{"id":1515,"date":"2023-06-22T02:40:16","date_gmt":"2023-06-22T02:40:16","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/bootstrap-distribution-and-confidence-interval-for-a-population-mean-apply-it-1\/"},"modified":"2023-10-22T01:13:16","modified_gmt":"2023-10-22T01:13:16","slug":"bootstrap-distribution-and-confidence-interval-for-a-population-mean-apply-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/bootstrap-distribution-and-confidence-interval-for-a-population-mean-apply-it-1\/","title":{"raw":"Bootstrap Distribution and Confidence Interval for a Population Mean - Apply It 1","rendered":"Bootstrap Distribution and Confidence Interval for a Population Mean &#8211; Apply 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;Create a bootstrap distribution for a sample mean&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;}\">Create a bootstrap distribution for a sample mean<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Find and describe a bootstrap percentile confidence interval for a population mean&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 and describe a bootstrap percentile confidence interval for a population mean<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<p>Recall that we are working with a sample of kWh\/100 miles ratings for [latex]10[\/latex] electric cars that were randomly selected from the population of all the 2021 models of electric cars sold in the United States, as reported by the EPA. The sample data are shown in the following table.<\/p>\r\n<table>\r\n<thead>\r\n<tr>\r\n<th>Observation<\/th>\r\n<th>Car model<\/th>\r\n<th>kWh\/100<span style=\"font-size: 1rem;\">\u00a0miles<\/span><\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>1<\/td>\r\n<td>Porsche Taycan 4S Cross Turismo<\/td>\r\n<td>45<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span style=\"font-size: inherit;\">2<\/span><\/td>\r\n<td>Volkswagen ID.4 Pro S<\/td>\r\n<td><span style=\"font-size: inherit;\">35<\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span style=\"font-size: inherit;\">3<\/span><\/td>\r\n<td>Hyundai Kona Electric<\/td>\r\n<td><span style=\"font-size: inherit;\">27<\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span style=\"font-size: inherit;\">4<\/span><\/td>\r\n<td>Ford Mustang Mach-E RWD<\/td>\r\n<td><span style=\"font-size: inherit;\">34<\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span style=\"font-size: inherit;\">5<\/span><\/td>\r\n<td>Tesla Model S Performance<\/td>\r\n<td><span style=\"font-size: inherit;\">35<\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span style=\"font-size: inherit;\">6<\/span><\/td>\r\n<td>Tesla Model X Performance<\/td>\r\n<td><span style=\"font-size: inherit;\">35<\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span style=\"font-size: inherit;\">7<\/span><\/td>\r\n<td>Nissan Leaf SV\/SL<\/td>\r\n<td><span style=\"font-size: inherit;\">32<\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span style=\"font-size: inherit;\">8<\/span><\/td>\r\n<td>Tesla Model S Plaid<\/td>\r\n<td><span style=\"font-size: inherit;\">33<\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span style=\"font-size: inherit;\">9<\/span><\/td>\r\n<td>Volkswagen ID.4 Pro<\/td>\r\n<td><span style=\"font-size: inherit;\">34<\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span style=\"font-size: inherit;\">10<\/span><\/td>\r\n<td>BMW i3s<\/td>\r\n<td><span id=\"MathJax-Element-37-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.15px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;\/p&gt; &lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mstyle displaystyle=&quot;true&quot;&gt;&lt;mn&gt;30&lt;\/mn&gt;&lt;\/mstyle&gt;&lt;\/math&gt; &lt;p&gt;\" data-asciimath=\"30\"><span id=\"MJXc-Node-181\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-182\" class=\"mjx-mrow\"><span id=\"MJXc-Node-183\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-184\" class=\"mjx-mrow\"><span id=\"MJXc-Node-185\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">30<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<section class=\"textbox interact\"><strong><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>.<\/strong><\/strong><\/strong>\u00a0\r\n\r\n<p><strong>Step 1: <\/strong>For the \u201cEnter Data\u201d option, choose \u201cYour Own.\"<br \/>\r\n<strong>Step 2: <\/strong>Type the values from the sample into the \u201cEnter Observations\u201d box. Separate the data values by spaces or commas.<br \/>\r\n<strong>Step 3:<\/strong> Recall the values for the sample are: 45, 35, 27, 34, 35, 35, 32, 33, 34, and 30.<br \/>\r\n<strong>Step 4:<\/strong> For the \u201cStatistic of Interest\u201d option, select \u201cMean.\u201d<br \/>\r\n<strong>Step 5: <\/strong>On the left-hand side of the display, under \u201cSelect how many bootstrap samples you want to generate,\u201d click on \u201c1,000.\u201d Then, click on \u201cDraw Bootstrap Sample(s).\u201d<br \/>\r\n<strong>Step 6: Y<\/strong>ou should see the bootstrap distribution in the lower part of the right-hand side of the display.