population parameters<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Describe what a bootstrap confidence interval means and use it make inference regarding the population&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;}\">Describe what a bootstrap confidence interval means and use it make inference regarding the population<\/span><\/li>\n<\/ul>\n<\/section>\n<h2><strong>Jumping Frog Jubilee<\/strong><\/h2>\n<p>Every year, bullfrogs compete in a jumping contest at the Calaveras County Jumping Frog Jubilee (a contest inspired by a short story by Mark Twain). One year, researchers recorded the jump distances of frogs entered in the contest.<a class=\"footnote\" title=\"Astley, H. C., Abbott, E. M., Azizi, E., Marsh, R. L., &amp; Roberts, T. J. (2013). Chasing maximal performance: A cautionary tale from the celebrated jumping frogs of Calaveras County. The Journal of Experimental Biology, 216(21), 3947\u20133953.\" id=\"return-footnote-1519-1\" href=\"#footnote-1519-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a><\/p>\n<p>The following are the jump distances (in meters) for a sample of [latex]15[\/latex] bullfrogs.<\/p>\n<table>\n<tbody>\n<tr>\n<td>0.1<\/td>\n<td>0.4<\/td>\n<td>0.6<\/td>\n<td>0.8<\/td>\n<td>1.3<\/td>\n<td>1.5<\/td>\n<td>1.6<\/td>\n<td>1.7<\/td>\n<\/tr>\n<tr>\n<td>1.8<\/td>\n<td>1.8<\/td>\n<td>1.9<\/td>\n<td>1.9<\/td>\n<td>1.9<\/td>\n<td>2.0<\/td>\n<td>2.2<\/td>\n<td>&nbsp;<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>A dotplot of the sample jump distances is shown here.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2393 size-full\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/06\/22024017\/Picture1-3-1.png\" alt=\"A dotplot of the data listed above.\" width=\"695\" height=\"130\" \/><\/p>\n<p>If we were interested in estimating the population mean jump distance (the mean jump distance for all frogs entered in the competition), it would not be appropriate to use a one-sample t confidence interval because the sample size is not greater than [latex]30[\/latex] and, because the data distribution is skewed, it is not reasonable to think that the population jump distance distribution is approximately normal.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3504\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3504&theme=lumen&iframe_resize_id=ohm3504&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section>Bootstrap confidence intervals can be constructed for population parameters other than the population mean. Bootstrap confidence intervals provide an alternative to traditional intervals based on [latex]z[\/latex] or [latex]t[\/latex] distributions that can be used in situations where conditions necessary for the traditional methods are not met.\u00a0<\/section>\n<section class=\"textbox interact\"><strong><strong>To calculate a bootstrap confidence interval, let&#8217;s use the statistical tool: <a href=\"https:\/\/istats.shinyapps.io\/Boot1samp\/\">https:\/\/istats.shinyapps.io\/Boot1samp\/<\/a>.<br \/>\n<\/strong><\/strong><strong><br \/>\nStep 1: <\/strong><span style=\"background-color: initial; font-size: 0.9em; word-spacing: normal;\">For the \u201cEnter Data\u201d option, choose \u201cYour Own.&#8221;<br \/>\n<\/span><strong>Step 2: <\/strong>For \u201cName of Variable,\u201d type \u201cJump Distance.\u201d<strong><br \/>\nStep 3:<\/strong> Type the values from the sample or copy and paste them into the \u201cEnter Observations\u201d box. Separate the data values by spaces or commas. The values for the sample are: 0.1, 0.4, 0.6, 1.2, 0.8, 1.5, 1.6, 1.7, 1.8, 1.8, 1.9, 1.9, 1.9, 2.0, and 2.2.<br \/>\n<strong>Step 4:<\/strong> For the \u201cStatistic of Interest\u201d option, select \u201cMedian.\u201d<br \/>\n<strong>Step 5: <\/strong>Click on \u201c1,000\u201d for \u201cSelect how many bootstrap samples you want to generate,\u201d and then click on \u201cDraw Bootstrap Sample(s).\u201d<br \/>\n<strong>Step 6:\u00a0<\/strong>To get the confidence interval, at the very top of the display, click on the <strong>Get Confidence Interval<\/strong> tab. Check to make sure that the confidence level is set to [latex]95\\%[\/latex]. The corresponding bootstrap confidence interval is on the right-hand side of the display.<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3506\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3506&theme=lumen&iframe_resize_id=ohm3506&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-1519-1\">Astley, H. C., Abbott, E. M., Azizi, E., Marsh, R. L., &amp; Roberts, T. J. (2013). Chasing maximal performance: A cautionary tale from the celebrated jumping frogs of Calaveras County. The Journal of Experimental Biology, 216(21), 3947\u20133953. <a href=\"#return-footnote-1519-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":8,"menu_order":15,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":1502,"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\/1519"}],"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\/1519\/revisions"}],"predecessor-version":[{"id":6927,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1519\/revisions\/6927"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/1502"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1519\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1519"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1519"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1519"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1519"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}