{"id":1459,"date":"2023-06-22T02:28:51","date_gmt":"2023-06-22T02:28:51","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/confidence-interval-and-prediction-interval-learn-it-1\/"},"modified":"2025-05-17T02:36:32","modified_gmt":"2025-05-17T02:36:32","slug":"confidence-interval-and-prediction-interval-learn-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/confidence-interval-and-prediction-interval-learn-it-1\/","title":{"raw":"Confidence Interval and Prediction Interval - Learn It 1","rendered":"Confidence Interval and Prediction Interval &#8211; 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;Find and interpret the confidence interval for the mean response&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 interpret the confidence interval for the mean response<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Find and interpret the prediction interval for the mean response&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 interpret the prediction interval for an individual response<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Identify whether a confidence interval or a prediction interval is more appropriate in context of the problem&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;}\">Identify whether a confidence interval or a prediction interval is more appropriate in context of the problem<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Penguins<\/h2>\r\n<p><strong>Research question: <\/strong>How much do we expect a penguin to weigh based on the length of its flipper?<\/p>\r\n<p>To answer this question, we will look at the \u201cPenguins\u201d data set.[footnote]Horst, A. M., Hill, A. P., &amp; Gorman, K. B. (2020). palmerpenguins. palmerpenguins 0.1.0. https:\/\/allisonhorst.github.io\/palmerpenguins\/[\/footnote] It contains characteristics for a sample of [latex]342[\/latex] penguins observed near Palmer Station, Antarctica. We will focus on the following two variables:<\/p>\r\n<ul>\r\n\t<li><em>flipper_length_mm<\/em>: Flipper length in millimeters<\/li>\r\n\t<li><em>body_mass_g<\/em>: Body mass (weight) in grams<\/li>\r\n<\/ul>\r\n<div>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3061[\/ohm2_question]<\/section>\r\n<section>\r\n<section class=\"textbox interact\"><strong>Step 1: <\/strong>Access spreadsheet <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Statistics+Exemplar\/Data+Set+Files\/Penguins_FINAL.xlsx\">Penguins<\/a>.<strong><br \/>\r\nStep 2: <\/strong>Under \u201cEnter Data,\u201d select \u201cEnter Own.\u201d<br \/>\r\n<strong>Step 3: <\/strong>Copy and paste the appropriate explanatory variable ([latex]x[\/latex]) and response variable ([latex]y[\/latex]).<\/section>\r\n<\/section>\r\n<p><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/linear_regression\/\" width=\"100%\" height=\"1050\" frameborder=\"no\"><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\">\ufeff<\/span><\/iframe><br \/>\r\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/linear_regression\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3062[\/ohm2_question]<\/section>\r\n<\/div>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Find and interpret the confidence interval for the mean response&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 interpret the confidence interval for the mean response<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Find and interpret the prediction interval for the mean response&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 interpret the prediction interval for an individual response<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Identify whether a confidence interval or a prediction interval is more appropriate in context of the problem&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;}\">Identify whether a confidence interval or a prediction interval is more appropriate in context of the problem<\/span><\/li>\n<\/ul>\n<\/section>\n<h2>Penguins<\/h2>\n<p><strong>Research question: <\/strong>How much do we expect a penguin to weigh based on the length of its flipper?<\/p>\n<p>To answer this question, we will look at the \u201cPenguins\u201d data set.<a class=\"footnote\" title=\"Horst, A. M., Hill, A. P., &amp; Gorman, K. B. (2020). palmerpenguins. palmerpenguins 0.1.0. https:\/\/allisonhorst.github.io\/palmerpenguins\/\" id=\"return-footnote-1459-1\" href=\"#footnote-1459-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a> It contains characteristics for a sample of [latex]342[\/latex] penguins observed near Palmer Station, Antarctica. We will focus on the following two variables:<\/p>\n<ul>\n<li><em>flipper_length_mm<\/em>: Flipper length in millimeters<\/li>\n<li><em>body_mass_g<\/em>: Body mass (weight) in grams<\/li>\n<\/ul>\n<div>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3061\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3061&theme=lumen&iframe_resize_id=ohm3061&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section>\n<section class=\"textbox interact\"><strong>Step 1: <\/strong>Access spreadsheet <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Statistics+Exemplar\/Data+Set+Files\/Penguins_FINAL.xlsx\">Penguins<\/a>.<strong><br \/>\nStep 2: <\/strong>Under \u201cEnter Data,\u201d select \u201cEnter Own.\u201d<br \/>\n<strong>Step 3: <\/strong>Copy and paste the appropriate explanatory variable ([latex]x[\/latex]) and response variable ([latex]y[\/latex]).<\/section>\n<\/section>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/linear_regression\/\" width=\"100%\" height=\"1050\" frameborder=\"no\"><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\">\ufeff<\/span><\/iframe><br \/>\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/linear_regression\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3062\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3062&theme=lumen&iframe_resize_id=ohm3062&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<\/div>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-1459-1\">Horst, A. M., Hill, A. P., &amp; Gorman, K. B. (2020). palmerpenguins. palmerpenguins 0.1.0. https:\/\/allisonhorst.github.io\/palmerpenguins\/ <a href=\"#return-footnote-1459-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":8,"menu_order":19,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":1438,"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\/1459"}],"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\/1459\/revisions"}],"predecessor-version":[{"id":6897,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1459\/revisions\/6897"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/1438"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1459\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1459"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1459"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1459"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1459"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}