<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\"><span style=\"font-size: 1rem; orphans: 1; text-align: initial; background-color: initial; word-spacing: normal;\">[ohm2_question hide_question_numbers=1]3488[\/ohm2_question]<\/span><\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Create a bootstrap distribution for a sample mean&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;}\">Create a bootstrap distribution for a sample mean<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Find and describe a bootstrap percentile confidence interval for a population mean&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 and describe a bootstrap percentile confidence interval for a population mean<\/span><\/li>\n<\/ul>\n<\/section>\n<p>Recall that we are working with a sample of kWh\/100 miles ratings for [latex]10[\/latex] electric cars that were randomly selected from the population of all the 2021 models of electric cars sold in the United States, as reported by the EPA. The sample data are shown in the following table.<\/p>\n<table>\n<thead>\n<tr>\n<th>Observation<\/th>\n<th>Car model<\/th>\n<th>kWh\/100<span style=\"font-size: 1rem;\">\u00a0miles<\/span><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>1<\/td>\n<td>Porsche Taycan 4S Cross Turismo<\/td>\n<td>45<\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-size: inherit;\">2<\/span><\/td>\n<td>Volkswagen ID.4 Pro S<\/td>\n<td><span style=\"font-size: inherit;\">35<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-size: inherit;\">3<\/span><\/td>\n<td>Hyundai Kona Electric<\/td>\n<td><span style=\"font-size: inherit;\">27<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-size: inherit;\">4<\/span><\/td>\n<td>Ford Mustang Mach-E RWD<\/td>\n<td><span style=\"font-size: inherit;\">34<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-size: inherit;\">5<\/span><\/td>\n<td>Tesla Model S Performance<\/td>\n<td><span style=\"font-size: inherit;\">35<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-size: inherit;\">6<\/span><\/td>\n<td>Tesla Model X Performance<\/td>\n<td><span style=\"font-size: inherit;\">35<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-size: inherit;\">7<\/span><\/td>\n<td>Nissan Leaf SV\/SL<\/td>\n<td><span style=\"font-size: inherit;\">32<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-size: inherit;\">8<\/span><\/td>\n<td>Tesla Model S Plaid<\/td>\n<td><span style=\"font-size: inherit;\">33<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-size: inherit;\">9<\/span><\/td>\n<td>Volkswagen ID.4 Pro<\/td>\n<td><span style=\"font-size: inherit;\">34<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-size: inherit;\">10<\/span><\/td>\n<td>BMW i3s<\/td>\n<td><span id=\"MathJax-Element-37-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.15px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;\/p&gt; &lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mstyle displaystyle=&quot;true&quot;&gt;&lt;mn&gt;30&lt;\/mn&gt;&lt;\/mstyle&gt;&lt;\/math&gt; &lt;p&gt;\" data-asciimath=\"30\"><span id=\"MJXc-Node-181\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-182\" class=\"mjx-mrow\"><span id=\"MJXc-Node-183\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-184\" class=\"mjx-mrow\"><span id=\"MJXc-Node-185\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">30<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<section class=\"textbox interact\"><strong><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>.<\/strong><\/strong><\/strong>\u00a0<\/p>\n<p><strong>Step 1: <\/strong>For the \u201cEnter Data\u201d option, choose \u201cYour Own.&#8221;<br \/>\n<strong>Step 2: <\/strong>Type the values from the sample into the \u201cEnter Observations\u201d box. Separate the data values by spaces or commas.<br \/>\n<strong>Step 3:<\/strong> Recall the values for the sample are: 45, 35, 27, 34, 35, 35, 32, 33, 34, and 30.<br \/>\n<strong>Step 4:<\/strong> For the \u201cStatistic of Interest\u201d option, select \u201cMean.\u201d<br \/>\n<strong>Step 5: <\/strong>On the left-hand side of the display, under \u201cSelect how many bootstrap samples you want to generate,\u201d click on \u201c1,000.\u201d Then, click on \u201cDraw Bootstrap Sample(s).\u201d<br \/>\n<strong>Step 6: Y<\/strong>ou should see the bootstrap distribution in the lower part of the right-hand side of the display.<\/p>\n<\/section>\n<section class=\"textbox tryIt\"><span style=\"font-size: 1rem; orphans: 1; text-align: initial; background-color: initial; word-spacing: normal;\"><iframe loading=\"lazy\" id=\"ohm3488\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3488&theme=lumen&iframe_resize_id=ohm3488&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/span><\/section>\n","protected":false},"author":8,"menu_order":12,"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":"apply_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\/1515"}],"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":6,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1515\/revisions"}],"predecessor-version":[{"id":4050,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1515\/revisions\/4050"}],"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\/1515\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1515"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1515"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1515"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1515"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}